Behavioral Risk Factors

There are presumably various predators towards the health issues within the society. As much as some of them are unprecedented, it is with deep concern that we can describe the role of the family on influencing and determining the aspect of health to its members.The natural setting of the family which comprises both the social, economic and cultural factors has a lot in determining the levels of risk in health of its members. The ingredient and lifestyle of the family setup plays a predominant role in determining the risk levels of the family.The social economic and cultural dispensations held by the family determines how the family is depended on the various sets of control measures such as dietary, physical exercise, family related health implications and the scores of preventive measures that govern the family (David, et al, 1998) Generally, the supportive ingredient for complimentary and alternative medicine for therapeutic response of many health related issues is modeled and go verned by the response of various family related precepts.The levels of education, region of family residence, family income, status of education and other sociodemographic factors are highly influential. However, their control and governance is modeled by the role of the family within its social setup in the society. Through the threshold of the family influence, various complimentary and alternative medicine factors such as using appropriate diet to control diseases and ailments, procurement to physical exercise, social controls arises.These are aimed at avoiding the negative influence towards behaviors such as drug use and abuse and engagement in morally health behaviors in support of good health that has been of necessity in control of health risk within the family setup. The social context of the family plays a predominant role in shaping the nature of health risks for its members. This is the social function of the family in control of the health of its members (David, et al, 1998)The origin and backgrounds of various ill-health and complications are determined by the state of the family as a control variable. The strength of the family in terms of income, level of education to its members, social stabilities such as stress controls, search for preventive attentions to health problems and the setup in its general medical attention governs the levels of risks in health related aspects.According to a research done on the relationship between socioeconomic factors and the response towards mortality and health behaviors of the family, positive results showed that the general setup of the family in terms of its commitment to health regulation through physical fitness, adequate diet and social influence were important in determining the levels of health related issues.As of great importance, the socioeconomic dimensions of the family are therefore implicit in determining the levels of its health matters for the family members. Reference David, R, et al (1998) Socioeconomic Factors, Health Behaviors, and Mortality. Journal of Pediatrics.

The Effects of Dysfunctional Families

Self-destruction of the Mind Many children grow up in dysfunctional families and in order to know what a dysfunctional family is, we have to understand how it operates. No family is perfect and disagreements, bickering and yelling are normal. But the word we are looking for here is â€Å"balance†. This is exactly what dysfunctional families’ lack, whether parents are controlling, deficient, alcoholic or abusive, they have an adverse, long term effect on the children even long after they have grown up and left home. Many of these adults from dysfunctional families often feel inadequate and incomplete.They have difficulty with intimate relationships and often develop compulsive behaviors and addictions, being self-destructive in their own mind. Let us consider a family that is too controlling, where parents are over dominating and do not allow their children simple fun and deny them of their independence. These parents continue to make decisions and control their children even at an age where it is unnecessary. So growing up and learning to be independent can be difficult, a feeling of anger and resentment may present itself.Transition into adulthood poses some struggle to these adults who often feel unsure of themselves and guilty because they feel as though they are disobeying their parents by making their own decisions. Let us take a look at the other extreme where parents are deficient in their roles and are not present in the rearing of their children. These parents leave their children to often fend for themselves which forces them to grow up too fast. Taking on adult responsibilities to make up for the parental inadequacy, these kids ignore their feelings and often grow up not knowing how to show emotion.They find it difficult to form and maintain intimate relationships, they fear getting close to others for fear of abandonment. They often develop a sense of helplessness and blame themselves for the absence of their parents. Whether there is too much parental discipline or a lack of guidance, children growing up without this balance often fear badly. And when alcohol, drug abuse and abusive behavior on the parents part is thrown in, this can be very damaging to these children all through their life. This kind of environment strikes terror in these children, they feel afraid to make mistakes and often live on the edge of fear.Abused children feel anger, frustration and are usually insecure. They do not feel comfortable at home and never voice their opinions. They do not trust easily and find it hard to maintain relationships. Adults grown up from alcoholic and abusive families develop all these negative character traits and often never grow out of them. Children of alcoholics and drug abusers are at much higher risk for developing substance abuse than are children in healthy families. Therefore, unfortunately many of these adults create their own pattern of compulsive behavior and addictions.The effects of dysfunctional families are long term and most times these children are robbed of their childhood. Whether families are over functioning by not allowing children breathing room to think for themselves or under functioning by neglecting the needs of their kids, these families are inconsistent and lack the proper balance of discipline and freedom. As a result these children grow up with trouble maintaining positive self-esteem, they often blame themselves for the dysfunctions in the family and this feeling of helplessness and unworthiness carries on throughout their adulthood.They struggle with trust and intimate relationships and sadly some fall into the pit of alcoholism and drug abuse. These children are victims and these negative self-images they have of themselves causes them to become self-destructive in their own mind. With positive thinking and the correct mindset and with the right help they can overcome these difficulties. References Bentont, S. (1993). www. k-state. edu. Retrieved from ht tp://www. k-state. edu/counseling/topics/relationships/dysfunc. html Bohli, E. (2012). Symptoms of adults from dysfunctional families. Retrieved from http://www. erikbohlin. net/Handouts/Coming_from_dysfunction. pdf

Discuss Why Culture Is Important To The State In Asia

Culture is very important to the state in Asia because most of the activities of the people in the region are deeply rooted in the cultural beliefs they hold. Indeed, most of the interactions that take place in the region especially the rising economy of China and the North Korea Nuclear program are deeply entrenched in the fabric of culture. This permeates both the local and international deals most of these countries have. Culture is the way of life of a group of people. This includes their behavior, their beliefs, societal norms and foundational tenets.It includes customs, lifestyles specificities, eating habits, party organization, religion, community activity and everything that forms part of interactive activities of people in a particular geographical location. Culture is specific to a group of people and varies from place to place. I can be adjusted or modified for the benefit of better erupting behavioral patterns or community development. The current situation in Asia is ma rked by wars and conflicts in the Middle East, terrorism in some parts of same location, increased and perpetual religious autocracy.In the same place, countries like Japan and China are improving the technological facilities while the Koreans are busy maintaining ‘peace’. In all the circumstances that surround the state of Asia, one realizes that culture has a major part; indeed it forms the only fulcrum upon which all acts are carried. The culture in China supports communism and individual multinational companies are only allowed to work or operate in this nation if they are ready to abide by existing rules and regulations of the country. The religious affiliation of people of this country also allows them to work effectively in the team, and even cater for the elderly.Every one is working for the good of the ‘colony’; and as such respected for that service. These factors have been responsible for the economic prowess of this emerging superpower. Another nation is United Arab Emirates. This is dominated by the ‘skeihic’ rulership method wherein there is no election,. It is deeply rooted in Islamic tenets, and most of the policies of the government of these emirates are governed by the content of the Holy Quran. One even realizes that there is segregation in work based on cultural beliefs directly linked to customary religion.One of the Emirates, Dubai, is a growing economy because of the accommodative approach to government and globalization it encourages. In the midst of this, contemporary culture little affected by Westernization is affected by this. As part of the culture of this people is the respect for the rule for the elders, responsibilities to the state and resistance to intrusion to cultural sanity. These factors form a bulk of the impetus for the current state of art and acts within Asia. This drives home the point that culture in intrinsic to events within Asia.

The Profession Of A Medical Assistant Essay Example | Topics and Well Written Essays - 500 words

The Profession Of A Medical Assistant - Essay Example Research shows that the virus kills approximately 20,000 people yearly and developing its vaccine to full functionality will be a milestone in the medical fraternity. 3. If you could practice medicine anywhere in the world, where would it be and why? I would like to work with underprivileged communities here in the states. It has become a burden for me to offer my service to people and families who have been sidelined by the society yet they equally need the healthcare services like anyone else does. It has become a concern to me, that an almost all medical practitioners want to practice in big towns and cities and in hospitals that are fully furnished with all medical equipment they require leaving out the option of marginalized areas with largely inadequate practitioners. For this reason, I am committed to giving service to the underserved communities at hospitals or doctor’s office where I will specialize in either primary care of cardiology work and be part of the solution towards addressing the health worker shortage in such underserved communities as well as provide affordable and accessible healthcare services. 4. Thinking of yourself, what is the best patient experience you’ve had and why? What is the worst patient experience you’ve had and why? The best patient experience that I have had is when as a medical assistant; I managed to attend to my client from vastly different social backgrounds from mine and was able to blend well with them despite the disparities in culture, values, and language.

The Pennine Center Essay Example | Topics and Well Written Essays - 1250 words

The Pennine Center - Essay Example 1.2 SWOT and PESTEL analysis Political Economical Social Technological Environmental Legal Strength - The environment of Pennine hotel is very friendly which is surrounded by lakes and gardens which attract customers and keep them satisfied. It provides luxuries benefits to society such as leisure centre, swimming pools and sports stadium. Centre has technology with nine screen cinema, stadiums and car parking, effectively managed retail outlets. It has a wide geographic coverage with remarkable locations. - Weaknesses Increase in competition reduces the chances to attract more customers. Profits of company are reducing rapidly and are resulting in low returns due to uncertain economic conditions. It is unable to target large number of people as most of the shops are empty due to lack of resources. It lacks the ability to incorporate new 21st technology and entertainment facilities in the centre The surroundings of the place is creating hurdle for the company such as roads following the centre are quite narrow. There is no system of maintenance of roads. There are environmental regulations in relation to safety of people, but most tourists have suffered from injury in the centre. Opportunities - Market size is large and the growth rate of industry is high in the region. Enter in new markets to further expand the business where there are more tourist seasons. New games are emerging in the market such as world student games. Company should launch such games in its stadium. Can gain more market share by diversifying business in other places. - Threats Likelihood of entrance of new and potent competitors. Due, to recession 19 outlets of company have been closed and there is a threat more outlets will be stopped due to less business in the economy Presently, the demand of exhibitions, conferences and hospitality has increased rapidly and many new tourist canters are emerging in the region. Many new companies have entered in the industry, some of which are providing same facilities to the customers through the retail outlets of Pennine centre. Environment is not friendly; they are subjected to uncertain conditions such as in case of floods and bad weather. Changes in relation to government policies for the safety measures of people. After analyzing the external and internal environment of the company, it is essential to focus on the weak points and proposing a strategy to overcome the situation, developments and to identity the company’s direction and objectives (L Fahey & V. K. Narayman, 1986). An organization is successful only if it has strong management systems and has an ability to be innovative and distinctive. This center is facing problem not only in financial aspect but also lacks management skills in the organization. Economic uncertainties is the factor which cannot be controlled, however one can take preventive measures against it on the basis of effective management. So, the center should imply new strategic goals and object ives which should be made clear among all staff. Thus it means that if management will be efficient than only company will lead to profitability (Hill T. & R. Westbrook, 1997, De Geus, 1998). 1.3 Proposed strategic option In accordance with the present situation of the company it needs to revise the strategy because of changing

INDIVIDUAL CASE STUDY Essay Example | Topics and Well Written Essays - 2250 words

INDIVIDUAL CASE STUDY - Essay Example Thus its organizational culture and leadership strategies are reflected in its focused strategic initiatives such as SWOT, PESTEL analysis and so on. However its leadership related and organizational culture centric problems have been highlighted in order to focus attention on its current level of operations. Business strategy is defined as the longer term directional thrust of the organization with specific focus of attention on resource capability enhancement strategies to achieve organizational goals in a competitive environment to satisfy stakeholders’ demands (Johnson and Scholes, 2002). The Real Chocolate Company Inc. has been in business for approximately three decades and now has become one of the top hundred fastest growing small public companies in the USA. Its concentration on gourmet niche chocolate market in the US is particularly significant against the backdrop of ever increasing diversity and complexity of the gourmet chocolate industry. With almost 300 chocolates in the portfolio and a further 100 turned out on special occasions like the Valentine’s Day, the company has achieved a marvelous feat of targeting every segment of the gourmet chocolate market. The company’s success is determined by the quality and strange enough the quantity of the product. With a gamut of popular proprietary recipes of its own, the company has positioned itself in the US market with unparalleled success. Its use of the best ingredients and chocolates has led to the current wave of demand for its caramel-coated apples, truffles, toffees and fudges among others which include even a range of sugar-free sweets. The company has been marketing a health-centric line of products to the health conscious customer. According to the National Confectioners’ Association (NCA) in 2006 alone the retail sales of confectionery topped $ 28.9 billion in the US while that of retail chocolate

Healthcare Ethics Case Study Example | Topics and Well Written Essays - 750 words

Healthcare Ethics - Case Study Example As part of his training, Alex is rotating through the emergency room and has been asked to take x-rays of the head and neck of an alert yet seriously injured patient Mr. Hanson. The x-ray supervisor/instructor, Ms. Dubois, is present when Alex attempts the x-rays that require the patient to be manipulated into particular and potentially painful positions. Nothing is said to the patient other than "we are going to take some x-rays sir!" After three unsuccessful attempts, the patient complains about the pain and the x-ray supervisor takes over and completes the procedures with success. Now, the importance of discussing this topic is in order for us to know the possible risks in medical trainings. If you were a student of some sort of a medical/health care and you don't know what to do next to proceed on to the next step and you forgot to seek assistance on your superior, it is essential to learn the ethics in healthcare. Sometimes, we neglect the importance of knowing the moral standards in every medical aspect. We just rely on our own capabilities and confidently do what it needs to be done and we forgot to consider some other things on handling that kind of situation. Now, let us deal with these following questions: (1) identify the people/parties that have a stake or interest in the scenario mentioned above, and explain how the interests may conflict. (2) Identify the ethical principles that may be applied in resolving the dilemma in the scenario. Discuss the prima facie duties and principles. The people/parties that are related in this scenario are the medical students who currently undergo trainings with the help of their instructors. But there are situations where in the instructor failed to inform the patient that he/she is with a student. It is good to expose the students on such trainings but they also need to consider some other things, such as educating the trainees well when it comes to proper healthcare ethics. Conflicts may rise if this cannot be fulfilled. But, it is also the responsibility of the trainer to remind the student to comply on all the instructions and it is important to orient the student first on how to have the right approach on every patient even though the student was on training. It is the right of the student to be well-informed, in order for him to know everything well. The ethical principle that can be applied on this scenario/situation is to have beneficence and that is to act in the best interest of the patient and to be more sensitive in the needs of every patient. And that is the end of this paper about the healthcare ethics that should be practiced on actual hospital/clinic duties or even on trainings. References: 1.)

HYPNOTHERAPY & NEURO LINGUISTIC PROGRAMMING Essay - 1

HYPNOTHERAPY & NEURO LINGUISTIC PROGRAMMING - Essay Example Therefore, all the suggestions are entered to the subconscious without conscious intervention. Once conscious faculties are sure that monotonous stimuli unlikely to endanger their subject, they become complacent and irresponsible. With attention gone there can be no conscious intervention which leads to the state of conscious suspension. Conscious faculties are alert and vigilant to check the security or any danger from external stimuli. Therefore, the conscious faculties intervene when suggestions are on their way to the subconscious. To produce monotony to the sense of feeling, the subject should be made very comfortable by reducing all possible external stimuli. The pressure on the subjects body should be released by avoiding any unpleasant sensation commonly known as pins and needles. The subject should be instructed to sit properly without the legs crossed. The room environment should be calm and temperature should be maintained at constant level. If the emotional force generated by thoughts or perceptions is not discharged through appropriate action, the pressure will build up and escape where it finds least barrier. If it is not discharged, building of such a force might lead to destructive level of pressure. Hypnotist displays posters before his performance which claims to possess mysterious hypnotic powers, the power to control minds, and the power to control the actions of others. At the actual show, special stage props, a carefully planned presentation, and the impressive appearance of the hypnotist, all play a part in contributing still further to building up emotion in the audience. In normal situations the emotion is discharged through appropriate action. The builded pressure escapes where it finds least barrier. When the asserting pressure is moderate, feelings such as satisfaction, dislikes etc. are released. It can render the conscious faculties inefficient and incapable of carrying out their normal duties. In our working model of the

Sliding Filament Theory Essay Example | Topics and Well Written Essays - 1500 words

Sliding Filament Theory - Essay Example Surrounding the whole muscle is a layer of connective tissue, epimysium that encloses the individual fascicules together. The individual muscle fibers are made up of filamentous bundles that run along the length of the fiber. Most of the interior of the fibre consists of the protein filaments which constitute the contractile apparatus, grouped together in bundles called myofibrils. Each myofibril consists of a repeating unit, known as a sarcomere. The alignment of the sarcomeres between adjacent muscle fibers is responsible for the characteristic striations in the striated skeletal muscle fibers. The sarcomere is the fundamental contractile unit of the skeletal muscles. When a muscle fiber is viewed by polarized light, the sarcomeres are seen as alternating dark and light zones. Some regions appear dark because they refract the polarized light. This property is called anisotropy, and the corresponding band is known as an A band. The light regions do not refract polarized light and ar e called isotropic and are denoted as I bands. Each I band is divided by a characteristic line known as a Z line, and the unit between successive Z lines is the sarcomere [1]. Under electron microscopic examination with high magnification, the A bands are seen to be composed of thick filaments arranged in a regular order. The I bands consist of thin filaments. When the muscle is in the resting state, that is, when there is no shortening of the fibers due to contraction, a pale area can be seen in the center of the A band. This is known as the H zone, and it corresponds to the region where the thick and thin filaments do not overlap, which otherwise is the case throughout the muscle fiber architecture. In the center of each H zone, there is a line called M line. It is in this line, links are formed between adjacent thick filaments. The principal protein of the A bands is myosin, while that of I bands is actin. The interaction between these proteins is fundamental to the contractile process in the skeletal muscle at the ultrastructural and molecular levels. There are two types of actin filaments. One is globular in shape, known as globular or G actin subuni ts, and the other is filamentous of F actin. The actin filaments of the I band are made by joining many G actin subunits together by polymerization to form F actin. The F actin, in turn, is stabilized by binding to the Z line. The thick filaments are made up of an assembly of myosin molecules together. Each myosin molecule consists of two heavy chains. Each of these heavy chains has two light chains associated with a head region that is globular. The junction between the head region and the long tail contains a hinge. This hinge allows the myosin to generate the force required for muscle contraction. The tail regions of the myosin molecules associate together to form the thick filaments. Each thick filament consists of several hundred myosin molecules [2]. The sliding filament theory explains muscle contraction, and the structure of skeletal muscle provides important clues to the mechanism of contraction. The width of the A bands or thick filament areas in striated muscle remains constant, regardless of the length of the entire muscle fiber, while the width of the I bands or the thin-filament areas varies

Purpose of the Education System Essay Example for Free

Purpose of the Education System Essay The question posed is What should the education system be? This question cannot be answered specifically because the education system means something different to everyone. The education system is, to an extent, what it should be, which is an institution devoted to the development of the intellect. American education should however, be more than rote instruction of mandated materials. Our children should be taught more life skills along with science and math. Children sit in rows, facing straight, not talking. They select and use educational materials in unison, and watch the teacher write on the board. The droning sound of the teachers voice attempts to fill their minds with knowledge. It sounds militaristic because it is. Students remember more of what they are taught if the material is presented in a less formal, more enjoyable atmosphere. School administrators and state agencies set forth guidelines from which teachers must not deviate. The problem is, these administrators are removed from the classroom and tend to forget that children have changing needs. Todays teachers learn more progressive teaching methods such as portfolio assessment vs. testing, and sitting in groups instead of rows. There are few administrators willing to incorporate these changes into their schools. Education management needs to allow teachers the flexibility to teach their students using whatever methods actually work. There is no reason why children should not look forward to school. For the most part, our education system is devoted to teaching students. There is great concern that students should be prepared to move on to higher stages of education. Tests are given periodically to gauge students progress. There is much discussion how improving education and better preparing students for the world. Students do learn, and many excel, but school is still viewed as drudgery by most students. If our education system is to prepare children for the world educators need to look more closely at curriculum. Art, philosophy, history, math, English  and science are all important subjects. They teach us about the world around us and how things work. The social setting of the educational facilities also compels students to learn about society and what is acceptable behavior. However, are we properly preparing our students for the world? Are we teaching life skills like personal finance and relationship dynamics? Can we lower the rate of divorce or the number of poverty-stricken retirees by educating students in these areas? Our education system needs to incorporate fundamental life skills into the curriculum. The focus on education should not stop at the goal to create an intelligent adult. The education system must also attempt to create a responsible citizen, an asset to the community. The American education system is not entirely broken. There are many positive things happening. Progressive teaching methods are being employed and the student is being recognized as more of an individual. America cannot stop here. We need to ask ourselves if the moral fabric of our country can be improved through education. The education system plays a larger role in our lives than any other one thing. The system needs to use this influence to improve society as a whole and people as individuals.

Heritage Tourism On Archaeological Sites In Egypt Tourism Essay

Heritage Tourism On Archaeological Sites In Egypt Tourism Essay Egypt is located in the North- Eastern corner of Africa and South-Western Asia and is commonly known as The Motherland of the World Land of Civilizations and The Greatest Power in Human History being reputable for its 7,000-year-old record of civilization and immense wealth of knowledge (SIS, 2011). Amongst all civilizations and nations, Egypt is known to be one of the worlds oldest tourist destinations, possessing one third of the worlds ancient monuments within its country. Besides its other archaeological and cultural monuments, the discovery of the Pharaonic antiquities long time ago has added a special appeal to Egypt, therefore boosting Egypts tourism industry. However, with the booming increase in Egypts tourism, conflicts and issues starts to surface concerning the management and conservation of the ancient Egyptian archaeological sites and treasures. What defines Egypt is its massive number of archaeological sites that can be found all over the country and of course, its extraordinary architectural and heritage attractions such as the legendary Pyramids of Giza, the world-famous Valley of the Kings and the temple at Abu Simbel. These well-known and remarkable sites are the lifeblood of the countrys tourism industry where it attracts over 2 million visitors annually to Egypt (Boniface and Cooper, 2001). Despite being one of the most highly industrialized country in the Arab region, Egypts petroleum and economy is not sufficient to provide adequate amount of jobs to its population of 73 million (e.g.: Boniface and Cooper, 2001; MINTEL, 2004). It is also mentioned by Weeks and Hetherington (2006) that tourism has been a key factor in Egypts economy for about the last two centuries and over the last generation. It has become a crucial component of the economy and is now the source of 45 percent of the countrys annual foreign currency earnings. Therefore tourism in Egypt plays a critical role of support for its economy where it benefits both the government and to all levels of the society. One of the main components of the tourism industry in Egypt is heritage tourism. Heritage itself as a concept has entered on to a global stage and penetrated into the local, regional and national arena (Burnett, 2001). The World Tourism Organization (UNWTO) states that heritage and culture have become an important element in almost 40 per cent of all international trips taken (Timothy and Boyd, 2003) and despite of recession, heritage tourism still continued to grow (Hanna, 1993, cited in Timothy and Boyd, 2003). Throughout the world, ancient venues and archaeological monuments have become major tourism attractions (Laws, 2011) and one such destination is Egypt where the impacts of flourishing heritage tourism on ancient archaeological sites are apparent through out the country. However, in spite of the thriving tourism industry in Egypt, conflicts and issues starts to arise that contradicts Egypts own tourism interest. In order to maximize revenue from the tourism industry, Egypt implemented the approach of opening more sites to visitors and promoting visits through advertising and high profile overseas tours of antiquities (Weeks and Hetherington, 2006). Ironically, the benefits of expanding Egypts tourism are being out weigh by the negative aspects. Lambert (2011) states that a bustling tourist industry is sadly known to be a double-edged sword. She added that, as most archaeological sites are very fragile and ancient, they were not meant to accommodate thousands of visitors on a daily basis. The overcrowding of tourists visiting, touching and stepping onto these sites, are destroying many archaeological attractions. One such incident happened in February of 1988. A chunk of limestone fell from the Egyptian Sphinx, the half lion, half man relic built by the ancient Egyptians over 4,000 years ago. Recently on January 2011, Egypts Supreme Council of Antiquities had announced plans to close the tomb of Tutankhamen to tourists by the end of the year. The tomb, which was discovered some 89 years ago, was damaged as a result of the overwhelming visits of tourist, particularly over the past three decades (http://www.redorbit.com). The mass tourism in Egypt has also impacted the Valley of the Kings, altering the physical and natural aspects of the environment. According to Gaetano Palumbo, the program director for North Africa, the Middle East and Central Asia for the World Monuments Fund, a New York-based nonprofit dedicated to preserving and protecting endangered historical sites around the world: One could say that, the heritage sites in Egypt are victims of their own success. In the Valley of the Kings, Luxor, visitor numbers have almost doubled in the past 10 years, from 1.5 million to close to 3 million, with peaks of 10,000 visitors a day. This creates massive problems in visitor management. Drastic decisions may have to be taken in order to regulate visitor numbers, including temporary or permanent closures of ancient sites.   Due to poor tourism and cultural heritage management, Bindlegas (1997) states that the decay of some of the worlds most fabulous ancient relics has been happening at a shocking rate. These major archaeological and cultural heritage sites represent the origins of human civilization and provide the best evidences of the historical and cultural development of humanity (Global Heritage Fund, 2010). If measures are not taken to start preserving and conserving the ancient monuments, it will be completely destroyed within centuries. However, increasing the tourism receipts into Egypt and on the other hand, conserving these heritage sites is not as simple as it seems. Leask (2006) described that balancing the development of tourism opportunities and heritage conservation activities has been a continuous struggle for countries with tourism and cultural heritage management. The different parties involved are unable to decide on the same agreement, resulting in the lack of proper management that can benefit both the tourism and conservation of the ancient Egyptian archaeological sites and treasures. Therefore this paper aims to identify the variables that constitute and associate to the impacts of heritage tourism on archaeological sites in Egypt. AIM To assess the impacts of heritage tourism on archaeological sites in Egypt OBJECTIVES To review secondary literature about the environmental impacts of heritage tourism on archaeological sites in Egypt. To study the conflict between heritage and tourism in Egypt. To assess the management and conservation of archaeological sites in Egypt. CHAPTER TWO: LITERATURE REVIEW DEFINING TOURISM According to the Advance Release of the World Tourism Organization (UNWTO) World Tourism Barometer, international tourism showed a strong recovery of almost 7% to 935 million in 2010, from the 4% decline during the global economic crisis in 2009. Through the decades, tourism is now known as one of the largest industry in the world, experiencing dynamic improvements and intense diversification, leading it to become one of the worlds fastest growing economic sector (e.g.: Youell, 1998; World Tourism Organization (UNWTO, 2011)). Therefore, prior to assessing the impacts of heritage tourism on archaeological sites in Egypt, it is first essential to define and understand the term tourism. Even in early researches, the term tourism had yielded, as many definitions as there were many studies of phenomenon (Cohen, 1974, cited in Wall and Mathieson, 2006). Guyer-Feuler who concentrated on the economical and statistical aspects of tourism, conceived the first definition of tourism in 1905, where it defined tourism as: A phenomenon unique to modern time which is dependent on the peoples increasing need for a change and relaxing, the wish of recognizing the beauties of nature and art and the belief that nature gives happiness to human beings and which helps nations and communities approaching to each other thanks to the developments in commerce and industry and the communication and transportation tools becoming excellent. (Bahar, 2005: 2, as cited in Esen and Uyar, 2010) The origin of the term tourism goes back to the 17th century where the root word tour is derived from the Hebrew word torah which means learning and examining. People who were sent on a voyage to explore distant areas to learn the social activities of the population living in those places are known by the Hebrews as tourist and the behaviour as touring. (Bahar, 2005) Some other few pioneers who attempted to define tourism were Professor Hunzikar and Krapf (1941, cited in Holloway, 1994:1) of Berne University who states that it is: The sum of phenomena and relationships arising from the travel and stay of non-resident, in so far as they do not lead to permanent residence and are not connected to any earning activity. Holloway (1994) then continues that tourism, besides being associated as a form of recreation or leisure; it might be where individuals or a group of individuals travel away from home. However, Holloway (1994) also questioned the specificity of the statement on whether tourism is defined by its purpose or the distance travelled. Indeed, it is a common perception and a popular understanding amongst people that the central aspects of tourism evolves around holidays, leisure and tours, engaging in different kinds of activities to have a good time and as long as being in a foreign land, it is considered to be tourism regardless of the distance travelled. However, tourism is more than just a cursory explanation of leisure, recreation and being in a foreign land. In 1993, after much reviews, researches and further analysis on existing works of tourism definitions, the UNWTO (1993, cited in Youell, 1998:9), with co-operations from many international organizations, finally announced the officially accepted definition as: à ¢Ã¢â€š ¬Ã‚ ¦the activities of persons travelling to and staying in places outside their usual environment for not more than one consecutive year for leisure, business and other purposes. Therefore with the multitude of tourism definitions given by researchers and studies, which of these, can academics, organizations and professionals use as an accurate guideline in the tourism industry? In spite of the existence of many variations of tourism definitions and the popularity of tourism studies in recent decades, it has been discussed and acknowledged by academic researchers, organizations and industry professionals that there has been no specific means in defining the principal concept of the term tourism due to its large complex nature of subject, involving diverse combinations of disciplines and industry sectors (e.g.: Morley, 1990; Youell, 1998; Goeldner, Ritchie and McIntosh, 2000; Dredge and Jenkins, 2007). Moreover, regardless of the complications of specifying definitions for tourism, tourism is nothing without the tourists. The main factor that drives tourism is the tourists who are travelling and therefore any effort to understand tourism as a concept has to first understand the motivations behind the tourists decision to travel. Also, the definition of tourism is dependent on an individuals perspectives and perception of tourism and also how it will fit into a particular purpose or situation (Dredge and Jenkins, 2007). In addition, the changes of the different definitions since the early 1900s till the present day demonstrates that tourism can no longer be associated to merely economics and geography (Arlt, 2010). As time passes with the continuous growth of the industry, researches into the concepts of tourism will persist to expand, eventually resulting in the creation of more definitions of tourism. IMPACTS OF TOURISM Tourism is an integration of close interactions involving the dynamic relationships of different variables or elements in the tourism travel process and thus, it can never be a standalone unit. Hence, any changes or effects to a variable will create a ripple effect within the whole tourism structure. With this, contributions made by the growth of the tourism industry will therefore lead to an increased economic activity within the country. Countries are increasingly becoming dependent on tourism, as it is one of the most rational and sustainable development choices that have the capability of creating employment to the communities and also acting as a main provision of foreign earnings to the economy. (UNWTO, 2010 Tourism and the Millennium Development Goals) While it is often the economic impacts of tourism that businesses and public organizations that are usually interested in (Stynes, 1999), the late twentieth century saw the emergence of environmental and socio-cultural impacts of tourism being controversial and critical issues discussed in tourism study (Youell, 1998). As the main objective of this paper aims to concentrate on the impacts of heritage tourism on the archaeological sites in Egypt, this section will therefore provide an overview of the positive and negative influences that tourism, in general, have on the economic, environment and socio-culture around the world. Economic Impacts It is predicted that by 2020, revenues earned from the tourism industry will be $1.5 trillion (Kumar and Prasad, n.d). Tourism being declared as one of the worlds largest industry is similar to any other businesses and industries; affecting the economy by generating income for the countrys economy, stimulating job opportunities for the people from the international level down to the local levels. Increasing competiveness amongst countries has also pushed the business capacity of the tourism industry to the level of, or, sometimes even exceeding trade commodities such as oil and food exports (UNWTO, 2011). Tourism being a major player in the service sector is naturally dependent on labor therefore stimulating a great deal of employment opportunities both in developed and developing countries. The fact that tourism is an intergration of many various individual elements in a tourism travel process, the economic impacts from tourism will therefore affect industries in the construction sector, agriculture sector, commercial services sector such as retail and customer services and also the health and finance sector (e.g.: Wall and Mathieson, 2006; ÃÆ'-nder and Durgu, 2007). Tourist expenditures contributing to the balance of payments through foreign exchange earnings, and revenue generated from tourism developments can represent a crucial source of income for a nations economy (Balaguer Cantavella-Jorda, 2002, cited in Seetanah, 2010). However on a negative note, seasonal tourism also known as induced employment, being influenced by the increase in the demand and supply of tourism causes the increase of low-paying jobs and often creating unemployment during off-peak seasons (Kreag, 2001). Peak periods of tourism can benefit the economy of a country, however on the expense of the locals, who might have to pay for the higher prices of goods and services in the community, thus increasing their cost of living. However, contributions of tourism to a countrys economic benefits is relative to factors such as the availability of facilities and resources, the countrys social and political stability, the host communities behavior towards tourist and the amount of investment injected by the government into tourism projects and development (Youell, 1998). Environmental Impacts The relationship between tourism and the physical environment, natural or man-made, is firmly interlinked and complicated. Controversial debates of tourism and the environment have been going on in determining whether they are friends or foes. The physical environment is an important aspect of tourism; it ensures the sustainability of attracting tourism in the long run. In fact, it is impossible to define the different types of tourism without the inclusion of the environment (Safakli, n.d). A tourists decision to travel and the duration of stay depends on the physical environment of the destination. According to Olali (2000), the estimation given by academics states that in the next 100 years, the environment will be the only option that will determine the demand of tourism. The environmental impacts of tourism can be categorised into two categories which are postive and negative impacts, and finding a balanced relationship with the environment is uncommon, if not, there is hardly a balanced relationship (Holden, 2000). The negative impacts of tourism on the environment caused by the increased in tourist visitations are visible through the changes, damages and depletion of natural resources, causing the destruction of wildlife habitat, improper waste disposal, air and water pollutions, and also erosion of the natural landscape such as the mountains and historical sites (e.g.: Youell, 1998; Holden, 2000; United Nations Environment Programme (UNEP), 2001; Wall and Mathieson, 2006). The lack of facilities and space to accommodate the increase in tourist visitations results in the overcrowding and the over usage of an environment, therefore also increasing improper waste disposal, loss of significant attractions and unethical behaviors due to the lack of supervision over the large number of visitors. The detrimental state of the environment will then lose its beauty and attractiveness to these tourists therefore causing a decline in tourist visitations. Despite of the attention on the negative impacts of tourism on the environment, there are still positive impacts of tourism that benefits the environment. Contradictory to the cause of degradation of these natural resources, the motivating factor behind a tourists decision to travel to these places are based on the sentimental attachment they have with the environments (Kreag, 2001). And because these environments are what attracted tourists visits in the first place, preservation efforts are heighened to keep them well managed, and protected from further deterioration. The positive environmental impacts of tourism are sometimes associated to the economic value of tourism earned revenue (Holden, 2000). The increase of tourism travel to a destination also increases the tourism funds flowing into the countrys economy. This additional funds allows governments to use the added revenue from its tourist industry to implement measures into proper management and invest in the restoration of the environment such as construction of new roads to accommodate overcrowding of vehicles, building and upgrading facilities to attract or accommodate the influx of visitors and installing modern technologies into the conservation and preservation of sensitive areas (e.g.: UNEP, 2001; Kreag, 2001). And as tourism travel increases, the impacts on the environment are also increasing. Therefore, it is of utmost importance for government agencies and tourism organizations to focus on the preservation and conservation of the environment. When the environment is restored to its original state or even better, the flow of visitors into the destination will resume once again. However if there is a lack of proper management or close facilitation of the situation, the environment will eventually return back to its damaged state. The attempt to balance the positive and negative aspects of the impacts of tourism on the environment tends go round a vicious cycle. This is where the importance of strategic planning intervenes and it is a crucial part of sustainable tourism of a destination. Socio-cultural Impacts The inclusion of social impact studies is an essential criterion for any tourism industry and tourism government agencies planning for a sustainable tourism industry as it provides an insight of the support for tourism development within host communities (e.g.: Nyaupane and Thapa, 2006; Zhang et al., 2006; Tovar and Lockwood, 2008; Deery, Jago and Fredline, 2011). Social cultural impacts on a destinations society such as traditions, identity, lifestyle, values and customs, are the results of the direct and indirect interactions between the host communities, the tourists and the tourism industry. These impacts of tourism development on the local society are identified through the evaluation of residents perceptions and behaviors towards tourism (Tovar and Lockwood, 2008). Regardless of the magnitude of the fluctuations of tourism demand, the impact on the host community will not only be dependent on the number of tourist arrivals but the type of tourist (Holloway, 2002). Of which, the se impacts can either have a positive or negative influence on the society. Firstly, improvements of infrastructures resulted from tourism development such as clean water and stable telecommunications, improved transportation and banking services, and new business investments are positive impacts that contributes in enriching the local communities way of life (http://www.gawler.sa.gov.au). Tourism also helps in boosting the quality of life in the society and provides opportunities for locals to experience cultural exchange and interactions with the rest of the world. The accumulative experience gained from engaging in the cultural exchange with visitors enhances the host communities ability to interact comfortably and confidently with future potential visitors in the long run. Having an influx of tourist arrivals to a destination can also encourage the preservation and conservation of cultural values and traditional customs which are in danger of losing its identity. The increased interest of tourists into the culture and traditions of the local society also helps to push the demand for historical and cultural education and local tourism agencies will be pressured to step up on preservation and conservation of possible endangered ancient sites, monuments or artifacts (Kreag, 2001). Despite of the positive and inspiring socio-cultural impacts of tourism on a host environment, the negative impacts of tourism, on the other hand, can equally cause a prominent damage on a culture. Ironically, instead of riviving a lost culture, the continuous development of tourism driven by the influx of tourist demand can very well cause the same cultural identity and value of the host communities to change and this issue has raised concerns amongst tourism organizations. This normally happens when local communites conformed to the needs, wants and desires of tourists expectations in the bid to respond to their growing demands. As such, this conformity leads to the commercialization of local culture into a commodity and the modification of traditional art and craft forms, resulting it to become reconstructed ethnicity which might end up causing the eradication of cultural goods (www.coastlearn.org). One of the negative aspect on the social status of a culture is the social differences between the host and the tourists. According to Mathieson and Wall (2006), more often than not, social tensions between host communities and tourists happens in developing countries whereby the tourist market are from a country with higher foreign currency rate than the host communities and thus unintentionally highlighting the disparity of wealth. They also mentioned that since the nature of tourism involves the movement of people around geographical locations, social conflicts occur as a result of differences in cultures, values, lifestyles and languages. TOURISM AND HERITAGE Defining Heritage in Tourism With the growth of the tourism sector, the types of tourist are also diversified and the collection of individual experiences of these tourists influence the different types of tourism offered today, thus the formation of the different types of tourism (Timothy and Boyd, 2003). Heritage tourism has been one of the oldest forms of tourism offered since the early ages, however in recent years, it has grown to popularity in the industry. It is the inheritance of the unrepeatable products of life from the past that is worth preserving for the benefits admiration and education of the current and future generations (e.g.: Nurick, 2000; Timothy and Boyd, 2003; Sethi, 2005; National Trust, 2011). Heritage could be anything that is tangible or intangible left behind by the past such as archaeological or historical sites that have been preserved, natural landscapes which are of a destinations significance, artifacts and documents, culture, values and sometimes even the people of the past such as the indigenous people. However over the years, heritage has been modified and commercialized to suit tourists demand and expectations, allowing it to be more accessible, attractive, educational and entertaining (Fyall and Rakic, 2006). Heritage itself as a concept has entered on to a global stage and penetrated into the local, regional and national arena (Burnett, 2001). The World Tourism Organization (WTO) states that heritage and culture have become an important element in almost 40 per cent of all international trips taken and despite of recession, heritage tourism still continued to grow (Hanna, 1993, cited in Timothy and Boyd, 2003). The different types of heritage attractions offered now are varse and wide, examples includes natural history attractions, religious attractions, sociocultural attractions, art galaries, ancestral dwellings, and genocide monuments. Fyall and Rakic (2006) adds that the demand for heritage based tourism has been on the rise because Lowenthal (1979) states that peoples sentimental reminensce of the past is deeply affected by the parallel ongoing eradication of historical antiquities while on the other hand, Hannabuss (1999) also claims that heritage enthusiasts are immersing themsevles in heritage for the purpose of finding a rational explanation for their post-modern lives. With the controversial issues happening in everyday life, it is no wonder that heritage behaves as a touchstone in reminding people the primary essence of life. Hence, an attempt to understand the demand of heritage tourism could best be determined by initiating a study on visitor psychographic characteristics as these visitors are the primary factors pushing the demand for heritage tourism. Determining the visitor demographics can also aid in better planning and management of visitor capacity control in relation to preservation and conservati on of the heritage sites which will be discussed further in the next section. According to Hall and McArthur (1993a, as cited in Timothy and Boyd, 2003), the significance of heritage can be categorised into four different areas in relation to its economic, social, political and scientific significance. The economic significance of heritage refers to the value of the heritage to visitors, in terms of the amount of revenue earned from visitations to the sites. The social significance refers to the personal identification that individuals have to associate themselves with their heritage. In terms of its political significance, the representations of heritage can behave as an aid in managing political issues due to its political nature behind its existance. Finally, heritage educates visitors on its history, culture and the population of a destination. It also acts as a benchmark for ecological studies on the environments and ecosystems, therefore presenting itself as a scientific significance to the people (ibid.). Impacts of Tourism on Heritage Through the globalization and increasing competiveness of the tourism industry, governments, tourism organizations and agencies are continuously pushed into the whirlpool of sustainable tourism development. Bramwell and Lane (1993) states that sustainable tourism development can be implemented if the balance of the economic, environmental and social aspects of the development is realised. It is certain that every country in the world will definitely have a heritage background attached to them, however, what makes heritage tourism in a country unique is the exclusiveness of the actual heritage product itself. The characteristics and uniqueness of that particular heritage product dictates the different types of visitors and the demand of heritage tourism in the destination. With tourism, comes impacts. As mentioned in earlier sections, tourism impacts the economy, environment and the socialcultural aspects of a destination. Likewise, heritage tourism being categorised into the four different aspects of significance, will therefore impact the economy, evironment and socialcultural aspects of a destination. An influx of tourist visitations can positively or negatively affect the destination in many aspects. Prosperity of the economy, job creations, improved quality of life are some of the positive impacts whilst seasonal unemployment, social tensions, pollution of the environment are some of the negative impacts. However when it comes to heritage, tourism is known to be impacting the environmental and sociocultural aspect of the destination more often than the economical aspect, unless otherwise, the countrys tourism economy is highly dependent on heritage tourism. Tourism is known to have an intitmate relationship with the matters of heritage conservatio n and preservation; a significant element in deciding the survival of a countrys heritage Hence, the impacts caused by tourism on heritage sites are in ways similar to that of a natural environment (pollution, lost of habitat, lost of attractiveness), however, the results and repercussions are amplified due to the uniqueness of the heritage enviroment that can never have an exact replica elsewhere in the world. CONCEPTUAL FRAMEWORK Heritage Sites in Egypt Demand of Tourism in Egypt IMPACTS OF TOURISM ON HERITAGE IN EGYPT Politcal Issues in Egypt CHAPTER THREE: ANALYSIS GROWTH OF TOURISM IN EGYPT Tourism and Heritage in Egypt The term history can be best epitomized by the ancient Egyptian civilization than to any other ancient culture (Grimal, 1994). Egypt is probably the worlds oldest civilization from the  Nile Valley  since the 3,100 BC and is reputable for its extensive collection of historical record on civilization and the immense wealth of knowledge (SIS, 2011). Five thousand years ago, a glimpse start of Egyptss tourism began with the start of cruising (Goeldner, Ritchie and McIntosh, 2000). Queen Hatshepsuts first cruise journey is recorded on the walls of the Temple of Deit El Bahari in Luxor, where it states that the purpose of cruising at that era was for peace and tourism (ibid.). However the genesis of heritage tourism in Egypt could mainly be attributed by the smart and innovative grandeur infrastructure of the Pharaonic burial tombs such as the Sphinx and the other ancient Egyptian pyramids, which saw the first early arrivals of tourists. The start of tourism playing as a core role in the economy of Egypt came with the completion of the Suez Canal in 1869 and after being announced by Khedive (Viceroy) Ismail that Egypt was to be part of Europe (www.thelonelyplanet.com). The Nile, Luxor, the ancient Pyramids of Giza and temples are what defines Egypt as a heritage destination. Egypts ancient civilization is an evidence of the evolution of mankind from the prehistoric days till the present. The rich history of Egypt acts as a connection to the distant past of humanity, which reveals mankinds greatest glories and achievements. Current Status of Egypts Tourism Industry Tourism in Egypt is a huge lucrative business that has flourish and become a major component in the economic development. Millions of tourists are travelling to Egypt each year, for the purpose of appreciating the abundance of the natural and historical phenomenon within the country (www.greenstarhotel.net). In 1995, international vis

Love Food, Hate Waste Campaign

Love Food, Hate Waste Campaign Food waste is a serious environmental, social and economic concern not only to United Kingdom but also to the whole world. Even though Food waste was recognized as a considerable problem, it was not identified as a serious concern to the environment till recently. Among environmentally significant activities, the production, trade, and consumption of food products have been identified as crucial contributors to numerous environmental problems One of the greatest threats of the century is Global Warming and Climate change. The need of the hour is to effectively tackle the climate change issue and GHG emission. According to Waste and resources action program (WRAP), about 20% of climate change emissions are related to the production, processing, transportation and storage of food. Agriculture contributes significantly to GHG emissions The domestic household in uk produces around 8,300,000 tons of food waste and is the single largest producer of food waste. Local authorities spend 1 billion pound a year disposing food waste. The foods we throw out to the landfill gets broken down to carbon dioxide and methane gas (green house gases) and are the prime reasons for global warming. If UK has to meet the international targets on climate change and GHG emissions, it is important to reduce the amount of food waste going to the landfill. Spaces for land filling of wastes are rapidly diminishing, alongside European Union legislation that demands large amounts of waste be diverted from landfill over the next 15 years* Food waste puts a large burden on the finances of each household and local councils in the UK; Local authorities spend 1 billion pound a year disposing food waste. Wasted food is estimated to cost each British household  £250- £400 per year, accumulating to  £15,000- £24,000 over a lifetime.. Objectives and Methadology Love Food Hate Waste is a social campaign, launched by WRAP, in 2007,with the aim of reducing the amount of food waste in UK. The campaign is focused on raising consumer awareness about the various problems caused by food waste. WRAP calculated that preventing good food going to waste could reduce the annual emission of carbon dioxide by 18 million tones, the same effect as taking one in 5 cars off the road. Love Food Hate Waste campaign is supported by the government and is backed by celebrity chefs. Love food Hate waste also has a website which provides practical advice and tips on how to use most of the food they buy. The objective of the campaign is to raise awareness of easy, practical, everyday ways that households can reduce food waste. Everyone including local authorities, community groups, retailers, food manufactures and consumers are part of this campaign. For example, Resource Futures recruited and managed two embedded Outreach Workers to support the North London Waste Authoritys, WRAP funded, Love Food Hate Waste campaign. During the seven month period, the Outreach Workers organized and delivered over sixty road shows in supermarkets, businesses, libraries and at community groups, across NLWAs seven constituent boroughs, to engage more than 3,500 people with the campaign. It focuses on consumers strong desire to reduce wastefulness by sending positive messages about the rewards and benefits that can be achieved through specific behavioral change. The campaign benefits the consumer and the environment by reducing budgets and minimizing land fill and carbon emissions. Some of the methods which can be used to reduce waste in an house hold are: Reduce your proportion size: Love Food Hate Waste website has a tool to help you calculate appropriate portion sizes. The portion planner removes the guesswork by suggesting how much to cook, depending on whos coming for dinner, and ways to measure it Plan ahead: By planning the meal for a week and by shopping accordingly can save you a lot of money and prevents good food going to the waste bin. Tips on storage: Gives you easy tips on how to store things and encourage you to make effective use of fridge and freezers if necessary. Special Recipes: which makes use of use of all the odds and ends that invariably get leftover from previous meals or forgotten in the fruit bowl or the back of the fridge If nothing above works, recycling can be done. Composting is one good option. Only Those waste which nothing can be done is dumped in to landfill The Love food Hate waste Organize Door stepping campaigns providing information packs and Advice, targeted at reducing household waste. They also organize road shows, surveys and do advertising through radio and printed Medias. It owns a website love food hate waste.com where you can find many useful tips to reduce food waste. Analysis of the Sustainable Consumption approach One of the main cause for environmental degradation is the over consumption by the developed countries and a switch towards sustainable consumption pattern is very essential. The definition proposed by the 1994 Oslo Symposium on Sustainable Consumption defines it as the use of services and related products which respond to basic needs and bring a better quality of life while minimizing the use of natural resources and toxic materials as well as emissions of waste and pollutants over the life cycle of the service or product so as not to jeopardise the needs of future generations. The two approaches towards sustainable consumption are the Main Stream approach and an alternative New Economics approach. The strategy of UK government in 2003 was continuous economic growth and social progress that respects the limits of earths eco systems to have a better quality of life. The concept of mainstream approach is of a strong stable and sustainable economy and include initiatives like initiatives for product labeling, consumer education and environmental taxation. mainstream economics is deeply embedded in modernitys vision of progress and growth. The critics of this approach claims that this method is quite ineffective and doesnt address the fundamental problem of consumption. Based on several factors on the environment and society, the critics of main stream model proposed a new model collectively known as New Economics. They argue that economics cannot be separated from its understructures in environmental and social contexts. The Love food hate waste is one such campaign which follows the alternative approach of sustainable consumption. The diagram below shows how the campaigns approach towards sustainable consumption. ECO-EFFICIENCY more productive use of materials and energy INCREASED . PRODUCT LIFE SPANS SLOW CONSUMPTION reduced throughput of products and services The campaign aims to reduce the amount of waste by consuming less by reducing your portion size and shopping less. In other words sufficiency is achieved by reduced consumption of products. The approach also defines green economics which means to increase the efficiency by more productive use of materials and energy. The model defines efficiency and sufficiency as the key towards sustainable consumption. The greater focus on sufficiency alone may lead to economic instability on a wider focus. Increased product life spans, may enable such problems to be overcome by providing for both efficiency and sufficiency. The efficiency can be increased by using the left overs and reusing and recycling. Theories Linked to LFHW Campaign. LFHW is basically a social marketing campaign aiming for a behavioral change by consuming more sensibly and thereby producing less waste. To understand the theories it is important to understand the driving forces to the same. Some of the forces influenced are: Knowledge, information, fashions beliefs (education, media, marketing) Price / affordabilit Tastes and Habits Demographic changes: ageing population, single person society, wealth Culture, social family expectations, norms, aspirations Availability Time and Season The campaign does its focus on the utilitarian theory and more importantly on social and psychological theories. The campaign targets the people who behave unsustainable because they lack information and help them to overcome the problems by rendering information to the needy. The utilitarian approach says that consumers seek to spend money on goods which gives greatest satisfaction or in other words consumers behave as utility maximizers. The LFHW campaign helps and encourage in cognitive thinking before you shop. It spread the importance of prior planning before shopping. By planning your meals for the whole week, you know what to buy and from where to buy. In the present scenario, people get tempted and buy things with offers like buy 1 get 1 free, even though they really dont need that. Its found that one in every 3 shopping bags goes directly to the waste bin. The campaign educates people how the value of food can be increased if the left over can be used to make new dishes. Human behavior is formed and routinized by social structure Apart from the conventionally acknowledged constraints like price and information, campaign also negotiates social, psychological and structural constraints. LFHW organizes public campaigns with celebrity chefs and attracts the whole society for a behavioral change. As a social marketing campaign, the main themes of the campaign are 4Es (Engage, Encourage, Enable and Exemplify). Engaging consumers and households to rethink their behavior is one of the main ways in which waste prevention can be progressed. Enabling households to take action or overcome barriers, through the provision of services like reduce reuse and recycling. Policy measures -Encouraging households to rethink their behavior so as to reduce their waste generation. The most frequently applied suite or package of waste prevention policy measures Appears to include most or all of the following activities. Collaboration between public, private and third sectors. Producer and responsibility. Variable rate charging (pay as you throw) systems (generally applied to householders residual waste). Public sector funding for pilot projects. Exemplified by means of monitoring and evaluation; Measuring and evaluation of waste prevention is challenging. The data collected should be true and of high quality. Some of the methods adopted are self-weighing Surveys done before and after the campaign, focusing on attitudes and behaviours and/or on participation rates Tracking the amount of waste from collection data and/or compositional nalysis estimation/modelling. Strength and weakness of Love food hate waste campaign Love food hate waste campaign claims that it has already prevented 1,37000 tonnes of waste goin to waste bin and have helped close on two million households reduce their food waste, amounting to savings of almost  £300 million. A persons willingness to change along with action and appropriate policies from the local authorities is essential to bring a social change. The campaign is funded and supported by the governmentand almost every county council has given its support to the campaign. Retailers and food manufacturers also support to reduce food waste and they are the official sponsors of the campaign. Unlike Other campaigns, consumer is also economically benefited and hence more people are willing take part in the campaign. It also helps in reducing the so called Value Action Gap. The campaign is both focused at individual and social aspects and hence is more effective. a large body of studies asserts that personal factors are necessary and essential to foster behavioral changes, even though the correspondence between attitudinal variables and behavior is often moderate {reference*(2} The website lovefoodhatewaste.com gives you a lot of information and makes it easily accessible at any point of time. A lot of people gives their experience and valuable opinion which encourage other people to minimize waste. Some of the weaknesses of the campaign are: The campaign is too focused on using left overs and freezing, whereas shopping storage and portion control are effective strategies. The campaign deals with utilitarian concept and socio-psychological theories where as doesnt consider Infrastructure of provision approach. The campaign doesnt focus on the production part of food. food that goes to waste during Production and distribution accounts for 5 percentage of the GHG emissions. Globally 15-50% of food produced is wasted post harvest and no action is taken prevent those waste. The campaign is more concentrated on the food after consumption and doesnt look in to the broader aspects of food. Food has different utility and meanings when it comes to Entertainment, pleasure satisfaction, love status, comfort, time pass, bribery, religious significance, social glue, power, habbit, need, guilt, culture and so on. The amount of waste generated differs for each case and no effort has been taken to realy understand this complex system. Oxfordshire council-tax payers have saved over  £50,000 in waste disposal costs by throwing away less food since Oxfordshire Waste Partnership (OWP) launched its Love Food Hate Waste campaign last March Love Food Hate waste Campaign is still in its early stage and has long way to go. The measurement of success of the campaign can be found by looking the amount of waste reduced as a result of this campaign. In the very first year, the campaign is successful in reducing 1,37000 tones of household waste. The initial statistics of the campaign sounds too intresting and shows how successful it has been. The campaign is successful in attaining attention of the large public. Even though the results are impressive, when compared to the true scale of the problem, it is just a mere drop in the ocean. To address the big issue like climate change we need to do a lot more to reduce the amount of waste produced. Some of the limitations are Lack of interest of certain individuals can be setback to the campaign. Some people consider that the protection of environment is governments job and are not concerned about the same. Some people think that their contribution is just marginal and hence dont do anything. Reduction of waste is moreover a private thing and since its not public there is no social pressure to do it. The lack of strong policies is certainly a limitation to the campaign Measuring and monitoring is a tough task to perform. The reliability on survey is questioned. Conclusion The sustainable consumption doesnt always means consuming less but It certainly should in the case of developed countries and in underdeveloped countries sustainable consumption means consuming more. Thus the aim of sustainable consumption is a high quality of life for every one- brought about by everyone consuming in ways that reduce the impacts of production and consumption. (UNESCO) Some of the challenges in achieving sustainable consumption are: Reccomendations The amount of waste produced by the supermarkets should be controlled and policy should be made to publish the waste generated by the supermarkets. The Whole concept of supermarket should change. The people should make some list for shopping and hand it over to the shopkeeper/salesman so that he will hand over the things you need. By doing so you wont be tempted by the offers like buy one get one free. The online shopping should be encouraged by avoiding tax. Refrigerant leakage accounts for 30 percentage of supermarkets direct GGHG emissions.( Environment investigation agency 2010). There should be some measure to control this pollution. Government should make strong policies and should introduce certain limits to the amount of waste that can be produced by each house. The threshold can be based on the total number of people living in the house. The waste above threshold limit should be fined. à ¢Ã¢â€š ¬Ã‚ ¦ http://apps.oxfordshire.gov.uk 2) Promoting sustainable consumption: Determinants of green purchases by Swiss consumers Carmen Tanner1,*, Sybille Wà ¶lfing Kast2 Article first published online: 12 SEP 2003 DOI: 10.1002/mar.10101

Jack Londons To Build a Fire Essay -- London Jack Build Fire Essays

Jack London's To Build a Fire Nature is always pushing man to his limits. When man heeds the warning signs that nature has to offer and those warnings of other men, he is most likely to conquer nature. When he ignores these warnings, nature is sure to defeat man. To build a fire is a prime example of this scenario. In the short story, â€Å"To Build a Fire† by Jack London, an inexperienced traveler in the Yukon travels alone with his dog, even though it is ill advised to do so. The man is strong and smart but nature humbled him during his quest to reach his friends. The man’s inexperience with traveling in the cold subzero temperatures doomed him from the beginning, but his strong focus under extreme pressure and his keen sense of observation are what allows him to survive as long as he did. The ignorance of the old-timer’s words of wisdom slowly haunts him and catches up with him in the end. The man’s disregard for nature’s power is his demise during his journey. Although the man’s inexperience is his demise, he has very keen observing skills and strong focusing abilities. London writes, â€Å"he was keenly observant, and he noticed the changes in the creek, the curves and bends and timber-jams, and always he sharply noted where he placed his feet.† (London, 527) These skills allow him to make his way through the Yukon. He lacks imagination of what could happen to him in the tundra of the Yukon. â€Å"The trouble with him was that he was without imagination,† (London, 525) Lo...

A Comparison of Nihilistic and Christian Archetypes in Beowulf and John

Grendel, Beowulf and the Relationship Between Nihilistic and Christian Archetypes The Wisdom god, Woden, went out to the king of trolls†¦and demanded to know how order might triumph over chaos. â€Å"Give me your left eye,† said the king of trolls, â€Å"and I’ll tell you.† Without hesitation, Woden gave up his left eye. â€Å"Now tell me.† The troll said, â€Å"The secret is, Watch with both eyes!† Woden’s left eye was the last sure hope of gods and men in their kingdom of light surrounded by darkness. All we have left is Thor’s hammer, which represents not brute force but art, or, counting both hammerheads, art and criticism†¦ The philosophies expressed in the Beowulf epic complement the exploration of existentialism throughout the modern work, Grendel, by John Gardner. Both works portray different perspectives of the same story, involving the same characters; Beowulf, the ancient Anglo-Saxon hero who destroys Grendel, and Grendel, the monster who terrorizes Hrothgar’s hall. Beowulf and Grendel act as archetypes that explore humanity’s perception of the world. In the Anglo-Saxon epic, Beowulf and his companions represent good, and the monsters, including Grendel, represent evil. When Beowulf kills Grendel, the world is less evil, but since Beowulf’s companions die in the struggle, the world is also less good. Ultimately, the two forces of good and evil will destroy each other, but the story maintains that God will interfere and save mankind from destruction. In Gardner’s story, the progression of society begins when mankind creates a monster and then creates a hero to fight the monster. Once the greater power of the hero had been established, once the conflict’s resolution strengthened society’s power, than a greater monster developed ... ...fact, it is the saving grace of mankind: the hope that God will save society and establish harmony and justice. The modern story takes the opposite view; it shows what happens when hope is lost, when society has nowhere to turn: it is a more pessimistic, more complicated view of humanity’s progress. [Throughout this paper, G after a character's name refers to Gardner; AS to Beowulf the poem.] Works Cited Gardner, John. Grendel , New York: Vintage Books Edition, 1989. Gardner, John. Moral Fiction. New York: Basic Books Inc, 1977. Heany, Seamus. Beowulf: A Modern Translation. New York: Farrer, Straus, and Giroux, 2000. Sources Cited Cohen, Jeffrey Jerome. Monster Theory. George Washington University: www.upress.umn.edu/Books/C/cohen_monster.html, 2001. Johnson, Tim. Grendel. New York: www.panix.com/~iayork/Literary/Grendel/grendel2.html, 2001.

Best Buy Market Segmentation

Best Buy Canada Ltd is a fully owned subsidiary of Best Buy Co. Inc with its headquarter in Burnaby, BC. Best Buy Co. Inc acquired the Canada-based electronics-chain Future Shop Inc in 2001. The company opened its first Canadian Best Buy store in Mississauga, Ontario the following year. 1 Today, with more than 51 stores across Canada, Best Buy Canada has become the fastest growing and the largest retailers and e-tailers of consumer electronics, entertainment products, accessories and services in Canada. 2 There are many reasons to which we chose Best Buy Canada as our research subject. First of all, it is a very well known retailer and can be easily related to. Secondly, the company fits well in our research structure and many of the concepts in marketing applies to Best Buy Canada as well. Lastly, we believe Best Buy Canada is largely an ethical and socially responsible company that has brought positive impact throughout our community. Best Buy Canada’s mission statement and objective is â€Å"To improve people's lives by making technology and entertainment products affordable and easy to use†. The four core values of the company are â€Å"Having fun while being the best†, â€Å"Learning from challenge and change†, â€Å"Showing respect, humility and integrity† and â€Å"Unleashing the power of our people† 4 In addition to being the biggest retailer of consumer electronics like big screen TVs, computers, cameras and entertainment products i n Canada, Best Buy Canada also has many exclusive brands such as Insignia, Dynex and RocketFish etc . covering a wide range of electronic products and accessories. Geek Squad – a 24 hour computer repair and tech support taskforce, enables Best Buy to offer its customers convenient installation and repair services. Since Best Buy Canada itself does not produce any real products, we are interested in the way Best Buy runs its retail business in the consumer electronics market. We are also interest in how Best Buy Canada attracts different groups of people with different needs and analyze its marketing strategy for staying competitive in the market.

Flow Induced Vibration

FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH IVAN GRANT Bachelor of Science in Mechanical Engineering Nagpur University Nagpur, India June, 2006 submitted in partial ful? llment of requirements for the degree MASTERS OF SCIENCE IN MECHANICAL ENGINEERING at the CLEVELAND STATE UNIVERSITY May, 2010 This thesis has been approved for the department of MECHANICAL ENGINEERING and the College of Graduate Studies by: Thesis Chairperson, Majid Rashidi, Ph. D. Department & Date Asuquo B. Ebiana, Ph. D. Department & Date Rama S. Gorla, Ph. D. Department & Date ACKNOWLEDGMENTS I would like to thank my advisor Dr. Majid Rashidi and Dr.Paul Bellini, who provided essential support and assistance throughout my graduate career, and also for their guidance which immensely contributed towards the completion of this thesis. This thesis would not have been realized without their support. I would also like to thank Dr. Asuquo. B. Ebiana and Dr. Rama. S. Gorla for being in my thesis committe e. Thanks are also due to my parents,my brother and friends who have encouraged, supported and inspired me. FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH IVAN GRANT ABSTRACT Flow induced vibrations of pipes with internal ? uid ? ow is studied in this work.Finite Element Analysis methodology is used to determine the critical ? uid velocity that induces the threshold of pipe instability. The partial di? erential equation of motion governing the lateral vibrations of the pipe is employed to develop the sti? ness and inertia matrices corresponding to two of the terms of the equations of motion. The Equation of motion further includes a mixed-derivative term that was treated as a source for a dissipative function. The corresponding matrix with this dissipative function was developed and recognized as the potentially destabilizing factor for the lateral vibrations of the ? id carrying pipe. Two types of boundary conditions, namely simply-supported and cantilevered were consi dered for the pipe. The appropriate mass, sti? ness, and dissipative matrices were developed at an elemental level for the ? uid carrying pipe. These matrices were then assembled to form the overall mass, sti? ness, and dissipative matrices of the entire system. Employing the ? nite element model developed in this work two series of parametric studies were conducted. First, a pipe with a constant wall thickness of 1 mm was analyzed. Then, the parametric studies were extended to a pipe with variable wall thickness.In this case, the wall thickness of the pipe was modeled to taper down from 2. 54 mm to 0. 01 mm. This study shows that the critical velocity of a pipe carrying ? uid can be increased by a factor of six as the result of tapering the wall thickness. iv TABLE OF CONTENTS ABSTRACT LIST OF FIGURES LIST OF TABLES I INTRODUCTION 1. 1 1. 2 1. 3 1. 4 II Overview of Internal Flow Induced Vibrations in Pipes . . . . . . Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Composition of Thesis . . . . . . . . . . . . . . . . . . . . . . . iv vii ix 1 1 2 2 3 FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 2. 1 Mathematical Modelling . . . . . . . . . . . . . . . . . . . . . . . 2. 1. 1 2. 2 Equations of Motion . . . . . . . . . . . . . . . . . . . 4 4 4 12 12 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 1 2. 2. 2 2. 2. 3 Shape Functions . . . . . . . . . . . . . . . . . . . . . Formulating the Sti? ness Matrix for a Pipe Carrying Fluid 14 Forming the Matrix for the Force that conforms the Fluid to the Pipe . . . . . . . . . . . . . . . . . . . . . 21 2. 2. 4 2. 2. 5Dissipation Matrix Formulation for a Pipe carrying Fluid 26 Inertia Matrix Formulation for a Pipe carrying Fluid . 28 III FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 31 v 3. 1 Forming Global Sti? ness Matrix from Elemental Sti? ness Matrices . . . . . . . . . . . . . . . . . . . . 31 3. 2 Applying Boundary Conditions to Global Sti? ness Matrix for simply supported pipe with ? uid ? ow . . . . 33 3. 3 Applying Boundary Conditions to Global Sti? ness Matrix for a cantilever pipe with ? uid ? ow . . . . . . . 34 3. 4 MATLAB Programs for Assembling Global Matrices for Simply Supported and Cantilever pipe carrying ? uid . . . . . . . . . . 35 35 36 3. 5 3. 6 MATLAB program for a simply supported pipe carrying ? uid . . MATLAB program for a cantilever pipe carrying ? uid . . . . . . IV FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 4. 1 V Parametric Study . . . . . . . . . . . . . . . . . . . . . . . . . . 37 37 FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 5. 1 Tapered Pipe Carrying Fluid . . . . . . . . . . . . . . . . . . . . 42 42 47 50 50 51 54 MATLAB program for Simply Supported Pipe Carrying Fluid . . MATLAB Program for Cantilever Pipe Carrying Fluid . . . . . . MATLAB Program for Tapered Pipe Carrying Flu id . . . . . . 54 61 68 VI RESULTS AND DISCUSSIONS 6. 1 6. 2 Contribution of the Thesis . . . . . . . . . . . . . . . . . . . . . Future Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY Appendices 0. 1 0. 2 0. 3 vi LIST OF FIGURES 2. 1 2. 2 Pinned-Pinned Pipe Carrying Fluid * . . . . . . . . . . . . . . Pipe Carrying Fluid, Forces and Moments acting on Elements (a) Fluid (b) Pipe ** . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 7 9 10 11 13 14 15 16 17 21 33 34 36 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 9 Force due to Bending . . . . . . . . . . . . . . . . . . . . . . . . .Force that Conforms Fluid to the Curvature of Pipe . . . . . Coriolis Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inertia Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pipe Carrying Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . Beam Element Model . . . . . . . . . . . . . . . . . . . . . . . . . Relationship between Stress and Stra in, Hooks Law . . . . . . 2. 10 Plain sections remain plane . . . . . . . . . . . . . . . . . . . . . 2. 11 Moment of Inertia for an Element in the Beam . . . . . . . . . 2. 12 Pipe Carrying Fluid Model . . . . . . . . . . . . . . . . . . . . . 3. 1 3. 2 3. 4. 1 Representation of Simply Supported Pipe Carrying Fluid . . Representation of Cantilever Pipe Carrying Fluid . . . . . . . Pinned-Free Pipe Carrying Fluid* . . . . . . . . . . . . . . . . . Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . 4. 2 Shape Function Plot for a Cantilever Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 3 Reduction of Fundamental Frequency for a Cantilever Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . 5. 1 Representation of Tapered Pipe Carrying Fluid . . . . . . . 39 40 41 42 vii 5. 2 6. 1 Introducing a Taper in the Pipe Carrying Fluid . . . . . . . . Representation of Pipe Carrying Fluid and Tapered Pipe Carrying Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 47 viii LIST OF TABLES 4. 1 Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . 38 4. 2 Reduction of Fundamental Frequency for a Pinned-Free Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . 40 5. 1 Reduction of Fundamental Frequency for a Tapered pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . . . 46 6. 1 Reduction of Fundamental Frequency for a Tapered Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . . . . 48 6. 2 Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . 49 ix CHAPTER I INTRODUCTION 1. 1 Overview of Internal Flow Induced Vibrations in Pipes The ? ow of a ? uid through a pipe can impose pressures on the walls of the pipe c ausing it to de? ect under certain ? ow conditions. This de? ection of the pipe may lead to structural instability of the pipe.The fundamental natural frequency of a pipe generally decreases with increasing velocity of ? uid ? ow. There are certain cases where decrease in this natural frequency can be very important, such as very high velocity ? ows through ? exible thin-walled pipes such as those used in feed lines to rocket motors and water turbines. The pipe becomes susceptible to resonance or fatigue failure if its natural frequency falls below certain limits. With large ? uid velocities the pipe may become unstable. The most familiar form of this instability is the whipping of an unrestricted garden hose.The study of dynamic response of a ? uid conveying pipe in conjunction with the transient vibration of ruptured pipes reveals that if a pipe ruptures through its cross section, then a ? exible length of unsupported pipe is left spewing out ? uid and is free to whip about and im pact other structures. In power plant plumbing pipe whip is a possible mode of failure. A 1 2 study of the in? uence of the resulting high velocity ? uid on the static and dynamic characteristics of the pipes is therefore necessary. 1. 2 Literature Review Initial investigations on the bending vibrations of a simply supported pipe containing ? id were carried out by Ashley and Haviland[2]. Subsequently,Housner[3] derived the equations of motion of a ? uid conveying pipe more completely and developed an equation relating the fundamental bending frequency of a simply supported pipe to the velocity of the internal ? ow of the ? uid. He also stated that at certain critical velocity, a statically unstable condition could exist. Long[4] presented an alternate solution to Housner’s[3] equation of motion for the simply supported end conditions and also treated the ? xed-free end conditions. He compared the analysis with experimental results to con? rm the mathematical model.His experi mental results were rather inconclusive since the maximum ? uid velocity available for the test was low and change in bending frequency was very small. Other e? orts to treat this subject were made by Benjamin, Niordson[6] and Ta Li. Other solutions to the equations of motion show that type of instability depends on the end conditions of the pipe carrying ? uid. If the ? ow velocity exceeds the critical velocity pipes supported at both ends bow out and buckle[1]. Straight Cantilever pipes fall into ? ow induced vibrations and vibrate at a large amplitude when ? ow velocity exceeds critical velocity[8-11]. . 3 Objective The objective of this thesis is to implement numerical solutions method, more specifically the Finite Element Analysis (FEA) to obtain solutions for di? erent pipe con? gurations and ? uid ? ow characteristics. The governing dynamic equation describing the induced structural vibrations due to internal ? uid ? ow has been formed and dis- 3 cussed. The governing equatio n of motion is a partial di? erential equation that is fourth order in spatial variable and second order in time. Parametric studies have been performed to examine the in? uence of mass distribution along the length of the pipe carrying ? id. 1. 4 Composition of Thesis This thesis is organized according to the following sequences. The equations of motions are derived in chapter(II)for pinned-pinned and ? xed-pinned pipe carrying ? uid. A ? nite element model is created to solve the equation of motion. Elemental matrices are formed for pinned-pinned and ? xed-pinned pipe carrying ? uid. Chapter(III)consists of MATLAB programs that are used to assemble global matrices for the above cases. Boundary conditions are applied and based on the user de? ned parameters fundamental natural frequency for free vibration is calculated for various pipe con? urations. Parametric studies are carried out in the following chapter and results are obtained and discussed. CHAPTER II FLOW INDUCED VIBRATION S IN PIPES, A FINITE ELEMENT APPROACH In this chapter,a mathematical model is formed by developing equations of a straight ? uid conveying pipe and these equations are later solved for the natural frequency and onset of instability of a cantilever and pinned-pinned pipe. 2. 1 2. 1. 1 Mathematical Modelling Equations of Motion Consider a pipe of length L, modulus of elasticity E, and its transverse area moment I. A ? uid ? ows through the pipe at pressure p and density ? t a constant velocity v through the internal pipe cross-section of area A. As the ? uid ? ows through the de? ecting pipe it is accelerated, because of the changing curvature of the pipe and the lateral vibration of the pipeline. The vertical component of ? uid pressure applied to the ? uid element and the pressure force F per unit length applied on the ? uid element by the tube walls oppose these accelerations. Referring to ? gures (2. 1) and 4 5 Figure 2. 1: Pinned-Pinned Pipe Carrying Fluid * (2. 2),balancing the forces in the Y direction on the ? uid element for small deformations, gives F ? A ? ? ? 2Y = ? A( + v )2 Y ? x2 ? t ? x (2. 1) The pressure gradient in the ? uid along the length of the pipe is opposed by the shear stress of the ? uid friction against the tube walls. The sum of the forces parallel Figure 2. 2: Pipe Carrying Fluid, Forces and Moments acting on Elements (a) Fluid (b) Pipe ** to the pipe axis for a constant ? ow velocity gives 0 0 * Flow Induced Vibrations,Robert D. Blevins,Krieger. 1977,P 289 ** Flow Induced Vibrations,Robert D. Blevins,Krieger. 1977,P 289 6 A ?p + ? S = 0 ? x (2. 2) Where S is the inner perimeter of the pipe, and ? s the shear stress on the internal surface of the pipe. The equations of motions of the pipe element are derived as follows. ?T ? 2Y + ? S ? Q 2 = 0 ? x ? x (2. 3) Where Q is the transverse shear force in the pipe and T is the longitudinal tension in the pipe. The forces on the element of the pipe normal to the pipe axis accelerate the pi pe element in the Y direction. For small deformations, ? 2Y ? 2Y ? Q +T 2 ? F =m 2 ? x ? x ? t (2. 4) Where m is the mass per unit length of the empty pipe. The bending moment M in the pipe, the transverse shear force Q and the pipe deformation are related by ? 3Y ?M = EI 3 ? x ? x Q=? (2. 5) Combining all the above equations and eliminating Q and F yields: EI ? 4Y ? 2Y ? ? ? Y + (? A ? T ) 2 + ? A( + v )2 Y + m 2 = 0 4 ? x ? x ? t ? x ? t (2. 6) The shear stress may be eliminated from equation 2. 2 and 2. 3 to give ? (? A ? T ) =0 ? x (2. 7) At the pipe end where x=L, the tension in the pipe is zero and the ? uid pressure is equal to ambient pressure. Thus p=T=0 at x=L, ? A ? T = 0 (2. 8) 7 The equation of motion for a free vibration of a ? uid conveying pipe is found out by substituting ? A ? T = 0 from equation 2. 8 in equation 2. 6 and is given by the equation 2. EI ? 2Y ? 2Y ? 4Y ? 2Y +M 2 =0 + ? Av 2 2 + 2? Av ? x4 ? x ? x? t ? t (2. 9) where the mass per unit length of the pi pe and the ? uid in the pipe is given by M = m + ? A. The next section describes the forces acting on the pipe carrying ? uid for each of the components of eq(2. 9) Y F1 X Z EI ? 4Y ? x4 Figure 2. 3: Force due to Bending Representation of the First Term in the Equation of Motion for a Pipe Carrying Fluid 8 The term EI ? Y is a force component acting on the pipe as a result of bending of ? x4 the pipe. Fig(2. 3) shows a schematic view of this force F1. 4 9 Y F2 X Z ?Av 2 ? 2Y ? x2 Figure 2. : Force that Conforms Fluid to the Curvature of Pipe Representation of the Second Term in the Equation of Motion for a Pipe Carrying Fluid The term ? Av 2 ? Y is a force component acting on the pipe as a result of ? ow ? x2 around a curved pipe. In other words the momentum of the ? uid is changed leading to a force component F2 shown schematically in Fig(2. 4) as a result of the curvature in the pipe. 2 10 Y F3 X Z 2? Av ? 2Y ? x? t Figure 2. 5: Coriolis Force Representation of the Third Term in t he Equation of Motion for a Pipe Carrying Fluid ? Y The term 2? Av ? x? t is the force required to rotate the ? id element as each point 2 in the span rotates with angular velocity. This force is a result of Coriolis E? ect. Fig(2. 5) shows a schematic view of this force F3. 11 Y F4 X Z M ? 2Y ? t2 Figure 2. 6: Inertia Force Representation of the Fourth Term in the Equation of Motion for a Pipe Carrying Fluid The term M ? Y is a force component acting on the pipe as a result of Inertia ? t2 of the pipe and the ? uid ? owing through it. Fig(2. 6) shows a schematic view of this force F4. 2 12 2. 2 Finite Element Model Consider a pipeline span that has a transverse de? ection Y(x,t) from its equillibrium position.The length of the pipe is L,modulus of elasticity of the pipe is E,and the area moment of inertia is I. The density of the ? uid ? owing through the pipe is ? at pressure p and constant velocity v,through the internal pipe cross section having area A. Flow of the ? uid through the de? ecting pipe is accelerated due to the changing curvature of the pipe and the lateral vibration of the pipeline. From the previous section we have the equation of motion for free vibration of a ? uid convering pipe: EI ? 2Y ? 2Y ? 2Y ? 4Y + ? Av 2 2 + 2? Av +M 2 =0 ? x4 ? x ? x? t ? t (2. 10) 2. 2. 1 Shape Functions The essence of the ? ite element method,is to approximate the unknown by an expression given as n w= i=1 Ni ai where Ni are the interpolating shape functions prescribed in terms of linear independent functions and ai are a set of unknown parameters. We shall now derive the shape functions for a pipe element. 13 Y R R x L2 L L1 X Figure 2. 7: Pipe Carrying Fluid Consider an pipe of length L and let at point R be at distance x from the left end. L2=x/L and L1=1-x/L. Forming Shape Functions N 1 = L12 (3 ? 2L1) N 2 = L12 L2L N 3 = L22 (3 ? 2L2) N 4 = ? L1L22 L Substituting the values of L1 and L2 we get (2. 11) (2. 12) (2. 13) (2. 14) N 1 = (1 ? /l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 15) (2. 16) (2. 17) (2. 18) 14 2. 2. 2 Formulating the Sti? ness Matrix for a Pipe Carrying Fluid ?1 ?2 W1 W2 Figure 2. 8: Beam Element Model For a two dimensional beam element, the displacement matrix in terms of shape functions can be expressed as ? ? w1 ? ? ? ? ? ?1 ? ? ? [W (x)] = N 1 N 2 N 3 N 4 ? ? ? ? ? w2? ? ? ?2 (2. 19) where N1, N2, N3 and N4 are the displacement shape functions for the two dimensional beam element as stated in equations (2. 15) to (2. 18). The displacements and rotations at end 1 is given by w1, ? and at end 2 is given by w2 , ? 2. Consider the point R inside the beam element of length L as shown in ? gure(2. 7) Let the internal strain energy at point R is given by UR . The internal strain energy at point R can be expressed as: 1 UR = ? 2 where ? is the stress and is the strain at the point R. (2. 20) 15 ? E 1 ? Figure 2. 9: Relationship between Stress and Strain, Hooks Law Also; ? =E Rel ation between stress and strain for elastic material, Hooks Law Substituting the value of ? from equation(2. 21) into equation(2. 20) yields 1 UR = E 2 (2. 21) 2 (2. 22) 16 A1 z B1 w A z B u x Figure 2. 0: Plain sections remain plane Assuming plane sections remain same, = du dx (2. 23) (2. 24) (2. 25) u=z dw dx d2 w =z 2 dx To obtain the internal energy for the whole beam we integrate the internal strain energy at point R over the volume. The internal strain energy for the entire beam is given as: UR dv = U vol (2. 26) Substituting the value of from equation(2. 25) into (2. 26) yields U= vol 1 2 E dv 2 (2. 27) Volume can be expressed as a product of area and length. dv = dA. dx (2. 28) 17 based on the above equation we now integrate equation (2. 27) over the area and over the length. L U= 0 A 1 2 E dAdx 2 (2. 29) Substituting the value of rom equation(2. 25) into equation (2. 28) yields L U= 0 A 1 d2 w E(z 2 )2 dAdx 2 dx (2. 30) Moment of Inertia I for the beam element is given as = dA z Figure 2. 11: Moment of Inertia for an Element in the Beam I= z 2 dA (2. 31) Substituting the value of I from equation(2. 31) into equation(2. 30) yields L U = EI 0 1 d2 w 2 ( ) dx 2 dx2 (2. 32) The above equation for total internal strain energy can be rewritten as L U = EI 0 1 d2 w d2 w ( )( )dx 2 dx2 dx2 (2. 33) 18 The potential energy of the beam is nothing but the total internal strain energy. Therefore, L ? = EI 0 1 d2 w d2 w ( )( )dx 2 dx2 dx2 (2. 34)If A and B are two matrices then applying matrix property of the transpose, yields (AB)T = B T AT (2. 35) We can express the Potential Energy expressed in equation(2. 34) in terms of displacement matrix W(x)equation(2. 19) as, 1 ? = EI 2 From equation (2. 19) we have ? ? w1 ? ? ? ? ? ?1 ? ? ? [W ] = N 1 N 2 N 3 N 4 ? ? ? ? ? w2? ? ? ?2 ? ? N1 ? ? ? ? ? N 2? ? ? [W ]T = ? ? w1 ? 1 w2 ? 2 ? ? ? N 3? ? ? N4 L (W )T (W )dx 0 (2. 36) (2. 37) (2. 38) Substituting the values of W and W T from equation(2. 37) and equation(2. 3 8) in equation(2. 36) yields ? N1 ? ? ? N 2 ? w1 ? 1 w2 ? 2 ? ? ? N 3 ? N4 ? ? ? ? ? ? N1 ? ? ? ? ? w1 ? ? ? ? ?1 ? ? ? ? ? dx (2. 39) ? ? ? w2? ? ? ?2 1 ? = EI 2 L 0 N2 N3 N4 19 where N1, N2, N3 and N4 are the displacement shape functions for the two dimensional beam element as stated in equations (2. 15) to (2. 18). The displacements and rotations at end 1 is given by w1, ? 1 and at end 2 is given by w2 , ? 2. 1 ? = EI 2 L 0 (N 1 ) ? ? ? N 2 N 1 ? w1 ? 1 w2 ? 2 ? ? ? N 3 N 1 ? N4 N1 ? 2 N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 )2 N4 N3 N1 N4 N2 N4 N3 N4 (N 4 )2 ? w1 ? ? ? ? ? 1 ? ? ? ? ? dx ? ? ?w2? ? ? 2 (2. 40) where ? 2 (N 1 ) ? ? L ? N 2 N 1 ? [K] = ? 0 ? N 3 N 1 ? ? N4 N1 N1 N2 (N 2 )2 N3 N2 N4 N2N1 N3 N2 N3 (N 3 ) 2 N1 N4 ? N4 N3 ? ? N2 N4 ? ? ? dx ? N3 N4 ? ? 2 (N 4 ) (2. 41) N 1 = (1 ? x/l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 42) (2. 43) (2. 44) (2. 45) The element sti? ness matrix for the beam is obtained by substit uting the values of shape functions from equations (2. 42) to (2. 45) into equation(2. 41) and integrating every element in the matrix in equation(2. 40) over the length L. 20 The Element sti? ness matrix for a beam element; ? ? 12 6l ? 12 6l ? ? ? ? 2 2? 4l ? 6l 2l ? EI ? 6l ? [K e ] = 3 ? ? l 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 6l 2l ? 6l 4l (2. 46) 1 2. 2. 3 Forming the Matrix for the Force that conforms the Fluid to the Pipe A X ? r ? _______________________ x R Y Figure 2. 12: Pipe Carrying Fluid Model B Consider a pipe carrying ? uid and let R be a point at a distance x from a reference plane AB as shown in ? gure(2. 12). Due to the ? ow of the ? uid through the pipe a force is introduced into the pipe causing the pipe to curve. This force conforms the ? uid to the pipe at all times. Let W be the transverse de? ection of the pipe and ? be angle made by the pipe due to the ? uid ? ow with the neutral axis. ? and ? represent the unit vectors along the X i j ? nd Y axis and r and ? rep resent the two unit vectors at point R along the r and ? ? ? axis. At point R,the vectors r and ? can be expressed as ? r = cos + sin ? i j (2. 47) ? ? = ? sin + cos i j Expression for slope at point R is given by; tan? = dW dx (2. 48) (2. 49) 22 Since the pipe undergoes a small de? ection, hence ? is very small. Therefore; tan? = ? ie ? = dW dx (2. 51) (2. 50) The displacement of a point R at a distance x from the reference plane can be expressed as; ? R = W ? + r? j r We di? erentiate the above equation to get velocity of the ? uid at point R ? ? ? j ? r ? R = W ? + r? + rr ? r = vf ? here vf is the velocity of the ? uid ? ow. Also at time t; r ? d? r= ? dt ie r ? d? d? = r= ? d? dt ? Substituting the value of r in equation(2. 53) yields ? ? ? ? j ? r R = W ? + r? + r (2. 57) (2. 56) (2. 55) (2. 53) (2. 54) (2. 52) ? Substituting the value of r and ? from equations(2. 47) and (2. 48) into equation(2. 56) ? yields; ? ? ? ?j ? R = W ? + r[cos + sin + r? [? sin + cos i j] i j] Sin ce ? is small The velocity at point R is expressed as; ? ? ? i ? j R = Rx? + Ry ? (2. 59) (2. 58) 23 ? ? i ? j ? ? R = (r ? r )? + (W + r? + r? )? ? ? The Y component of velocity R cause the pipe carrying ? id to curve. Therefore, (2. 60) 1 ? ? ? ? T = ? f ARy Ry (2. 61) 2 ? ? where T is the kinetic energy at the point R and Ry is the Y component of velocity,? f is the density of the ? uid,A is the area of cross-section of the pipe. ? ? Substituting the value of Ry from equation(2. 60) yields; 1 ? ? ? ? ? ? ? ? ? T = ? f A[W 2 + r2 ? 2 + r2 ? 2 + 2W r? + 2W ? r + 2rr ] 2 (2. 62) Substituting the value of r from equation(2. 54) and selecting the ? rst,second and the ? fourth terms yields; 1 2 ? ? T = ? f A[W 2 + vf ? 2 + 2W vf ? ] 2 (2. 63) Now substituting the value of ? from equation(2. 51) into equation(2. 3) yields; dW 2 dW dW 1 2 dW 2 ) + vf ( ) + 2vf ( )( )] T = ? f A[( 2 dt dx dt dx From the above equation we have these two terms; 1 2 dW 2 ? f Avf ( ) 2 dx 2? f Avf ( dW dW )( ) dt dx (2. 65) (2. 66) (2. 64) The force acting on the pipe due to the ? uid ? ow can be calculated by integrating the expressions in equations (2. 65) and (2. 66) over the length L. 1 2 dW 2 ? f Avf ( ) 2 dx (2. 67) L The expression in equation(2. 67) represents the force that causes the ? uid to conform to the curvature of the pipe. 2? f Avf ( L dW dW )( ) dt dx (2. 68) 24 The expression in equation(2. 68) represents the coriolis force which causes the ? id in the pipe to whip. The equation(2. 67) can be expressed in terms of displacement shape functions derived for the pipe ? =T ? V ? = L 1 2 dW 2 ? f Avf ( ) 2 dx (2. 69) Rearranging the equation; 2 ? = ? f Avf L 1 dW dW ( )( ) 2 dx dx (2. 70) For a pipe element, the displacement matrix in terms of shape functions can be expressed as ? ? w1 ? ? ? ? ? ?1 ? ? ? [W (x)] = N 1 N 2 N 3 N 4 ? ? ? ? ? w2? ? ? ?2 (2. 71) where N1, N2, N3 and N4 are the displacement shape functions pipe element as stated in equations (2. 15) to (2. 18). The displacements and rotations at end 1 is given by w1, ? 1 and at end 2 is given by w2 , ? . Refer to ? gure(2. 8). Substituting the shape functions determined in equations (2. 15) to (2. 18) ? ? N1 ? ? ? ? ? N 2 ? ? ? ? N1 w1 ? 1 w2 ? 2 ? ? ? N3 ? ? ? ? N4 ? ? w1 ? ? ? ? ? ?1 ? ? ? N 4 ? ? dx (2. 72) ? ? ? w2? ? ? ?2 L 2 ? = ? f Avf 0 N2 N3 25 L 2 ? = ? f Avf 0 (N 1 ) ? ? ? N 2 N 1 ? w1 ? 1 w2 ? 2 ? ? ? N 3 N 1 ? N4 N1 ? 2 N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 )2 N4 N3 N1 N4 N2 N4 N3 N4 (N 4 )2 ? w1 ? ? ? ? ? 1 ? ? ? ? ? dx ? ? ?w2? ? ? 2 (2. 73) where (N 1 ) ? ? L ? N 2 N 1 ? ? 0 ? N 3 N 1 ? ? N4 N1 ? 2 N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 ) 2 N1 N4 ? 2 [K2 ] = ? f Avf N4 N3 ? N2 N4 ? ? ? dx ? N3 N4 ? ? 2 (N 4 ) (2. 74) The matrix K2 represents the force that conforms the ? uid to the pipe. Substituting the values of shape functions equations(2. 15) to (2. 18) and integrating it over the length gives us the elemental matrix for the ? 36 3 ? 36 ? ? 4 ? 3 ? Av 2 ? 3 ? [K2 ]e = ? 30l 36 ? 3 36 ? ? 3 ? 1 ? 3 above force. ? 3 ? ? ? 1? ? ? ? ? 3? ? 4 (2. 75) 26 2. 2. 4 Dissipation Matrix Formulation for a Pipe carrying Fluid The dissipation matrix represents the force that causes the ? uid in the pipe to whip creating instability in the system. To formulate this matrix we recall equation (2. 4) and (2. 68) The dissipation function is given by; D= L 2? f Avf ( dW dW )( ) dt dx (2. 76) Where L is the length of the pipe element, ? f is the density of the ? uid, A area of cross-section of the pipe, and vf velocity of the ? uid ? ow. Recalling the displacement shape functions mentioned in equations(2. 15) to (2. 18); N 1 = (1 ? x/l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 77) (2. 78) (2. 79) (2. 80) The Dissipation Matrix can be expressed in terms of its displacement shape functions as shown in equations(2. 77) to (2. 80). ? ? N1 ? ? ? ? ? N 2 ? L ? ? D = 2? Avf ? N1 N2 N3 N4 w1 ? 1 w2 ? 2 ? ? ? 0 N3 ? ? ? ? N4 (N 1 ) ? ? ? N 2 N 1 ? w1 ? 1 w2 ? 2 ? ? ? N 3 N 1 ? N4 N1 ? 2 ? ? w1 ? ? ? ? ? ?1 ? ? ? ? ? dx ? ? ? w2? ? ? ?2 (2. 81) N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 )2 N4 N3 N1 N4 N2 N4 N3 N4 (N 4 )2 L 2? f Avf 0 ? w1 ? ? ? ? ? 1 ? ? ? ? ? dx ? ? ?w2? ? ? 2 (2. 82) 27 Substituting the values of shape functions from equations(2. 77) to (2. 80) and integrating over the length L yields; ? ? ? 30 6 30 ? 6 ? ? ? ? 0 6 ? 1? ?Av ? 6 ? ? [D]e = ? ? 30 30 ? 6 30 6 ? ? ? ? ? 6 1 ? 6 0 [D]e represents the elemental dissipation matrix. (2. 83) 28 2. 2. 5Inertia Matrix Formulation for a Pipe carrying Fluid Consider an element in the pipe having an area dA, length x, volume dv and mass dm. The density of the pipe is ? and let W represent the transverse displacement of the pipe. The displacement model for the Assuming the displacement model of the element to be W (x, t) = [N ]we (t) (2. 84) where W is the vector of displacements,[N] is the matrix of shape functions and we is the vecto r of nodal displacements which is assumed to be a function of time. Let the nodal displacement be expressed as; W = weiwt Nodal Velocity can be found by di? erentiating the equation() with time. W = (iw)weiwt (2. 86) (2. 85) Kinetic Energy of a particle can be expressed as a product of mass and the square of velocity 1 T = mv 2 2 (2. 87) Kinetic energy of the element can be found out by integrating equation(2. 87) over the volume. Also,mass can be expressed as the product of density and volume ie dm = ? dv T = v 1 ? 2 ? W dv 2 (2. 88) The volume of the element can be expressed as the product of area and the length. dv = dA. dx (2. 89) Substituting the value of volume dv from equation(2. 89) into equation(2. 88) and integrating over the area and the length yields; T = ? w2 2 ? ?W 2 dA. dx A L (2. 90) 29 ?dA = ?A A (2. 91) Substituting the value of A ?dA in equation(2. 90) yields; Aw2 2 T = ? W 2 dx L (2. 92) Equation(2. 92) can be written as; Aw2 2 T = ? ? W W dx L (2. 93) The Lagr ange equations are given by d dt where L=T ? V (2. 95) ? L ? w ? ? ? L ? w = (0) (2. 94) is called the Lagrangian function, T is the kinetic energy, V is the potential energy, ? W is the nodal displacement and W is the nodal velocity. The kinetic energy of the element †e† can be expressed as Te = Aw2 2 ? ? W T W dx L (2. 96) ? and where ? is the density and W is the vector of velocities of element e. The expression for T using the eq(2. 9)to (2. 21) can be written as; ? ? N1 ? ? ? ? ? N 2? ? ? w1 ? 1 w2 ? 2 ? ? N 1 N 2 N 3 N 4 ? ? ? N 3? ? ? N4 ? ? w1 ? ? ? ? ? ?1 ? ? ? ? ? dx ? ? ? w2? ? ? ?2 Aw2 T = 2 e (2. 97) L 30 Rewriting the above expression we get; ? (N 1)2 ? ? ? N 2N 1 Aw2 ? Te = w1 ? 1 w2 ? 2 ? ? 2 L ? N 3N 1 ? N 4N 1 ? N 1N 2 N 1N 3 N 1N 4 w1 ? ? 2 (N 2) N 2N 3 N 2N 4? ? ? 1 ? ? ? ? ? dx ? N 3N 2 (N 3)2 N 3N 4? ?w2? ? 2 N 4N 2 N 4N 3 (N 4) ? 2 (2. 98) Recalling the shape functions derived in equations(2. 15) to (2. 18) N 1 = (1 ? x/l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 9) (2. 100) (2. 101) (2. 102) Substituting the shape functions from eqs(2. 99) to (2. 102) into eqs(2. 98) yields the elemental mass matrix for a pipe. ? ? 156 22l 54 ? 13l ? ? ? ? 2 2? ? 22l 4l 13l ? 3l ? Ml ? [M ]e = ? ? ? 420 ? 54 13l 156 ? 22l? ? ? ? 2 2 ? 13l ? 3l ? 22l 4l (2. 103) CHAPTER III FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 3. 1 Forming Global Sti? ness Matrix from Elemental Sti? ness Matrices Inorder to form a Global Matrix,we start with a 6Ãâ€"6 null matrix,with its six degrees of freedom being translation and rotation of each of the nodes. So our Global Sti? ness matrix looks like this: ? 0 ? ?0 ? ? ? ?0 =? ? ? 0 ? ? ? 0 ? ? 0 ? 0? ? 0? ? ? ? 0? ? ? 0? ? ? 0? ? ? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KGlobal (3. 1) 31 32 The two 4Ãâ€"4 element sti? ness matrices are: ? ? 12 6l ? 12 6l ? ? ? ? 4l2 ? 6l 2l2 ? EI ? 6l ? ? e [k1 ] = 3 ? ? l 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 6l 2l ? 6l 4l ? 12 6l ? 12 6l ? (3. 2) ? ? ? ? 2 2? 4l ? 6l 2l ? EI ? 6l ? e [k2 ] = 3 ? ? l 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 6l 2l ? 6l 4l (3. 3) We shall now build the global sti? ness matrix by inserting element 1 ? rst into the global sti? ness matrix. 6l ? 12 6l 0 0? ? 12 ? ? ? 6l 4l2 ? 6l 2l2 0 0? ? ? ? ? ? ? 12 ? 6l 12 ? l 0 0? EI ? ? = 3 ? ? l ? 6l 2 2 2l ? 6l 4l 0 0? ? ? ? ? ? 0 0 0 0 0 0? ? ? ? ? 0 0 0 0 0 0 ? ? KGlobal (3. 4) Inserting element 2 into the global sti? ness matrix ? ? 6l ? 12 6l 0 0 ? ? 12 ? ? ? 6l 4l2 ? 6l 2l2 0 0 ? ? ? ? ? ? ? EI 12 ? 6l (12 + 12) (? 6l + 6l) ? 12 6l ? ? KGlobal = 3 ? ? l ? 6l 2 2 2 2? ? 2l (? 6l + 6l) (4l + 4l ) ? 6l 2l ? ? ? ? ? 0 0 ? 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 0 0 6l 2l ? 6l 4l (3. 5) 33 3. 2 Applying Boundary Conditions to Global Sti? ness Matrix for simply supported pipe with ? uid ? ow When the boundary conditions are applied to a simply supported pipe carrying ? uid, the 6Ãâ€"6 Global Sti? ess Matrix formulated in eq(3. 5) is mo di? ed to a 4Ãâ€"4 Global Sti? ness Matrix. It is as follows; Y 1 2 X L Figure 3. 1: Representation of Simply Supported Pipe Carrying Fluid ? ? 4l2 ?6l 2l2 0 KGlobalS ? ? ? ? EI 6l (12 + 12) (? 6l + 6l) 6l ? ? ? = 3 ? ? l ? 2l2 (? 6l + 6l) (4l2 + 4l2 ) 2l2 ? ? ? ? ? 2 2 0 6l 2l 4l (3. 6) Since the pipe is supported at the two ends the pipe does not de? ect causing its two translational degrees of freedom to go to zero. Hence we end up with the Sti? ness Matrix shown in eq(3. 6) 34 3. 3 Applying Boundary Conditions to Global Sti? ness Matrix for a cantilever pipe with ? id ? ow Y E, I 1 2 X L Figure 3. 2: Representation of Cantilever Pipe Carrying Fluid When the boundary conditions are applied to a Cantilever pipe carrying ? uid, the 6Ãâ€"6 Global Sti? ness Matrix formulated in eq(3. 5) is modi? ed to a 4Ãâ€"4 Global Sti? ness Matrix. It is as follows; ? (12 + 12) (? 6l + 6l) ? 12 6l ? KGlobalS ? ? ? ? ?(? 6l + 6l) (4l2 + 4l2 ) ? 6l 2l2 ? EI ? ? = 3 ? ? ? l ? ?12 ? 6l 12 ? 6l? ? ? ? 6l 2l2 ? 6l 4l2 (3. 7) Since the pipe is supported at one end the pipe does not de? ect or rotate at that end causing translational and rotational degrees of freedom at that end to go to zero.Hence we end up with the Sti? ness Matrix shown in eq(3. 8) 35 3. 4 MATLAB Programs for Assembling Global Matrices for Simply Supported and Cantilever pipe carrying ? uid In this section,we implement the method discussed in section(3. 1) to (3. 3) to form global matrices from the developed elemental matrices of a straight ? uid conveying pipe and these assembled matrices are later solved for the natural frequency and onset of instability of a cantlilever and simply supported pipe carrying ? uid utilizing MATLAB Programs. Consider a pipe of length L, modulus of elasticity E has ? uid ? wing with a velocity v through its inner cross-section having an outside diameter od,and thickness t1. The expression for critical velocity and natural frequency of the simply supported pipe carrying ? uid is given by; wn = ((3. 14)2 /L2 ) vc = (3. 14/L) (E ? I/M ) (3. 8) (3. 9) (E ? I/? A) 3. 5 MATLAB program for a simply supported pipe carrying ? uid The number of elements,density,length,modulus of elasticity of the pipe,density and velocity of ? uid ? owing through the pipe and the thickness of the pipe can be de? ned by the user. Refer to Appendix 1 for the complete MATLAB Program. 36 3. 6MATLAB program for a cantilever pipe carrying ? uid Figure 3. 3: Pinned-Free Pipe Carrying Fluid* The number of elements,density,length,modulus of elasticity of the pipe,density and velocity of ? uid ? owing through the pipe and the thickness of the pipe can be de? ned by the user. The expression for critical velocity and natural frequency of the cantilever pipe carrying ? uid is given by; wn = ((1. 875)2 /L2 ) (E ? I/M ) Where, wn = ((an2 )/L2 ) (EI/M )an = 1. 875, 4. 694, 7. 855 vc = (1. 875/L) (E ? I/? A) (3. 11) (3. 10) Refer to Appendix 2 for the complete MATLAB Program. 0 * Flow Induced Vibrat ions,Robert D.Blevins,Krieger. 1977,P 297 CHAPTER IV FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 4. 1 Parametric Study Parametric study has been carried out in this chapter. The study is carried out on a single span steel pipe with a 0. 01 m (0. 4 in. ) diameter and a . 0001 m (0. 004 in. ) thick wall. The other parameters are: Density of the pipe ? p (Kg/m3 ) 8000 Density of the ? uid ? f (Kg/m3 ) 1000 Length of the pipe L (m) 2 Number of elements n 10 Modulus Elasticity E (Gpa) 207 of MATLAB program for the simply supported pipe with ? uid ? ow is utilized for these set of parameters with varying ? uid velocity.Results from this study are shown in the form of graphs and tables. The fundamental frequency of vibration and the critical velocity of ? uid for a simply supported pipe 37 38 carrying ? uid are: ? n 21. 8582 rad/sec vc 16. 0553 m/sec Table 4. 1: Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity Velocity of Fluid(v) Ve locity Ratio(v/vc) 0 2 4 6 8 10 12 14 16. 0553 0 0. 1246 0. 2491 0. 3737 0. 4983 0. 6228 0. 7474 0. 8720 1 Frequency(w) 21. 8806 21. 5619 20. 5830 18. 8644 16. 2206 12. 1602 3. 7349 0. 3935 0 Frequency Ratio(w/wn) 1 0. 9864 0. 9417 0. 8630 0. 7421 0. 5563 0. 709 0. 0180 0 39 Figure 4. 1: Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity The fundamental frequency of vibration and the critical velocity of ? uid for a Cantilever pipe carrying ? uid are: ? n 7. 7940 rad/sec vc 9. 5872 m/sec 40 Figure 4. 2: Shape Function Plot for a Cantilever Pipe with increasing Flow Velocity Table 4. 2: Reduction of Fundamental Frequency for a Pinned-Free Pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 2 4 6 8 9 9. 5872 0 0. 2086 0. 4172 0. 6258 0. 8344 0. 9388 1 Frequency(w) 7. 7940 7. 5968 6. 9807 5. 8549 3. 825 1. 9897 0 Frequency Ratio(w/wn) 1 0. 9747 0. 8957 0. 7512 0. 4981 0. 2553 0 41 Figure 4. 3: Reduction of Fundamental Fr equency for a Cantilever Pipe with increasing Flow Velocity CHAPTER V FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH E, I v L Figure 5. 1: Representation of Tapered Pipe Carrying Fluid 5. 1 Tapered Pipe Carrying Fluid Consider a pipe of length L, modulus of elasticity E. A ? uid ? ows through the pipe at a velocity v and density ? through the internal pipe cross-section. As the ? uid ? ows through the de? ecting pipe it is accelerated, because of the changing curvature 42 43 f the pipe and the lateral vibration of the pipeline. The vertical component of ? uid pressure applied to the ? uid element and the pressure force F per unit length applied on the ? uid element by the tube walls oppose these accelerations. The input parameters are given by the user. Density of the pipe ? p (Kg/m3 ) 8000 Density of the ? uid ? f (Kg/m3 ) 1000 Length of the pipe L (m) 2 Number of elements n 10 Modulus Elasticity E (Gpa) 207 of For these user de? ned values we introduce a taper in the pipe so that the material property and the length of the pipe with the taper or without the taper remain the same.This is done by keeping the inner diameter of the pipe constant and varying the outer diameter. Refer to ? gure (5. 2) The pipe tapers from one end having a thickness x to the other end having a thickness Pipe Carrying Fluid 9. 8mm OD= 10 mm L=2000 mm x mm t =0. 01 mm ID= 9. 8 mm Tapered Pipe Carrying Fluid Figure 5. 2: Introducing a Taper in the Pipe Carrying Fluid of t = 0. 01mm such that the volume of material is equal to the volume of material 44 for a pipe with no taper. The thickness x of the tapered pipe is now calculated: From ? gure(5. 2) we have †¢ Outer Diameter of the pipe with no taper(OD) 10 mm †¢ Inner Diameter of the pipe(ID) 9. mm †¢ Outer Diameter of thick end of the Tapered pipe (OD1 ) †¢ Length of the pipe(L) 2000 mm †¢ Thickness of thin end of the taper(t) 0. 01 mm †¢ Thickness of thick end of the taper x mm Volume of th e pipe without the taper: V1 = Volume of the pipe with the taper: ? ? L ? 2 V2 = [ (OD1 ) + (ID + 2t)2 ] ? [ (ID2 )] 4 4 3 4 (5. 2) ? (OD2 ? ID2 )L 4 (5. 1) Since the volume of material distributed over the length of the two pipes is equal We have, V1 = V2 (5. 3) Substituting the value for V1 and V2 from equations(5. 1) and (5. 2) into equation(5. 3) yields ? ? ? L ? 2 (OD2 ? ID2 )L = [ (OD1 ) + (ID + 2t)2 ] ? (ID2 )] 4 4 4 3 4 The outer diameter for the thick end of the tapered pipe can be expressed as (5. 4) OD1 = ID + 2x (5. 5) 45 Substituting values of outer diameter(OD),inner diameter(ID),length(L) and thickness(t) into equation (5. 6) yields ? 2 ? ? 2000 ? (10 ? 9. 82 )2000 = [ (9. 8 + 2x)2 + (9. 8 + 0. 02)2 ] ? [ (9. 82 )] 4 4 4 3 4 Solving equation (5. 6) yields (5. 6) x = 2. 24mm (5. 7) Substituting the value of thickness x into equation(5. 5) we get the outer diameter OD1 as OD1 = 14. 268mm (5. 8) Thus, the taper in the pipe varies from a outer diameters of 14. 268 mm to 9 . 82 mm. 46The following MATLAB program is utilized to calculate the fundamental natural frequency of vibration for a tapered pipe carrying ? uid. Refer to Appendix 3 for the complete MATLAB program. Results obtained from the program are given in table (5. 1) Table 5. 1: Reduction of Fundamental Frequency for a Tapered pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 20 40 60 80 100 103. 3487 0 0. 1935 0. 3870 0. 5806 0. 7741 0. 9676 1 Frequency(w) 40. 8228 40. 083 37. 7783 33. 5980 26. 5798 10. 7122 0 Frequency Ratio(w/wn) . 8100 0. 7784 0. 7337 0. 6525 0. 5162 0. 2080 0The fundamental frequency of vibration and the critical velocity of ? uid for a tapered pipe carrying ? uid obtained from the MATLAB program are: ? n 51. 4917 rad/sec vc 103. 3487 m/sec CHAPTER VI RESULTS AND DISCUSSIONS In the present work, we have utilized numerical method techniques to form the basic elemental matrices for the pinned-pinned and pinned-free pipe carrying ? uid. Matlab programs have been developed and utilized to form global matrices from these elemental matrices and fundamental frequency for free vibration has been calculated for various pipe con? gurations and varying ? uid ? ow velocities.Consider a pipe carrying ? uid having the following user de? ned parameters. E, I v L v Figure 6. 1: Representation of Pipe Carrying Fluid and Tapered Pipe Carrying Fluid 47 48 Density of the pipe ? p (Kg/m3 ) 8000 Density of the ? uid ? f (Kg/m3 ) 1000 Length of the pipe L (m) 2 Number of elements n 10 Modulus Elasticity E (Gpa) 207 of Refer to Appendix 1 and Appendix 3 for the complete MATLAB program Parametric study carried out on a pinned-pinned and tapered pipe for the same material of the pipe and subjected to the same conditions reveal that the tapered pipe is more stable than a pinned-pinned pipe.Comparing the following set of tables justi? es the above statement. The fundamental frequency of vibration and the critical velocity of ? uid for a tapered and a pinned-pinned pipe carrying ? uid are: ? nt 51. 4917 rad/sec ? np 21. 8582 rad/sec vct 103. 3487 m/sec vcp 16. 0553 m/sec Table 6. 1: Reduction of Fundamental Frequency for a Tapered Pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 20 40 60 80 100 103. 3487 0 0. 1935 0. 3870 0. 5806 0. 7741 0. 9676 1 Frequency(w) 40. 8228 40. 083 37. 7783 33. 5980 26. 5798 10. 7122 0 Frequency Ratio(w/wn) 0. 8100 0. 7784 0. 7337 0. 6525 0. 5162 0. 2080 0 9 Table 6. 2: Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 2 4 6 8 10 12 14 16. 0553 0 0. 1246 0. 2491 0. 3737 0. 4983 0. 6228 0. 7474 0. 8720 1 Frequency(w) 21. 8806 21. 5619 20. 5830 18. 8644 16. 2206 12. 1602 3. 7349 0. 3935 0 Frequency Ratio(w/wn) 1 0. 9864 0. 9417 0. 8630 0. 7421 0. 5563 0. 1709 0. 0180 0 The fundamental frequency for vibration and critical velocity for the onset of instability in tapered pipe is approxim ately three times larger than the pinned-pinned pipe,thus making it more stable. 50 6. 1 Contribution of the Thesis Developed Finite Element Model for vibration analysis of a Pipe Carrying Fluid. †¢ Implemented the above developed model to two di? erent pipe con? gurations: Simply Supported and Cantilever Pipe Carrying Fluid. †¢ Developed MATLAB Programs to solve the Finite Element Models. †¢ Determined the e? ect of ? uid velocities and density on the vibrations of a thin walled Simply Supported and Cantilever pipe carrying ? uid. †¢ The critical velocity and natural frequency of vibrations were determined for the above con? gurations. †¢ Study was carried out on a variable wall thickness pipe and the results obtained show that the critical ? id velocity can be increased when the wall thickness is tapered. 6. 2 Future Scope †¢ Turbulence in Two-Phase Fluids In single-phase ? ow,? uctuations are a direct consequence of turbulence developed in ? uid, whe reas the situation is clearly more complex in two-phase ? ow since the ? uctuation of the mixture itself is added to the inherent turbulence of each phase. †¢ Extend the study to a time dependent ? uid velocity ? owing through the pipe. BIBLIOGRAPHY [1] Doods. H. L and H. Runyan †E? ects of High-Velocity Fluid Flow in the Bending Vibrations and Static Divergence of a Simply Supported Pipe†.National Aeronautics and Space Administration Report NASA TN D-2870 June(1965). [2] Ashley,H and G. Haviland †Bending Vibrations of a Pipe Line Containing Flowing Fluid†. J. Appl. Mech. 17,229-232(1950). [3] Housner,G. W †Bending Vibrations of a Pipe Line Containing Flowing Fluid†. J. Appl. Mech. 19,205-208(1952). [4] Long. R. H †Experimental and Theoretical Study of Transverse Vibration of a tube Containing Flowing Fluid†. J. Appl. Mech. 22,65-68(1955). [5] Liu. H. S and C. D. Mote †Dynamic Response of Pipes Transporting Fluids†. J. Eng. for Industry 96,591-596(1974). 6] Niordson,F. I. N †Vibrations of a Cylinderical Tube Containing Flowing Fluid†. Trans. Roy. Inst. Technol. Stockholm 73(1953). [7] Handelman,G. H †A Note on the transverse Vibration of a tube Containing Flowing Fluid†. Quarterly of Applied Mathematics 13,326-329(1955). [8] Nemat-Nassar,S. S. N. Prasad and G. Herrmann †Destabilizing E? ect on VelocityDependent Forces in Nonconservative Systems†. AIAA J. 4,1276-1280(1966). 51 52 [9] Naguleswaran,S and C. J. H. Williams †Lateral Vibrations of a Pipe Conveying a Fluid†. J. Mech. Eng. Sci. 10,228-238(1968). [10] Herrmann. G and R. W.Bungay †On the Stability of Elastic Systems Subjected to Nonconservative Forces†. J. Appl. Mech. 31,435-440(1964). [11] Gregory. R. W and M. P. Paidoussis †Unstable Oscillations of Tubular Cantilevers Conveying Fluid-I Theory†. Proc. Roy. Soc. (London). Ser. A 293,512-527(1966). [12] S. S. Rao †The Finite Element Method in Engineering†. Pergamon Press Inc. 245294(1982). [13] Michael. R. Hatch †Vibration Simulation Using Matlab and Ansys†. Chapman and Hall/CRC 349-361,392(2001). [14] Robert D. Blevins †Flow Induced Vibrations†. Krieger 289,297(1977). Appendices 53 54 0. 1 MATLAB program for Simply Supported Pipe Carrying FluidMATLAB program for Simply Supported Pipe Carrying Fluid. % The f o l l o w i n g MATLAB Program c a l c u l a t e s t h e Fundamental % N a t u r a l f r e q u e n c y o f v i b r a t i o n , f r e q u e n c y r a t i o (w/wn) % and v e l o c i t y r a t i o ( v / vc ) , f o r a % simply supported pipe carrying f l u i d . % I n o r d e r t o perform t h e above t a s k t h e program a s s e m b l e s % E l e m e n t a l S t i f f n e s s , D i s s i p a t i o n , and I n e r t i a m a t r i c e s % t o form G l o b a l M a t r i c e s which are used t o c a l c u l a t e % Fundamental N a t u r a l % Frequency w . lc ; n um elements =input ( ’ Input number o f e l e m e n t s f o r beam : ’ ) ; % num elements = The u s e r e n t e r s t h e number o f e l e m e n t s % i n which t h e p i p e % has t o be d i v i d e d . n=1: num elements +1;% Number o f nodes ( n ) i s e q u a l t o number o f %e l e m e n t s p l u s one n o d e l =1: num elements ; node2 =2: num elements +1; max nodel=max( n o d e l ) ; max node2=max( node2 ) ; max node used=max( [ max nodel max node2 ] ) ; mnu=max node used ; k=zeros (2? mnu ) ;% C r e a t i n g a G l o b a l S t i f f n e s s Matrix o f z e r o s 55 m =zeros (2? nu ) ;% C r e a t i n g G l o b a l Mass Matrix o f z e r o s x=zeros (2? mnu ) ;% C r e a t i n g G l o b a l Matrix o f z e r o s % f o r t h e f o r c e t h a t conforms f l u i d % to the curvature of the % pipe d=zeros (2? mnu ) ;% C r e a t i n g G l o b a l D i s s i p a t i o n Matrix o f z e r o s %( C o r i o l i s Component ) t=num elements ? 2 ; L=2; % T o t a l l e n g t h o f t h e p i p e i n meters l=L/ num elements ; % Length o f an e l e m e n t t1 =. 0001; od = . 0 1 ; i d=od? 2? t 1 % t h i c k n e s s o f t h e p i p e i n meter % outer diameter of the pipe % inner diameter of the pipeI=pi ? ( od? 4? i d ? 4)/64 % moment o f i n e r t i a o f t h e p i p e E=207? 10? 9; roh =8000; rohw =1000; % Modulus o f e l a s t i c i t y o f t h e p i p e % Density of the pipe % d e n s i t y o f water ( FLuid ) M =roh ? pi ? ( od? 2? i d ? 2)/4 + rohw? pi ? . 2 5 ? i d ? 2 ; % mass per u n i t l e n g t h o f % the pipe + f l u i d rohA=rohw? pi ? ( . 2 5 ? i d ? 2 ) ; l=L/ num elements ; v=0 % v e l o c i t y o f t h e f l u i d f l o w i n g t h r o u g h t h e p i p e %v =16. 0553 z=rohA/M i=sqrt ( ? 1); wn= ( ( 3 . 1 4 ) ? 2 /L? 2)? sqrt (E? I /M) % N a t u r a l Frequency vc =(3. 14/L)? sqrt (E?I /rohA ) % C r i t i c a l V e l o c i t y 56 % Assembling G l o b a l S t i f f n e s s , D i s s i p a t i o n and I n e r t i a M a t r i c e s for j =1: nu m elements d o f 1 =2? n o d e l ( j ) ? 1; d o f 2 =2? n o d e l ( j ) ; d o f 3 =2? node2 ( j ) ? 1; d o f 4 =2? node2 ( j ) ; % S t i f f n e s s Matrix Assembly k ( dof1 , d o f 1 )=k ( dof1 , d o f 1 )+ (12? E? I / l ? 3 ) ; k ( dof2 , d o f 1 )=k ( dof2 , d o f 1 )+ (6? E? I / l ? 2 ) ; k ( dof3 , d o f 1 )=k ( dof3 , d o f 1 )+ (? 12? E? I / l ? 3 ) ; k ( dof4 , d o f 1 )=k ( dof4 , d o f 1 )+ (6? E? I / l ? 2 ) ; k ( dof1 , d o f 2 )=k ( dof1 , d o f 2 )+ (6? E?I / l ? 2 ) ; k ( dof2 , d o f 2 )=k ( dof2 , d o f 2 )+ (4? E? I / l ) ; k ( dof3 , d o f 2 )=k ( dof3 , d o f 2 )+ (? 6? E? I / l ? 2 ) ; k ( dof4 , d o f 2 )=k ( dof4 , d o f 2 )+ (2? E? I / l ) ; k ( dof1 , d o f 3 )=k ( dof1 , d o f 3 )+ (? 12? E? I / l ? 3 ) ; k ( dof2 , d o f 3 )=k ( dof2 , d o f 3 )+ (? 6? E? I / l ? 2 ) ; k ( dof3 , d o f 3 )=k ( dof3 , d o f 3 )+ (12? E? I / l ? 3 ) ; k ( dof4 , d o f 3 )=k ( dof4 , d o f 3 )+ (? 6? E? I / l ? 2 ) ; k ( dof1 , d o f 4 )=k ( dof1 , d o f 4 )+ (6? E? I / l ? 2 ) ; k ( dof2 , d o f 4 )=k ( dof2 , d o f 4 )+ (2? E? I / l ) ; k ( dof3 , d o f 4 )=k ( dof3 , d o f 4 )+ (? ? E? I / l ? 2 ) ; k ( dof4 , d o f 4 )=k ( dof4 , d o f 4 )+ (4? E? I / l ) ; % 57 % Matrix a s s e m b l y f o r t h e second term i e % f o r t h e f o r c e t h a t conforms % f l u i d to the curvature of the pipe x ( dof1 , d o f 1 )=x ( dof1 , d o f 1 )+ ( ( 3 6 ? rohA? v ? 2)/30? l ) ; x ( dof2 , d o f 1 )=x ( dof2 , d o f 1 )+ ( ( 3 ? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 1 )=x ( dof3 , d o f 1 )+ (( ? 36? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 1 )=x ( dof4 , d o f 1 )+ ( ( 3 ? rohA? v ? 2)/30? l ) ; x ( dof1 , d o f 2 )=x ( dof1 , d o f 2 )+ ( ( 3 ? ohA? v ? 2)/30? l ) ; x ( dof2 , d o f 2 )=x ( dof2 , d o f 2 )+ ( ( 4 ? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 2 )=x ( dof3 , d o f 2 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 2 )=x ( dof4 , d o f 2 )+ (( ? 1? rohA? v ? 2)/30? l ) ; x ( dof1 , d o f 3 )=x ( dof1 , d o f 3 )+ (( ? 36? rohA? v ? 2)/30? l ) ; x ( dof2 , d o f 3 )=x ( dof2 , d o f 3 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 3 )=x ( dof3 , d o f 3 )+ ( ( 3 6 ? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 3 )=x ( dof4 , d o f 3 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof1 , d o f 4 )=x ( dof1 , d o f 4 )+ ( ( 3 ? rohA? v ? 2)/30? ) ; x ( dof2 , d o f 4 )=x ( dof2 , d o f 4 )+ (( ? 1? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 4 )=x ( dof3 , d o f 4 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 4 )=x ( dof4 , d o f 4 )+ ( ( 4 ? rohA? v ? 2)/30? l ) ; % % D i s s i p a t i o n Matrix Assembly d ( dof1 , d o f 1 )=d ( dof1 , d o f 1 )+ (2? ( ? 30? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 1 )=d ( dof2 , d o f 1 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; d ( dof3 , d o f 1 )=d ( dof3 , d o f 1 )+ ( 2 ? ( 3 0 ? rohA? v ) / 6 0 ) ; 58 d ( dof4 , d o f 1 )=d ( dof4 , d o f 1 )+ (2? ( ? 6? rohA? ) / 6 0 ) ; d ( dof1 , d o f 2 )=d ( dof1 , d o f 2 )+ (2? ( ? 6? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 2 )=d ( dof2 , d o f 2 )+ ( 2 ? ( 0 ? ro hA? v ) / 6 0 ) ; d ( dof3 , d o f 2 )=d ( dof3 , d o f 2 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; d ( dof4 , d o f 2 )=d ( dof4 , d o f 2 )+ (2? ( ? 1? rohA? v ) / 6 0 ) ; d ( dof1 , d o f 3 )=d ( dof1 , d o f 3 )+ (2? ( ? 30? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 3 )=d ( dof2 , d o f 3 )+ (2? ( ? 6? rohA? v ) / 6 0 ) ; d ( dof3 , d o f 3 )=d ( dof3 , d o f 3 )+ ( 2 ? ( 3 0 ? rohA? v ) / 6 0 ) ; d ( dof4 , d o f 3 )=d ( dof4 , d o f 3 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; ( dof1 , d o f 4 )=d ( dof1 , d o f 4 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 4 )=d ( dof2 , d o f 4 )+ ( 2 ? ( 1 ? rohA? v ) / 6 0 ) ; d ( dof3 , d o f 4 )=d ( dof3 , d o f 4 )+ (2? ( ? 6? rohA? v ) / 6 0 ) ; d ( dof4 , d o f 4 )=d ( dof4 , d o f 4 )+ ( 2 ? ( 0 ? rohA? v ) / 6 0 ) ; % % I n e r t i a Matrix Assembly m( dof1 , d o f 1 )=m( dof1 , d o f 1 )+ (156? M? l / 4 2 0 ) ; m( dof2 , d o f 1 )=m( dof2 , d o f 1 )+ (22? l ? 2? M/ 4 2 0 ) ; m( dof3 , d o f 1 )=m( dof3 , d o f 1 )+ (54? l ? M/ 4 2 0 ) ; m( d of4 , d o f 1 )=m( dof4 , d o f 1 )+ (? 3? l ? 2? M/ 4 2 0 ) ; m( dof1 , d o f 2 )=m( dof1 , d o f 2 )+ (22? l ? 2? M/ 4 2 0 ) ; m( dof2 , d o f 2 )=m( dof2 , d o f 2 )+ (4? M? l ? 3 / 4 2 0 ) ; m( dof3 , d o f 2 )=m( dof3 , d o f 2 )+ (13? l ? 2? M/ 4 2 0 ) ; m( dof4 , d o f 2 )=m( dof4 , d o f 2 )+ (? 3? M? l ? 3 / 4 2 0 ) ; 59 m( dof1 , d o f 3 )=m( dof1 , d o f 3 )+ (54? M? l / 4 2 0 ) ; m( dof2 , d o f 3 )=m( dof2 , d o f 3 )+ (13? l ? 2? M/ 4 2 0 ) ; m( dof3 , d o f 3 )=m( dof3 , d o f 3 )+ (156? l ? M/ 4 2 0 ) ; m( dof4 , d o f 3 )=m( dof4 , d o f 3 )+ (? 22? l ? 2? M/ 4 2 0 ) ; m( dof1 , d o f 4 )=m( dof1 , d o f 4 )+ (? 13? l ? 2?M/ 4 2 0 ) ; m( dof2 , d o f 4 )=m( dof2 , d o f 4 )+ (? 3? M? l ? 3 / 4 2 0 ) ; m( dof3 , d o f 4 )=m( dof3 , d o f 4 )+ (? 22? l ? 2? M/ 4 2 0 ) ; m( dof4 , d o f 4 )=m( dof4 , d o f 4 )+ (4? M? l ? 3 / 4 2 0 ) ; end k ( 1 : 1 , : ) = [ ] ;% A p p l y i n g Boundary c o n d i t i o n s k(: ,1:1)=[]; k ( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; k ( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; k x(1:1 ,:)=[]; x(: ,1:1)=[]; x ( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; x ( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; x; % G l o b a l Matrix f o r t h e % Force t h a t conforms f l u i d t o p i p e x1=? d(1:1 ,:)=[]; d(: ,1:1)=[]; d ( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; % G l o b a l S t i f f n e s s Matrix 60 d ( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; d d1=(? d ) Kg lobal=k+10? x1 ; m( 1 : 1 , : ) = [ ] ; m( : , 1 : 1 ) = [ ] ; m( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; m( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; m; eye ( t ) ; zeros ( t ) ; H=[? inv (m) ? ( d1 ) ? inv (m)? Kglobal ; eye ( t ) zeros ( t ) ] ; Evalue=eig (H) % E i g e n v a l u e s v r a t i o=v/ vc % V e l o c i t y Ratio % G l o b a l Mass Matrix % G l o b a l D i s s i p a t i o nMatrix i v 2=imag ( Evalue ) ; i v 2 1=min( abs ( i v 2 ) ) ; w1 = ( i v 2 1 ) wn w r a t i o=w1/wn vc % Frequency Ratio % Fundamental N a t u r a l f r e q u e n c y 61 0. 2 MATLAB Program for Cantilever Pipe Carrying Fluid MATLAB Program for Cantilever Pipe Carrying Fluid. % The f o l l o w i n g MATLAB Program c a l c u l a t e s t h e Fundamental % N a t u r a l f r e q u e n c y o f v i b r a t i o n , f r e q u e n c y r a t i o (w/wn) % and v e l o c i t y r a t i o ( v / vc ) , f o r a c a n t i l e v e r p i p e % carrying f l u i d . I n o r d e r t o perform t h e above t a s k t h e program a s s e m b l e s % E l e m e n t a l S t i f f n e s s , D i s s i p a t i o n , and I n e r t i a m a t r i c e s % t o form G l o b a l M a t r i c e s which are used % t o c a l c u l a t e Fundamental N a t u r a l % Frequency w . clc ; num elements =input ( ’ Input number o f e l e m e n t s f o r Pipe : ’ ) ; % num elements = The u s e r e n t e r s t h e number o f e l e m e n t s % i n which t h e p i p e has t o be d i v i d e d . =1: num elements +1;% Number o f nodes ( n ) i s % e q u a l t o num ber o f e l e m e n t s p l u s one n o d e l =1: num elements ; % Parameters used i n t h e l o o p s node2 =2: num elements +1; max nodel=max( n o d e l ) ; max node2=max( node2 ) ; max node used=max( [ max nodel max node2 ] ) ; mnu=max node used ; k=zeros (2? mnu ) ;% C r e a t i n g a G l o b a l S t i f f n e s s Matrix o f z e r o s 62 m =zeros (2? mnu ) ;% C r e a t i n g G l o b a l Mass Matrix o f z e r o s