Should Scotland be independent Essay Example | Topics and Well Written Essays - 1500 words - 1

Should Scotland be independent - Essay Example For the understanding of the phenomenon from every angle, let’s try to consider should Scotland be dependent or not by researching pros and cons of the question. To begin with it must be said that the Scottish referendum of 2014 has brightly demonstrated the whole picture of Scots’ unsteady views about their future. Numerous surveys are the evidence of such a position. The people tend to shift their opinions under the influence of this or that factors. Today they are for the independence or undetermined with decision, and tomorrow they can radically change it or accept any of sides. â€Å"For the independence camp it is in many ways a race against time: Over the last six months the momentum has shifted toward independence, but at least one-sixth of Scottish voters in recent polls have said they were undecided or refused to answer† (Erlanger, 2014). One of the rationales is weight of political leaders’ speeches for a particular result, namely: being within (the Unionists) or being without the United Kingdom (the Scottish National Party). The other reason of Scots’ uncertainty is absence of precise understanding of times to come under the new governing, or in other words, the disparity in successful life after the winning of independency. In practice, the latter serves as a great ground for the first reason causing the appearance of great many supporters of Scotland secession of the United Kingdom. But it is an extremely controversial matter whether they really want or need it. Naturally, there are positive and negative motives of Scots’ aspiration for independence. Well-known reasoning of independence supporters includes several points. First of all, it is a need of increase of Scottish participating in affairs relating solely Scotland, and decrease of England’s interference into them, for only the absolute Scottish Parliament outright familiar with amount problems of its country is capable of solving them. Now â€Å"It has

Role of Inflammation in the Development of Atherosclerosis Essay

Role of Inflammation in the Development of Atherosclerosis - Essay Example As the discussion highlights atherosclerosis is a condition in which the wall of the artery thickens due to accumulation of fatty substances like cholesterol and triglycerides. The condition affects arterial blood vessels secondary to chronic inflammation of the innermost wall of the arteries and is mainly caused due to accumulation of macrophages. Accumulation of macrophages is promoted by low density lipoproteins. Stiffening of arteries occurs due to formation of multiple plaques within the arteries. There are basically 3 groups of atherosclerotic lesions and they are progressive atherosclerotic lesions, nonatherosclerotic intimal lesions and healed atherosclerotic plaques. Certain preexisting intimal lesions have intimal thickening and fatty streaks and adult lesions can arise from these Intimal thickening mainly involves the smooth muscles cells which lie in a proteoglycan-rich matrix. In early lesions, moderate cell replication can occur, but in adult lesions, they are mainly cl onal. Fatty streaks are basically intimal xanthomata in which there is accumulation of fat-laden macrophages. These lesions have lesser number of smooth muscle cells and lesser number of T-lymphocytes. These are nonatherosclerotic lesions. In progressive atherosclerosis lesions, there can be stable or non stable plaques. The plaques have intimal thickening with deposition of lipid. But there is no evidence of necrosis. Smooth muscle cells and proteoglycans overly the area of plaques along with T-lymphocytes and macrophages. Healed atherosclerotic plaques are those which have had thrombotic lesions, but have recovered.  

Emerging retail formats in india

Emerging retail formats in india Retailing has been defined as business activities involved in selling goods and services to consumers for their personal, family or household use (Berman and Evans, 2001). Although retailing has been around for millennia, the 20th century witnessed a lot of change in the retail sector, especially in the developed countries. Modern formats such as department stores, discount stores, supermarkets, convenience stores, fast food outlets, speciality stores, warehouse retailers and hypermarkets have emerged. Retailing has become more organized and chain stores have been growing at the expense of independent shops. The chains are utilizing sophisticated information technology and communication to manage their operations and have grown rapidly not only within their home countries like US, UK, France, Germany and Holland but to other developed countries. Walmart Stores, the US retailer, was recognized as the largest firm in terms of sales in 2002 in Fortune magazines list of 500 largest globa l firms. Modern retail formats have also spread beyond developed countries and are becoming more important in the NICs and developing countries. 3 The emergence of new formats and the evolution of modern retail in India has attracted attention in recent years. The business press in India has carried several articles and news items in the last three years about the modern formats (Shukla 2001; Anand Rajshekhar, 2001; Bhattacharjee, 2001). The consulting firm KSA Technopak has organized retail meetings or summits in major metros which have witnessed participation from major domestic and international retailers, and also from manufacturers. Venugopal (2001), has discussed the census studies of retail outlets that the market research firm ORG MARG conducted in the 1990s. This census provided data and estimates on a number of parameters relating to Indian retail such as number and type of outlets and growth of outlets over time separately for urban and rural areas. Due to these reports and activities, there is good deal of information available about what is happening in Indian retail. However Indian retailing has received sparse a ttention by way of academic research with the exception of a few articles in academic journals and some case studies. Purpose of the study. The purpose of this report is to develop an understanding of the factors influencing the evolution of modern formats in Indian retailing Objective of the study The report investigates modern retail developments and growth of modern formats in this country. The challenges and opportunities available to the retailers to succeed in this country. Literature review: Indian retailing is undergoing a process of evolution and is poised to undergo dramatic transformation. The retail sector employs over 8% of the national workforce but is characterized by a high degree of fragmentation with over 5 million outlets, 96% of whom are very small with an area of less than 50 m2 (Aggarwal, 2000). The retail universe more than doubled between 1978 and 1996 and the number of outlets per 1000 people at an All India level, increased from 3.7 in 1978 to 5.6 in 1996. For the urban sector alone, the shop density increased from 4 per 1000 people in 1978 to 7.6 per 1000 people in 1996 (Venugopal, 2001). Because of their small size, Indian retailers have very little bargaining power with manufacturers and perform only a few of the flows in marketing channels unlike in the case of retailers in developed countries, ( Sarma , 2000). The corner grocer or the kirana store is a key element in the retail in India due to the housewifes unwillingness to go long distances for purchasing daily needs. An empirical study was carried out by Sinha et al ( 2002) to identify factors that influenced consumers choice of a store. Although convenience and merchandise were the two most important reasons for choosing a store, the choice criteria varied across product categories. Convenience was indicated by consumers as the most important reason in the choice of groceries and fruit outlets, chemists and lifestyle items while merchandise was indicated as the most important in durables, books and apparel. The traditional formats like hawkers, grocers and paan shops co exist with modern formats like supermarkets, and non store retailing channels such as multi level marketing and teleshopping. Example of modern formats include department stores like Akbarallys , supermarkets like Food World, franchise stores like Van Heusen and Lee, discount stores like Subhiksha, shop-in-shops, factory outlets and service retailers ( Nathan , 2001). Modern stores tend to be larger, carry more stock keeping units have a self service format and an experiential ambience. Modern formats also tend to have higher levels of sales per unit of space, stock turnover and gross margin but lower levels of net margin as compared to traditional formats (Radhakrishnan, 2003). Modernisation in retail formats is likely to happen quicker in categories like Dry groceries, electronics, Mens apparel, Books, Music. Some reshaping and adaptation my also happen in Fresh groceries, Womens apparel, fast food, and personal care p roducts (Fernandes et al, 2000). In recent years, there has been a slow spread of retail chains in some formats like supermarkets, department stores, malls and discount stores. Factors facilitating the spread of chains are the availability of quality products at lower prices, improved shopping standards, convenient shopping and display, and blending of shopping withentertainment, and the entry of industrial houses like Goenkas, Rahejas, Piramals and Tatas into retailing ( Ramaswamy and Namakumari, 2002). However formats are not easily scalable across the country. Several companies have found that it is not easy to expand beyond some regions and cities as evident from the examples of Margin Free Market and Foodworld, which are active only in a few states or cities. Affordable real estate prices and availability of sufficient number of economically well off households in the catchment area are critical requirements that will determine new store viability and thus the possibility of further expansion (Anand and Rajashekhar, 2001). According to Rao (2001), foreign direct investment in the retail sector in India, although not yet permitted by government, is desirable, as it would improve productivity and increase competitiveness. New stores will introduce efficiency. Customers also gain as prices in the new stores tend to be lower. The consequences of modernization in India may be somewhat different due to lower purchasing power and the new stores may cater to only to branded products aimed at upper income segments. However it will be wise for old style stores to join together into wholesale and retail groups to improve bargaining power as experience in developed markets such as UK has shown that the modernization in retail has led to the decline of independent mom and pop stores. The need for a fresh perspective while developing theories to explain the new developments has been stressed by Bennett et al (1998). The Indian retail environment is witnessing several changes on the demand side due to increased per capita income, changing lifestyle and increased product availability. Experience of retailing in US shows that existing theories of retail development based on changing consumer needs, are inadequate to explain new developments. In developed markets, there has been a power shift with power moving from manufacturers towards retailers. The strategies used by retailers to wrest power include the development of retailers own brands, and the introduction of slotting allowances which necessitate payments by manufacturers to retailers for providing shelf space for new products. Retailers have also used technology effectively to obtain usable information about consumer buying patterns. The increased power of retailers has led to the introduction of new tactics b y manufacturers such as everyday low pricing, partnerships with retailers and increased use of direct marketing methods. Because of these issues, a supply side perspective needs to be fused with the demand side in developing theories for explaining modernization in retail. Research design: In order to fulfill the objectives of the study primary as well as secondary data have been collected to analyze the trends in modern retail formats meticulously. To analyze the emerging trends in shoppers behavior 30 shop keepers from 6 Malls operating in Ahmedabad will be interviewed. And for the rest part of the country secondary data published by different research institutions like TSMG, CSSO, Future Group, NCAER etc have been considered to draw the key inferences.

International Relations Essays -- Literary Analysis, Realism, Neo-Real

The first paradigm of international relations is the theory of Realism. Realism is focused on ideas of self-interest and the balance of power. Realism is also divided into two categories, classical realism and neo-realism. Famous political theorist, Hans Morgenthau was a classical realist who believed that national interest was based on three elements, balance of power, military force, and self interest (Kleinberg 2010, 32). He uses four levels of analysis to evaluate the power of a state. The first is that power and influence are not always the same thing. Influence means the ability to affect the decision of those who have the power to control outcomes and power is the ability to determine outcomes. An example of influence and power would be the UN’s ability to influence the actions of states within the UN but the state itself has the power to determine how they act. Morgenthau goes on to his next level of analysis in which he explains the difference in force and power in t he international realm. Force is physical violence, the use of military power but power is so much more than that. A powerful state can control the actions of another state with the threat of force but not actually need to physical force. He believed that the ability to have power over another state simply with the threat of force was likely to be the most important element in analysis the power of as state (Kleinberg 2010, 33-34). Morgenthau goes onto his third method of analysis which is reviewing a state’s usable and unusable power. The most popular example of this is the possession of nuclear weaponry. Nuclear capabilities and that threat of their use is a form of useable power for states like the US and Russia but not for states with underdeveloped nu... ...th 2001). Roth argues that the concept of international jurisdiction is not a new idea but was exercised by the US government in the 1970 after an aircraft hijacking. Also the war crime courts established after the end of World War II exercised international jurisdiction. In fact the Geneva Convention states that is a person regardless of their nationality should be brought before the court of any state in which that person has committed grave breaches of law and convention. Roth states that the concept of international jurisdiction is not a new one but that only in recent years have states been willing to act on universal jurisdiction and go after criminals of the international community regardless of their stating or power within the international community. Roth believes in the ability and authority of international organizations and institutions (Roth 2001). International Relations Essays -- Literary Analysis, Realism, Neo-Real The first paradigm of international relations is the theory of Realism. Realism is focused on ideas of self-interest and the balance of power. Realism is also divided into two categories, classical realism and neo-realism. Famous political theorist, Hans Morgenthau was a classical realist who believed that national interest was based on three elements, balance of power, military force, and self interest (Kleinberg 2010, 32). He uses four levels of analysis to evaluate the power of a state. The first is that power and influence are not always the same thing. Influence means the ability to affect the decision of those who have the power to control outcomes and power is the ability to determine outcomes. An example of influence and power would be the UN’s ability to influence the actions of states within the UN but the state itself has the power to determine how they act. Morgenthau goes on to his next level of analysis in which he explains the difference in force and power in t he international realm. Force is physical violence, the use of military power but power is so much more than that. A powerful state can control the actions of another state with the threat of force but not actually need to physical force. He believed that the ability to have power over another state simply with the threat of force was likely to be the most important element in analysis the power of as state (Kleinberg 2010, 33-34). Morgenthau goes onto his third method of analysis which is reviewing a state’s usable and unusable power. The most popular example of this is the possession of nuclear weaponry. Nuclear capabilities and that threat of their use is a form of useable power for states like the US and Russia but not for states with underdeveloped nu... ...th 2001). Roth argues that the concept of international jurisdiction is not a new idea but was exercised by the US government in the 1970 after an aircraft hijacking. Also the war crime courts established after the end of World War II exercised international jurisdiction. In fact the Geneva Convention states that is a person regardless of their nationality should be brought before the court of any state in which that person has committed grave breaches of law and convention. Roth states that the concept of international jurisdiction is not a new one but that only in recent years have states been willing to act on universal jurisdiction and go after criminals of the international community regardless of their stating or power within the international community. Roth believes in the ability and authority of international organizations and institutions (Roth 2001).

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

Introduction Floyd

Defines communication competence as communicating in means that are effective and appropriate in a given situation. Practitioners of competent communication can be observed to share several common characteristics. I will attempt to surface 4 of these characteristics, with specific references made to Mr. Ian Low, flogger of The Silver Chef. Self-Awareness Self-awareness is defined as the awareness of how an individual's behavior affects others (Floyd, 2010).An effective communicator must be aware of his individuality and behavior and how others may be affected by his behavior, more specifically, whether it fits within the situation as well as social setting. Emotional intelligence would therefore be key and would allow an Individual to better comprehend the social behaviors and emotions of others, and In turn, translate Into competent communication. The Silver Chef blob was started in 2010 whereas 2 of the blobs he listed in his post, started a year after that in 2011.Despite being a more established food flogger, he demonstrates self-awareness in his posts and refrains from harboring on this fact. If he had, readers may not find his opinions to be credible. Adaptability This trait is defined as one's ability to modify one's own behavior to better suit a changing situation. A competent communicator must be able to adapt to changes in social settings and modify his own behavior appropriately. With reference to the blob, Mr. Low had previously posted a Top 5 Singapore Food Blob when he first started out as a food flogger.However, after 3 years of blobbing and galling more experience within the food community, Mr. Low Is adaptable enough to make a similar post, demonstrating adaptability as a communicator. Cognitive Complexity Being able to understand a given situation in multiple ways defines cognitive complexity (Floyd, 2010). To better understand what Is occurring In a specific situation, It Is Important for an Individual to be aware of the different perspective s. This would prevent him from misjudging what is going on in the said situation, leading to inappropriate responses.In his post, Mr. Low highlighted several aspects of The Dirty Stall such as short descriptions, simple cooking and infrequent blob posts. It would be easy to misconceive these facts and describe â€Å"alkaline† as lazy but Mr. Low demonstrates s a flogger who priorities quality over quantity. Ethics Floyd (2010) defines ethics as a set of ideas that guides us in deciding what is right or wrong. Fair treatment of others and honest communication are examples of ethical communication but cultural plurality may complicate one's understanding of ethical communication due to cultural differences.In his blob, Mr. Low demonstrated this when he admitted to not having met flogger â€Å"alkaline† in person before and that â€Å"alkaline† does not blob as often. It would have been easy to omit these facts to lend more credibility to his post but instead, he c ited to mention this fact. 494 words Question 2 The communication process possesses several key characteristics that would define it as being dynamic in nature. Apart from being irreversible, multi-dimensional and inevitable, communication is also transactional.Transactional communication involves simultaneous initiation and interpretation of messages by communicators (Dobbin & Pace, 2006). When an individual initiates a message, the initiator will look for feedback from other communicators. The initiator will then adapt his messages to the changing situation. This implies that communication can be a continuously changing process and that people may modify their behavior and messages throughout the process.With reference to the article, â€Å"1 in 2 Singapore residents do not have a close friend from another race: survey', I will attempt to provide examples to show how messages are coded and decoded effectively, or otherwise, to help me better understand the news reported in the ar ticle. Encoding and decoding of messages In the process of communication, encoding and decoding are two processes that enable communicators to initiate and interpret messages (Dobbin & Pace, 2006).Encoding is further defined as the initiation and creation of messages that enables a communicator to translate feelings, ideas and thoughts into symbols. Decoding refers to the interpretation of messages by deciphering symbols into comprehensible and meaningful feelings, ideas and thoughts by communicators. Effective coding and decoding Ideally, when messages are interpreted in the way they were meant to be conveyed, coding and decoding leads to shared meaning by communicators. This results in successful communication as the symbols would be meaningful and recognizable byExample 1 (Effective coding of article) Within the article, sub-headlines such as â€Å"No inter-racial and religious tension in Singapore† effectively summarizes the following paragraph into an easy-to- comprehend sentence. Effective coding of the article such as this, contributes to the effective decoding of the article by readers. Example 2 (Effective coding and decoding of postings) User Karl commented â€Å"the Divide and Conquer tactics deployed sure works, isn't it? Who is behind all this thing? † in reply to a post by another user Suffering Singapore.In reply User Suffering Singapore posted I was having that in mind and wanted to add to my posting but I thought that I should hear from others posters who share the same thoughts YES the divisive policies in the name of ethnic integration have created the reverse effect. What do you think? † In this example, Karl had effectively encoded his opinion that a â€Å"Divide and Conquer† strategy had been implemented leading to the problem previously highlighted by Suffering Singapore. This was then effectively decoded by Suffering Singapore, leading to shared meaning of the topic they were both discussing.Ineffective coding and decoding When messages are ineffectively coded and/or decoded, this could lead to the miscommunication as messages are misinterpreted. Example 1 (Ineffective encoding of article) When decoding the article's headline, communicators might misinterpret the article as focusing on an existing racial divide in Singapore. In trying to sensationalist the article to boost readership, the writer may not have effectively encoded the actual content of the article, which highlights several positives found in the survey. A reader may Jump to conclusions, assume the worst and let his opinions and feelings known n a post.Example 2 (Ineffective decoding of article) The article features a survey carried out with Singapore Residents on the state of racial and religious harmony in Singapore and focuses on several indicators such as inter-racial tension, discrimination and openness to embracing diversity. Several users have misinterpreted this article and user â€Å"BRB† in particular, comme nted the article as being racist in nature. The user posted â€Å"Wow.. This article is Just racist.. Why will my bestrides need to be of community something we never really thought much of or cared!.. â€Å"

Do Colleges Use Weighted or Unweighted GPA

Do Colleges Use Weighted or Unweighted GPA SAT / ACT Prep Online Guides and Tips High schools may record students' GPAs as weighted or unweighted. But which type of GPA is taken more seriously in the college admissions process? In this article, I’ll provide an overview of the differences between weighted and unweighted GPAs and tell you which type is more important. What’s the Difference Between Weighted and Unweighted GPA? First off, you should know what constitutes weighted and unweighted GPA in high school. Traditional GPAs are unweighted, which means they'remeasured on a scale from 0 to 4.0.A 4.0 is an A average, a 3.0 is a B average, a 2.0 is a C average, a 1.0 is a D average, and anything below that represents a failing grade. Unweighted GPAs do not take the levels of your classes into account.An A in an AP or honors class will translate into a 4.0 GPA, and so will an A in a low-level class. Basically, an unweighted GPA won’t change based on the types of classes you’re taking; it represents your grades in isolation. Weighted GPAs are a bit more complicated.Many high schools now record weighted GPAs instead of standard unweighted GPAs.Weighted GPAs are measured on a scale that goes up higher than 4.0 to account for more difficult classes.For many schools, this means a 0-5.0 scale,but some scales go up higher (like to 6.0). In the lowest-level classes, grades will still stand for the same numbers as they would on an unweighted GPA scale (i.e., an A is a 4.0, a B is a 3.0, etc.).However, in honors or AP classes, an A will translate into a 5.0 GPA, a B will be a 4.0, and so on. If your school has mid-level classes, an A might translate into a 4.5 GPA. Keep in mind that these are general estimates.If your school records weighted GPAs, check its specific policies.Weighted GPAs are used in an effort to present a more accurate picture of academic abilities based on the rigor of a student's coursework. Your A+ in Intro to Yoga will only get you so far. Do some mindful breathing to help yourself accept this. Which GPA Do Colleges Care About? Of course, every college is different, but in general colleges care more about your record of coursework thanyour GPA out of context.For this reason, I can’t say that colleges necessarily care â€Å"more† about unweighted or weighted GPA.Between the two, weighted GPA provides more useful information, but they will still look closely at your transcript instead of just taking your GPA at face value. Your GPA is an overview of how you did in high school, but every admissions department will dig deeper (unless your GPA is exceptionally low- think below 2.0) before making a blanket judgment based solely on that number,whether it's weighted or unweighted. This is because the GPA scales of different high schools can't be compared directly. Some schools might count honors and AP classes as "high level" for weighted GPAs, and some might only count APs. Some AP classes are also easier than others. It wouldn't be fair for colleges to give a student who earned an A in a notoriously difficult class like AP Physics the same credit as a student who earned an A in AP Psychology, even if they have the same weighted GPA. Colleges want to see that you have pushed yourself to take on academic challenges and managed to grow over time.If your academic record demonstrates increasing difficulty of coursework, this will look impressive to colleges, even if your GPA isn’t stellar.If you have a 4.0 but remained in all the least challenging classes in high school, colleges will be less impressed since you didn’t push yourself further academically. even though you were clearly capable of doing so. If you’re getting all As in low-level classes, don’t stay complacent just because you have a good GPA.It’s absolutely worth it to move up a level and challenge yourself, even if it leads to a slight drop in your GPA. Colleges look at the whole picture, and they will make note of the fact that you forced yourself to leave your comfort zone and grow intellectually. This plant is a metaphor for your brain over the course of high school. What Do College Admissions Departments Say About GPA? Just to make sure we're on the right track, let's check the official policies of a range of schools. Here are some quotes about GPA taken from the admissions websites for Harvard, Ithaca College, Stanford, Claremont McKenna College, and the University of Texas at Austin. Harvard Admissions Department According to the admissions website, here are two key questions Harvard admissions officers ask themselves when reviewing potential applicants: â€Å"Have you reached your maximum academic and personal potential?† â€Å"Have you been stretching yourself?† Obviously, to get into Harvard, you'll need a great GPA.However, notice thatthey don’t say, â€Å"Your unweighted GPA must be at least 3.8,† or make any sort of concrete statement about numbers.What they want to see is that you’ve been constantly striving for more advanced learning opportunities and have also been pushing yourself to your limits academically. Students who've grown a lot in high school and who were motivated to take difficult classes are probably students who will continue to do the same in college.This demonstrates my point in the previous section that colleges really want to see students who have taken challenging coursework and proved themselves to be dedicated to fulfilling their academic potential. Harvard College Ithaca College Admissions Department Here’s what Ithaca's admissions department has to say about its admissions process: â€Å"An Ithaca College education requires that every student be actively engaged in their academic experiences. ...We are most focused on the rigor of your curriculum and the level of success you’ve demonstrated in your academic work.† Again, the admissions department is looking for students who were engaged in their high school coursework and are interested in learning more.Though grades are important, the level of your coursework and your demonstrated academic growth will also go a long way toward impressing admissions officers. Ithaca College Want to build the best possible college application with your GPA? We can help. PrepScholar Admissions is the world's best admissions consulting service. We combine world-class admissions counselors with our data-driven, proprietary admissions strategies. We've overseen thousands of students get into their top choice schools, from state colleges to the Ivy League. We know what kinds of students colleges want to admit. We want to get you admitted to your dream schools. Learn more about PrepScholar Admissions to maximize your chance of getting in. Stanford Admissions Department According toStanford, what itvalues most in its applicants is as follows: "The primary criterion for admission to Stanford is academic excellence. We look for your preparation and potential to succeed. We expect you to challenge yourself throughout high school and to do very well. ... There is no minimum GPA or test score; nor is there any specific number of AP or honors courses you must have on your transcript in order to be admitted to Stanford." As we saw with Harvard, academic excellence is a given- you obviously need to have strong grades in order to have a solid chance at getting into Stanford. That said, Stanford is clear that "there is no minimum GPA."Once again, the important idea here is that you're proving you have the potential to succeed and challenge yourself- not that you're necessarily getting As in every single class you take. Stanford University Claremont McKenna College Admissions Department Here’s what Claremont McKenna says about its admissions process: "Competitive candidates for admission pursue the most demanding course work possible, receive strong grades, and are highly regarded by their teachers and counselors. The minimum requirements are: English: Four years. Mathematics: Three years, preferably four. Candidates should recognize that mathematical skill is as important for professionals in government and economics as it is in engineering and the physical sciences. Foreign Language: At least three years. History: At least one year. Science: At least two years required, three strongly preferred." This brings up a good point: many schools might not have GPA requirements, but they do require applicants to take certain classes in high school. Once again, this emphasizes coursework over straight GPA in the admissions process.â€Å"Strong grades† are expected, but a desire for students who have pursued â€Å"the most demanding course work† is far more important. Claremont McKenna College University of Texas at Austin Admissions Department Finally, UT Austin says the following on its admissions website: "To be competitive for admission, freshman applicants must complete or be on track to complete certain high school coursework: Language Arts:Four credits Mathematics:Four credits Science:Four credits Social Studies:Four credits Foreign Language:Two credits Fine Arts:One credit Physical Education:One credit Electives:Six credits" Like Claremont McKenna College, UT Austin requires specific coursework in high school. In fact, the school doesn't say much at all about GPA on its website, indicating that GPA alone is not a particularly important part of admissions- rather,the courses you take are important. UT Austin (Stephen M. Scott/Flickr) Conclusion: Colleges and Weighted vs. Unweighted GPA Ultimately, you shouldn’t worry too much about whether colleges will look at your weighted or unweighted GPA.The value of your GPA, whether weighted or unweighted, isn’t the final word on whether you've demonstrated your academic potential in high school. Instead, focus on your coursework. Have you been consistently challenging yourself and living up to your abilities? Are you making the most of the academic opportunities your school offers? If you can answer yes to these two questions, you’re on your way to success in college admissions! What's Next? Worried about how your GPA will impact your chances of getting into college? Check out this list of the best colleges with less competitive GPA requirements. Not sure whether your GPA is considered high or low? Read my article on what constitutes a good and bad GPA for college admissions. For a complete overview of how GPA is calculated and what it means for you, take a look at this article. Want to improve your SAT score by 160 points or your ACT score by 4 points?We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

Polygamy essays

Polygamy essays Why do people cohabit and not marry? It is a decision that entails many motives. Mistrust of marriage is increasing, as a result of very high divorce levels, which causes many to be cautious about entering such a legally binding relationship. Support for the religious views of marriage and many traditional moral standards are declining. There is more acceptance of unwed motherhood, homosexuality, premarital sex and divorce(baker, 1996). One-sixth of never-married cohabiting couples have a child that was born since they began living together.This represents a significant component of unmarried births (about a quarter) that are not born into single-parent households (Bumpass and Sweet, 1989a). Advantages for living in a cohabitation and as a temporary or permanent solution to marriage include the following. Marriage is much easier to end than a cohabiting relationship than a marriage. About 40% of cohabiting unions in the United States break up without the couple getting married, and this tends to occur rather quickly (Bumpass and Sweet, 1989a).This happens quickly because they cohabiting couples have a much easier time deciding financial subjects etc. The ease at enduring a cohabitation. Almost three times as many cohabiters think that their freedom to do what they want would be worse in a marriage than at present (Sweet, Bumpass, Cohabiting will effect future relationships in the following ways. Those who cohabit less than one year are most likely to marry, 1 to 2.9 years is in between, 3+ years of cohabitation is least likely to marry (NSHF, 1987-88). we know that cohabi ...

American Civic Values Essay Example for Free

American Civic Values Essay In America our society has always been a morals run country, from our domestic everyday lives. Our society, groups with different civic values with who have a lot of power on our lives that we live everyday which includes schools and religious groups. There are some individuals who hold our civic values to a higher standard than those who have no regard for other members in their community. When it comes to undermining American civic values our media has a lot to be blame for as they promote and glamorize violence and illegal activities and does not show how communities can help each other adhere to civic policies. It is important for large groups to have set behaviors to adhere to, and civic values are important in keeping America a peaceful place that is safe for us as well as children. America has become a haven for special interest groups. If people don’t like something you say or do, plan on your freedom turning inwards and being used against you. Our society is no longer based off a country and its people as a whole, but by individual groups. The American civic values have dropped as special interest groups are in favor of political ground. There are several penalties that fail to adhere to the civic value such as â€Å"blue laws† these laws regulate behavior and restrict activities or the sale of goods on a Sunday to accommodate religious means. For an example in parts of one county here in North-East Florida we are not allowed to purchase alcohol on Sunday this day is constituted for religious matters. Another example of a blue law is the law in Pennsylvania where hunting is prohibited on Sunday’s as this day is recognized for a day of rest according to the religious groups. American Civic Values. (2017, Feb 21).

Ethical issues in packaging practices Research Paper

Ethical issues in packaging practices - Research Paper Example The ethical perception of issues related to packaging can be demarcated based on opinionated judgments of related packaging professionals, ethically interested customers along with brand managers. Moreover, the difference of opinions between consumers and business practitioners can be observed in terms of ethical sensitivity, perceived norms of industry along with apparent outcomes of practices of business. It can also be observed that business practitioners are identified to be possessing lower ethical sensitivity. On the other hand, ethically interested customers are very much concerned about the issue of packaging as compared to the business people. Furthermore, in this regard, it can be apparently viewed that ethical issues in packaging practices include label information, packaging safety, packaging graphics as well as environmental issues (Bone & Corey, 2000). Contextually, green packaging can be considered as a new breakthrough of consumer issue in order to deal with and shed more light on the modern day consumer standpoints related to the ethical issues associated with packaging. From the above evidences, it is quite evident that packaging in the sustainable manner has been preferred by customers in the global market context. Green packaging has been the standout facet which is based on rendering environmental friendly offerings for consumers in order to decrease unwanted substances and other significant aspects. Packaging is also considered as the lowest expensive form of advertisement. Thus, this invaluable source of inexpensive communication media needs to be carefully handled by concerned marketers keeping in consideration the ethical aspects associated with the use of this imperative facet (Shimp, 2010). With these considerations, the paper aims to explain the ethical stand on one of the major environmental concerning issues i.e. packaging. Prevalent Packaging Practices and Ethical Concerns The practices which are related to packaging both directly and indirectly can be observed on the basis of quality and quantity of the product. It can be stated that the size of packaging along with the contents are employed to create awareness about the varied product related information. The offered quality and substance of the product are generally demarcated on the packaging. However, at times, it is evidently observed that design for packaging depicts information for misleading consumers towards purchasing that product. Therein lays the emergence of ethical issues which can severely dent the prevailing trust of the consumers in the long run. Another implication related to packaging practices can be identified as producer at times imitates packaging patterns for misleading about actual product quality as well as at times pricing is indicated wrongly or eliminated from packaging (European Parliament, 2012). In the modern day context, packaging issues can be considered to be significant in terms of creating environmental concerns. As a re sult of which, most of the organizations are emphasizing on using lesser amount of packaging in order to keep the environment free from waste and pollution. Modern day marketers have been compelled to focus on the materials used for packaging which are reusable and renewable and are produced from proper utilization of natural resources. It can also be mentioned that packaging accounts for nearly half of the carbon