实例介绍
【实例简介】
Fundamentals of Vibrations - L.Meirovitch
aHill Higher Education A Division of The McGraw-Hill companies FUNDAMENTALS OF VIBRATIONS International Edition 2001 Exclusive rights by McGraw-Hill Book Co- Singapore for manufacture and export. This book cannot be re-exported from the country to which it is sold by McGraw-Hill. The International Edition is not available in north america Published by McGraw-Hill, an imprint of The McGraw-Hill Companies, Inc. 1221 Avenue of the Americas, New York, NY, 10020. Copyright C 2001, by The McGraw Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher Some ancillaries, including electronic and print components, may not be available to customers outside the United States 10090807060504030201 2009080706050403020100 CTP SLP Library of Congress Cataloging-in-Publication Data Meirovitch, Leonard Fundamentals of vibrations /Leonard meirovitch p Includes bibliographical references and indexes ISBN007-041345-2 Vibration i. title TA355M432001 620.3dc21 00-030494 www.mhhe.com When ordering this title, use ISBN 0-07-118174-1 Printed in Singapore To My Wife and to the Memory of My parents and Eldest Brother …;””… ABOUT THE AUTHOR Leonard Meirovitch, a well-known researcher and educator, is a University distinguished Professor Emeritus at Virginia Polytechnic Institute and State University(vPI&SU).He is the author of a very large number of journal publications in the areas of analytical vibrations, computational structural dynamics and control of structures and of the books nalytical Methods in vibrations(macmillan, 1967), Methods of Analytical dynam ics(McGraw-Hill, 1970), Elements of vibration analysis, first edition(McGraw-Hill, 1975), Computational Methods in Structural Dynamics(Sijthoff Noordhoff, 1980) Introduction to Dynamics and Control (Wiley, 1985), Elements of Vibration anal sis,second edition (McGraw-Hill, 1986), Dynamics and Control of Structures(Wiley Interscience, 1990) and Principles and Techniques of Vibrations(Prentice-Hall, 1997) Dr Meirovitch is a Fellow of the American Institute of Aeronautics and Astronautics (AlAA)and the recipient of the vPl&su alumni Award for Research Excellence(1981) the AIAA Structures, Structural Dynamics, and Materials Award(1983), the AIAA Pendray Aerospace Literature Award(1984), the AIAA Mechanics and Control of Flight Award(1987), the Japan Society of Mechanical Engineers Award(1989), an Alexander von Humboldt Award for Senior U. S. Scientists(Germany, 1991) and the American Society of Mechanical Engineers J. P. Den Hartog Award (1999) 体你攻 PREFACE This book presents material fundamental to a modern treatment of vibrations, placing the emphasis on analytical developments and computational solutions. It is intended as a textbook. for a number of courses on vibrations ranging from the junior level to duate level; the book can also serve as a reference for practicing engineers Certain material from pertinent disciplines was included to render the book self-contained, and hence suitable for self-study Consistent with this, the book begins with very elementary material and raises the level gradually. A large number of exam ples and homework problems, as well as computer programs written in MaTLaB,are provided The following review is designed to help the reader decide how best to use. the book. Chapter 1. Concepts from Vibrations--Sections 1 1-1.6 are devoted to a review of ba sic concepts from Newtonian mechanics. Issues concerning the modeling of mechanical systems, from components to assembled systems, are discussed in Secs. 1.7 to 1. 9, and the differential equations of motion for such systems are derived in Sec. 1. 10. Sections 1. 11 and 1.12 are concerned with the nature of the excitations, the system characteristics and the nature of the response; the concept of linearity and the closely related principle of superposition are discussed. Finally, in Sec. 1. 13, the concepts of equilibrium points and motions about equilibrium points are introduced The whole chapter is suitable for a first course on vibrations at the undergraduate level, but Secs. 1.1-1.6 may be omitted from a first course at the graduate level Chapter 2. Response of Single-Degree-of-Freedom Systems to Initial Excitations- This chapter is concerned with the free vibration of undamped, viscously damped and Coulomb damped systems to initial displacements and velocities. It includes a matlab program for plotting the response of viscously damped systems This chapter is essential to a first course on vibrations at any level Chapter 3. Response of Single-Degree-of-Freedom Systems to Harmonic and Peri- odic Excitations--In Secs. 3. 1 and 3. 2, the response to harmonic excitations is repre- nted in the frequency domain, through magnitude and phase angle frequency response plots. Sections 3.3-3.7 discuss applications such as systems with rotating eccentric masses, systems with harmonically moving support, vibration isolation and vibration measuring instruments. In Sec. 3.8, structural damping is treated by means of an anal ogy with viscous damping. Finally, in Sec. 3. 9, the approach to the response of systems to harmonic excitations is extended to periodic excitations through the use of Fourier series. A MATLAB program generating frequency response plots is provided in Sec 3.10 The material in Secs. 3.1-3.6 is to be included in a first course on vibrations, but the material in Secs.3.7-3.9 is optional MATLAB is a registered trademark of The Math Works, Inc Ⅵ I PREFACE Chapter 4. Response of Single-Degree-of-Freedom Systems to Nonperiodic Exci- tations--Sections 4 1-43 introduce the unit impulse, unit step function and unit ramp function and the respective response. Then, regarding arbitrary excitations as a super- position of impulses of varying magnitude, the system response is represented in Sec 4.4 as a corresponding superposition of impulse responses, becoming the convolution integral in the limit. Section 4.5 discusses the concept of shock spectrum. Sections 4.6 and 4.7 are devoted to the system response by the Laplace transformation; the concept of transfer function is introduced. Next, in Sec. 4.8, the response is obtained by the state transition matrix. Numerical solutions for the response are carried out in discrete time by the convolution sum in Sec. 4.9 and by the discrete-time transition matrix in Sec. 4. 10. A MATLAB program for the response using the convolution sum is given in Sec. 4.11 and another program using the discrete-time transition matrix is given in SeC.4.12 Sections 4. 1-4. 4 are to be included in a first course on vibrations at all levels Section 4.5 is optional, but recommended for a design-oriented course. Sections 4.6 4. 10 are optional for a junior course, recommended for a senior course and to be included in a first course at the graduate level Chapter 5. Two-Degree-of-Freedom Systems--Sections 5.1-5.6 present in a simple fashion such topics as the eigenvalue problem, natural modes, response to initial exci tations, coupling, orthogonality of modes and modal analysis. Section 5.7 is concerned with the beat phenomenon, Sec. 5. 8 derives the response to harmonic excitations and Sec. 5.9 discusses vibration absorbers. The response to nonperiodic excitations is carried out in continuous time in Sec. 5.10 and in discrete time in Sec. 5.11. Three MATLAB programs are included, the first in Sec. 5. 12 for the response to initial excitations, the second in Sec. 5.13 for producing frequency response plots and the third in Sec.5.14 for the response to a rectangular pulse by the convolution sum The material belongs in an undergraduate course on vibrations but is not essential to a graduate course, unless a gradual transition to multi-degree-of-freedom systems is deemed desirable Chapter 6. Elements of Analytical Dynamics--Sections 6.1-6.3 provide the prereg uisite material for the development in Sec. 6.4 of the extended Hamilton principle, which permits the derivation of all the equations of motion. In Sec. 6.5, the principle is used to produce a generic form of the equations of motion, namely, Lagrange's equations This chapter is suitable for a senior course on vibrations and is a virtual necessity for a first-year graduate course Chapter 7. Multi-Degree-of-Freedom System--Sections 7 1-7.4 are concerned with the formulation of the equations of motion for linear and linearized systems, as well as with some basic properties of such systems. In Secs. 7.5-7.7, some of the concepts discussed in Ch. 5, such as linear transformations, coupling, the eigenvalue problem, natural modes and orthogonality of modes, are presented in a more compact manner by means of matrix algebra. Then, in Sec. 7. 8, the question of rigid-body motions i addressed. In Secs. 7.9 and 7. 10, modal analysis is first developed in a rigorous manner and then used to obtain the response to initial excitations. Certain issues associated with the eigenvalue problem are discussed in Secs. 7. 11 and 7. 12. Section 7.13 is devoted PREFACE VII to Rayleighs quotient, a concept of great importance in vibrations. The response to external excitations is obtained in continuous time in Secs. 7. 14 and 7 15 and in discrete time in Sec. 7. 17. MATLAB programs are provided as follows: the solution of the eigenvalue problem for conservative systems and for nonconservative systems, both in Sec. 7.18, the response to initial excitations in Sec. 7.19 and the response to external excitations by the discrete-time transition matrix in Sec. 7.20 This chapter, in full or in part, is suitable for a senior course on vibrations, and should be considered as an alternative to Ch. 5. The material rightfully belongs in a first-year graduate course Chapter 8 Distributed-Parameter Systems: Exact Solutions-In Sec 8. 1, the equa tions of motion for a set of lumped masses on a string are first derived by the Newtonian approach and then transformed in the limit into a boundary-value problem for a dis- tributed string. The same boundary-value problem is derived in Sec. 8.2 by the extended Hamilton principle. In Sec. 8.3, the boundary-value problem for a beam in bending is derived by both the Newtonian approach and the extended Hamilton principle. Sections 8.4-8.8 are devoted to the differential eigenvalue problem and its solution. Rayleigh's quotient is used in Sec.8.8 to develop the variational approach to the differential eigen value problem. The response to initial excitations and external excitations by modal analysis is considered in Secs. 8.9 and 8.10, respectively. A modal solution to the prob lem of a rod subjected to a boundary force is obtained in Sec.8.11. The wave equation and its solution in terms of traveling waves and standing waves are introduced in Sec 8. 12. and in Sec. 8.13 it is shown that a traveling wave solution matches the standing waves solution obtained in Sec.8.11 Sections 8.1-8.5.8.9 and 8.10 are suitable for a senior course ora first-year graduate course on vibrations. The balance of the chapter belongs in a second-year graduate course Chapter 9. Distributed-Parameter Systems: Approximate methods--Sections 9.1 9.4 discuss four lumped-parameter methods, including Holzer's method and Myklestad's method. The balance of the chapter is concerned with series discretization techniques Section 9.5 presents Rayleigh's principle, which is the basis for the variational approach to the differential eigenvalue problem identified with the Rayleigh-Ritz method, as ex pounded in Secs. 9.69.8. Sections 9.9 and 9.10 consider two weighted residuals meth ods, Galerkins method and the collocation method, respectively. A MATLAB program for the solution of the eigenvalue problem for a nonuniform rod by the Rayleigh-Ritz method is provided in Sec. 9.11 The material is suitable for a senior or a first-year graduate course on vibrations with the exception of the second half of Sec. 9. 6 and the entire Sec. 9.7, which are more suitable for a second-year graduate course Chapter 10. The Finite Element Method-Section 10.1 presents the formalism of the finite element method. Sections 10.2 and 10.3 consider strings, rods and shafts in terms of linear, quadratic and cubic interpolation functions. Then, Sec. 10.4 discusses beams in bending. Estimates of errors incurred- in using the finite element method are provided in Sec. 10.5. In Secs. 10.6 and 10.7, trusses and frames are treated as assemblages of rods and beams, respectively. Then, system response by the finite element method is 52以::一,; discussed in Sec. 10.8. A MATLAB program for the solution of the eigenvalue problem for a nonuniform pinned-pinned beam is provided in Sec. 10.9 This chapter is suitable for a senior or a first-year graduate course on vibrations th the on of Sec. 10.3 which al and Secs 10.6 and 10. 7. which are more suitable for a second-year graduate course Chapter 11. Nonlinear Oscillations-Sections 11 1-11.3 are concerned with qualita tive aspects of nonlinear systems, such as equilibrium points, stability of motion about equilibrium, trajectories in the neighborhood of equilibrium and motions in the large Section 11.4 discusses the van der pol oscillator and the concept of limit cycle. Sections 11.5-11.7 introduce the perturbation approach and how to obtain periodic perturbation solutions by Lindstedt's method. Using the perturbation approach, the jump phenomenon is discussed in Sec. 11.8, subharmonic solutions in Sec. 11.9 and linear systems with time-dependent coefficients in Sec. 11. 10. Section 11.11 is devoted to numerical inte gration of differential equations of motion by the Runge-Kutta methods. A MATLAB program for plotting trajectories for the van der pol oscillator is provided in Sec. 11.1 12 The material is suitable for a senior or a graduate course on nonlinear vibrations Chapter 12. Random Vibrations--Sections 12 1-12.3 introduce such concepts as ran- dom process, stationarity, ergodicity, mean value, autocorrelation function, mean square value and standard deviation. Sections 12.4 and 12.5 are concerned with probabilit density functions. Properties of the autocorrelation function are discussed in Sec. 12.6 Sections 12.7-12 1 1 are devoted to the response to random excitations using frequency domain techniques Sections 12.12-12 15 are concerned with joint properties of two random processes. The response of multi-degree-of-freedom systems and distributed systems to random excitations is discussed in Secs. 12.16 and 12.17, respectively The. material is suitable for a graduate course on random vibrations Appendix A. Fourier Series-The material is concerned with the representation of periodic functions by Fourier series. Both the real form and the complex form of fourier series are discussed Appendix B Laplace Transformation-The appendix contains an introduction to the Laplace transformation and its use to solve ordinary differential equations with constant coefficients, such as those encountered in vibrations Appendix C. Linear Algebra-The appendix represents an introduction to matrices, vector spaces and linear transformations. The material is indispensable to an efficient and rigorous treatment of multi-degree-O of-freedom systems In recent years, computational algorithms of interest in vibrations have matured to the extent that they are now standard. Examples of these are the Qr method for solving algebraic eigenvalue problems and the method based on the discrete-time transition ma- trix for computing the response of linear systems. At the same time, computers capable of handling such algorithms have become ubiquitous. Moreover, the software for the implementation of these algorithms has become easier to use. In this regard, MATLAB must be considered the software of choice. It is quite intuitive, it can be used interactively and it possesses an inventory of routines, referred to as functions which simplify the task of programming even more. This book contains 14 MATLAB programs solving typical vibrations problems; they have been written using Version 5.3 of MATLAB. The PREFACE IX programs can be used as they are, or they can be modified as needed particularly the data.In addition, a number of MATLAB problems are included. Further information concerning MATLAB can be obtained from The Math Works Ii 3 Apple hill drive Natick. MA01760 It should be stressed that the book is independent of the matLAB material and can be used with or without it. Of course the MATLAB material is designed to enhance the study of vibrations, and its use is highly recommended The author wishes to express his appreciation to William J. Atherton, Cleveland State University; Amr M. Baz, University of Maryland; Itzhak Green, Georgia Institute of Technology; Robert H. Lipp, University of New Orleans; Hayrani Ali Oz, Ohio State University; and Alan B Palazzolo, Texas A&M University, for their extensive review of the manuscript and their many useful suggestions. He also wishes to thank Timothy J temple, Virginia polytechnic Institute and State University, for producing the computer generated figures and for reviewing an early version of the manuscript. Special thanks are due to lhan Tuzcu, Virginia Polytechnic Institute and State University, for his major role in developing the maTlAB programs, as well as for his thorough review of the manuscript. Last but not least, the author would like to thank Norma B. Guynn for typing the book essentially as it appears in its final form; the book places in evidence the excellent quality of her work Leonard: meirovitch 【实例截图】
【核心代码】
Fundamentals of Vibrations - L.Meirovitch
aHill Higher Education A Division of The McGraw-Hill companies FUNDAMENTALS OF VIBRATIONS International Edition 2001 Exclusive rights by McGraw-Hill Book Co- Singapore for manufacture and export. This book cannot be re-exported from the country to which it is sold by McGraw-Hill. The International Edition is not available in north america Published by McGraw-Hill, an imprint of The McGraw-Hill Companies, Inc. 1221 Avenue of the Americas, New York, NY, 10020. Copyright C 2001, by The McGraw Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher Some ancillaries, including electronic and print components, may not be available to customers outside the United States 10090807060504030201 2009080706050403020100 CTP SLP Library of Congress Cataloging-in-Publication Data Meirovitch, Leonard Fundamentals of vibrations /Leonard meirovitch p Includes bibliographical references and indexes ISBN007-041345-2 Vibration i. title TA355M432001 620.3dc21 00-030494 www.mhhe.com When ordering this title, use ISBN 0-07-118174-1 Printed in Singapore To My Wife and to the Memory of My parents and Eldest Brother …;””… ABOUT THE AUTHOR Leonard Meirovitch, a well-known researcher and educator, is a University distinguished Professor Emeritus at Virginia Polytechnic Institute and State University(vPI&SU).He is the author of a very large number of journal publications in the areas of analytical vibrations, computational structural dynamics and control of structures and of the books nalytical Methods in vibrations(macmillan, 1967), Methods of Analytical dynam ics(McGraw-Hill, 1970), Elements of vibration analysis, first edition(McGraw-Hill, 1975), Computational Methods in Structural Dynamics(Sijthoff Noordhoff, 1980) Introduction to Dynamics and Control (Wiley, 1985), Elements of Vibration anal sis,second edition (McGraw-Hill, 1986), Dynamics and Control of Structures(Wiley Interscience, 1990) and Principles and Techniques of Vibrations(Prentice-Hall, 1997) Dr Meirovitch is a Fellow of the American Institute of Aeronautics and Astronautics (AlAA)and the recipient of the vPl&su alumni Award for Research Excellence(1981) the AIAA Structures, Structural Dynamics, and Materials Award(1983), the AIAA Pendray Aerospace Literature Award(1984), the AIAA Mechanics and Control of Flight Award(1987), the Japan Society of Mechanical Engineers Award(1989), an Alexander von Humboldt Award for Senior U. S. Scientists(Germany, 1991) and the American Society of Mechanical Engineers J. P. Den Hartog Award (1999) 体你攻 PREFACE This book presents material fundamental to a modern treatment of vibrations, placing the emphasis on analytical developments and computational solutions. It is intended as a textbook. for a number of courses on vibrations ranging from the junior level to duate level; the book can also serve as a reference for practicing engineers Certain material from pertinent disciplines was included to render the book self-contained, and hence suitable for self-study Consistent with this, the book begins with very elementary material and raises the level gradually. A large number of exam ples and homework problems, as well as computer programs written in MaTLaB,are provided The following review is designed to help the reader decide how best to use. the book. Chapter 1. Concepts from Vibrations--Sections 1 1-1.6 are devoted to a review of ba sic concepts from Newtonian mechanics. Issues concerning the modeling of mechanical systems, from components to assembled systems, are discussed in Secs. 1.7 to 1. 9, and the differential equations of motion for such systems are derived in Sec. 1. 10. Sections 1. 11 and 1.12 are concerned with the nature of the excitations, the system characteristics and the nature of the response; the concept of linearity and the closely related principle of superposition are discussed. Finally, in Sec. 1. 13, the concepts of equilibrium points and motions about equilibrium points are introduced The whole chapter is suitable for a first course on vibrations at the undergraduate level, but Secs. 1.1-1.6 may be omitted from a first course at the graduate level Chapter 2. Response of Single-Degree-of-Freedom Systems to Initial Excitations- This chapter is concerned with the free vibration of undamped, viscously damped and Coulomb damped systems to initial displacements and velocities. It includes a matlab program for plotting the response of viscously damped systems This chapter is essential to a first course on vibrations at any level Chapter 3. Response of Single-Degree-of-Freedom Systems to Harmonic and Peri- odic Excitations--In Secs. 3. 1 and 3. 2, the response to harmonic excitations is repre- nted in the frequency domain, through magnitude and phase angle frequency response plots. Sections 3.3-3.7 discuss applications such as systems with rotating eccentric masses, systems with harmonically moving support, vibration isolation and vibration measuring instruments. In Sec. 3.8, structural damping is treated by means of an anal ogy with viscous damping. Finally, in Sec. 3. 9, the approach to the response of systems to harmonic excitations is extended to periodic excitations through the use of Fourier series. A MATLAB program generating frequency response plots is provided in Sec 3.10 The material in Secs. 3.1-3.6 is to be included in a first course on vibrations, but the material in Secs.3.7-3.9 is optional MATLAB is a registered trademark of The Math Works, Inc Ⅵ I PREFACE Chapter 4. Response of Single-Degree-of-Freedom Systems to Nonperiodic Exci- tations--Sections 4 1-43 introduce the unit impulse, unit step function and unit ramp function and the respective response. Then, regarding arbitrary excitations as a super- position of impulses of varying magnitude, the system response is represented in Sec 4.4 as a corresponding superposition of impulse responses, becoming the convolution integral in the limit. Section 4.5 discusses the concept of shock spectrum. Sections 4.6 and 4.7 are devoted to the system response by the Laplace transformation; the concept of transfer function is introduced. Next, in Sec. 4.8, the response is obtained by the state transition matrix. Numerical solutions for the response are carried out in discrete time by the convolution sum in Sec. 4.9 and by the discrete-time transition matrix in Sec. 4. 10. A MATLAB program for the response using the convolution sum is given in Sec. 4.11 and another program using the discrete-time transition matrix is given in SeC.4.12 Sections 4. 1-4. 4 are to be included in a first course on vibrations at all levels Section 4.5 is optional, but recommended for a design-oriented course. Sections 4.6 4. 10 are optional for a junior course, recommended for a senior course and to be included in a first course at the graduate level Chapter 5. Two-Degree-of-Freedom Systems--Sections 5.1-5.6 present in a simple fashion such topics as the eigenvalue problem, natural modes, response to initial exci tations, coupling, orthogonality of modes and modal analysis. Section 5.7 is concerned with the beat phenomenon, Sec. 5. 8 derives the response to harmonic excitations and Sec. 5.9 discusses vibration absorbers. The response to nonperiodic excitations is carried out in continuous time in Sec. 5.10 and in discrete time in Sec. 5.11. Three MATLAB programs are included, the first in Sec. 5. 12 for the response to initial excitations, the second in Sec. 5.13 for producing frequency response plots and the third in Sec.5.14 for the response to a rectangular pulse by the convolution sum The material belongs in an undergraduate course on vibrations but is not essential to a graduate course, unless a gradual transition to multi-degree-of-freedom systems is deemed desirable Chapter 6. Elements of Analytical Dynamics--Sections 6.1-6.3 provide the prereg uisite material for the development in Sec. 6.4 of the extended Hamilton principle, which permits the derivation of all the equations of motion. In Sec. 6.5, the principle is used to produce a generic form of the equations of motion, namely, Lagrange's equations This chapter is suitable for a senior course on vibrations and is a virtual necessity for a first-year graduate course Chapter 7. Multi-Degree-of-Freedom System--Sections 7 1-7.4 are concerned with the formulation of the equations of motion for linear and linearized systems, as well as with some basic properties of such systems. In Secs. 7.5-7.7, some of the concepts discussed in Ch. 5, such as linear transformations, coupling, the eigenvalue problem, natural modes and orthogonality of modes, are presented in a more compact manner by means of matrix algebra. Then, in Sec. 7. 8, the question of rigid-body motions i addressed. In Secs. 7.9 and 7. 10, modal analysis is first developed in a rigorous manner and then used to obtain the response to initial excitations. Certain issues associated with the eigenvalue problem are discussed in Secs. 7. 11 and 7. 12. Section 7.13 is devoted PREFACE VII to Rayleighs quotient, a concept of great importance in vibrations. The response to external excitations is obtained in continuous time in Secs. 7. 14 and 7 15 and in discrete time in Sec. 7. 17. MATLAB programs are provided as follows: the solution of the eigenvalue problem for conservative systems and for nonconservative systems, both in Sec. 7.18, the response to initial excitations in Sec. 7.19 and the response to external excitations by the discrete-time transition matrix in Sec. 7.20 This chapter, in full or in part, is suitable for a senior course on vibrations, and should be considered as an alternative to Ch. 5. The material rightfully belongs in a first-year graduate course Chapter 8 Distributed-Parameter Systems: Exact Solutions-In Sec 8. 1, the equa tions of motion for a set of lumped masses on a string are first derived by the Newtonian approach and then transformed in the limit into a boundary-value problem for a dis- tributed string. The same boundary-value problem is derived in Sec. 8.2 by the extended Hamilton principle. In Sec. 8.3, the boundary-value problem for a beam in bending is derived by both the Newtonian approach and the extended Hamilton principle. Sections 8.4-8.8 are devoted to the differential eigenvalue problem and its solution. Rayleigh's quotient is used in Sec.8.8 to develop the variational approach to the differential eigen value problem. The response to initial excitations and external excitations by modal analysis is considered in Secs. 8.9 and 8.10, respectively. A modal solution to the prob lem of a rod subjected to a boundary force is obtained in Sec.8.11. The wave equation and its solution in terms of traveling waves and standing waves are introduced in Sec 8. 12. and in Sec. 8.13 it is shown that a traveling wave solution matches the standing waves solution obtained in Sec.8.11 Sections 8.1-8.5.8.9 and 8.10 are suitable for a senior course ora first-year graduate course on vibrations. The balance of the chapter belongs in a second-year graduate course Chapter 9. Distributed-Parameter Systems: Approximate methods--Sections 9.1 9.4 discuss four lumped-parameter methods, including Holzer's method and Myklestad's method. The balance of the chapter is concerned with series discretization techniques Section 9.5 presents Rayleigh's principle, which is the basis for the variational approach to the differential eigenvalue problem identified with the Rayleigh-Ritz method, as ex pounded in Secs. 9.69.8. Sections 9.9 and 9.10 consider two weighted residuals meth ods, Galerkins method and the collocation method, respectively. A MATLAB program for the solution of the eigenvalue problem for a nonuniform rod by the Rayleigh-Ritz method is provided in Sec. 9.11 The material is suitable for a senior or a first-year graduate course on vibrations with the exception of the second half of Sec. 9. 6 and the entire Sec. 9.7, which are more suitable for a second-year graduate course Chapter 10. The Finite Element Method-Section 10.1 presents the formalism of the finite element method. Sections 10.2 and 10.3 consider strings, rods and shafts in terms of linear, quadratic and cubic interpolation functions. Then, Sec. 10.4 discusses beams in bending. Estimates of errors incurred- in using the finite element method are provided in Sec. 10.5. In Secs. 10.6 and 10.7, trusses and frames are treated as assemblages of rods and beams, respectively. Then, system response by the finite element method is 52以::一,; discussed in Sec. 10.8. A MATLAB program for the solution of the eigenvalue problem for a nonuniform pinned-pinned beam is provided in Sec. 10.9 This chapter is suitable for a senior or a first-year graduate course on vibrations th the on of Sec. 10.3 which al and Secs 10.6 and 10. 7. which are more suitable for a second-year graduate course Chapter 11. Nonlinear Oscillations-Sections 11 1-11.3 are concerned with qualita tive aspects of nonlinear systems, such as equilibrium points, stability of motion about equilibrium, trajectories in the neighborhood of equilibrium and motions in the large Section 11.4 discusses the van der pol oscillator and the concept of limit cycle. Sections 11.5-11.7 introduce the perturbation approach and how to obtain periodic perturbation solutions by Lindstedt's method. Using the perturbation approach, the jump phenomenon is discussed in Sec. 11.8, subharmonic solutions in Sec. 11.9 and linear systems with time-dependent coefficients in Sec. 11. 10. Section 11.11 is devoted to numerical inte gration of differential equations of motion by the Runge-Kutta methods. A MATLAB program for plotting trajectories for the van der pol oscillator is provided in Sec. 11.1 12 The material is suitable for a senior or a graduate course on nonlinear vibrations Chapter 12. Random Vibrations--Sections 12 1-12.3 introduce such concepts as ran- dom process, stationarity, ergodicity, mean value, autocorrelation function, mean square value and standard deviation. Sections 12.4 and 12.5 are concerned with probabilit density functions. Properties of the autocorrelation function are discussed in Sec. 12.6 Sections 12.7-12 1 1 are devoted to the response to random excitations using frequency domain techniques Sections 12.12-12 15 are concerned with joint properties of two random processes. The response of multi-degree-of-freedom systems and distributed systems to random excitations is discussed in Secs. 12.16 and 12.17, respectively The. material is suitable for a graduate course on random vibrations Appendix A. Fourier Series-The material is concerned with the representation of periodic functions by Fourier series. Both the real form and the complex form of fourier series are discussed Appendix B Laplace Transformation-The appendix contains an introduction to the Laplace transformation and its use to solve ordinary differential equations with constant coefficients, such as those encountered in vibrations Appendix C. Linear Algebra-The appendix represents an introduction to matrices, vector spaces and linear transformations. The material is indispensable to an efficient and rigorous treatment of multi-degree-O of-freedom systems In recent years, computational algorithms of interest in vibrations have matured to the extent that they are now standard. Examples of these are the Qr method for solving algebraic eigenvalue problems and the method based on the discrete-time transition ma- trix for computing the response of linear systems. At the same time, computers capable of handling such algorithms have become ubiquitous. Moreover, the software for the implementation of these algorithms has become easier to use. In this regard, MATLAB must be considered the software of choice. It is quite intuitive, it can be used interactively and it possesses an inventory of routines, referred to as functions which simplify the task of programming even more. This book contains 14 MATLAB programs solving typical vibrations problems; they have been written using Version 5.3 of MATLAB. The PREFACE IX programs can be used as they are, or they can be modified as needed particularly the data.In addition, a number of MATLAB problems are included. Further information concerning MATLAB can be obtained from The Math Works Ii 3 Apple hill drive Natick. MA01760 It should be stressed that the book is independent of the matLAB material and can be used with or without it. Of course the MATLAB material is designed to enhance the study of vibrations, and its use is highly recommended The author wishes to express his appreciation to William J. Atherton, Cleveland State University; Amr M. Baz, University of Maryland; Itzhak Green, Georgia Institute of Technology; Robert H. Lipp, University of New Orleans; Hayrani Ali Oz, Ohio State University; and Alan B Palazzolo, Texas A&M University, for their extensive review of the manuscript and their many useful suggestions. He also wishes to thank Timothy J temple, Virginia polytechnic Institute and State University, for producing the computer generated figures and for reviewing an early version of the manuscript. Special thanks are due to lhan Tuzcu, Virginia Polytechnic Institute and State University, for his major role in developing the maTlAB programs, as well as for his thorough review of the manuscript. Last but not least, the author would like to thank Norma B. Guynn for typing the book essentially as it appears in its final form; the book places in evidence the excellent quality of her work Leonard: meirovitch 【实例截图】
【核心代码】
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