Mechanical Vibrations 4e / Edition 4

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With an emphasis on computer techniques of analysis, this book presents the theory, computational aspects, and applications of vibrations in as simple a manner as possible.

This text gives expanded explanations of the fundamentals of vibration including history of vibration, degree of freedom systems, vibration control, vibration measurement, and more.

For engineers and other professionals who want a clear introduction to vibration engineering.

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Product Details

  • ISBN-13: 9780130489876
  • Publisher: Prentice Hall
  • Publication date: 2/20/2003
  • Edition description: REV
  • Edition number: 4
  • Pages: 1104
  • Product dimensions: 7.68 (w) x 9.44 (h) x 1.60 (d)

Read an Excerpt

This book serves as an introduction to the subject of vibration engineering at the undergraduate level. The style of the prior editions has been retained, with the theory, computational aspects, and applications of vibrations presented in as simple a manner as possible. As in the previous editions, computer techniques of analysis are emphasized. Expanded explanations of the fundamentals are given, emphasizing physical significance and interpretation that build upon previous experiences in undergraduate mechanics. Numerous examples and problems are used to illustrate principles and concepts. Favorable reactions and encouragement from professors and students have provided me with the impetus to write the fourth edition of this book. Several new features have been added and many topics modified and rewritten. Most of the additions were suggested by those who have used the text and by numerous reviewers. Some important changes should be noted:

  • More than 900 new review questions have been added to help students in reviewing and testing their understanding of the text material. The review questions include multiple choice questions, questions with brief answers, true-false questions, questions involving matching of related descriptions, and fill-in-the-blank type questions.
  • A new appendix has been added to introduce the basic ideas of MATLAB programming.
  • Several MATLAB-based examples are included in every chapter.
  • General-purpose computer programs using MATLAB, C++, and Fortran programming are given, along with applications, in all chapters for the solution of vibration problems.
  • Several new problems-including problems that are based on the use of MATLAB, C++, and Fortran problems-are given at the end of each chapter to expose students to many important computational and programming details.
  • Answers to the review questions and the source codes of all MATLAB, C++, and Fortran programs are posted at the website of the book.
  • More than 50 new illustrative examples appear throughout the book.
  • More than 100 new problems have been added at the ends of various chapters.

Each topic in Mechanical Vibrations is self-contained, with all concepts explained fully and the derivations presented with complete details. The computational aspects are emphasized throughout the book. MATLAB-based examples are given in all chapters. Several MATLAB, interactive C++, and Fortran computer programs, most of them in the form of general purpose subroutines, are included in all the chapters. These programs are intended for use by the students. Although the programs have been tested, no warranty is implied as to their accuracy. Examples as well as problems that are based on the use of the various computer programs are given in each chapter to expose students to many important computational and programming details.

Certain subjects are presented in a somewhat unconventional manner. The topics of Chapters 9, 10, and 11 fall in this category. Most textbooks discuss isolators, absorbers, and balancing in different places. Since one of the main purposes of the study of vibrations is to control vibration response, all topics directly related to vibration control are given in Chapter 9. The vibration-measuring instruments, along with vibration exciters, experimental modal analysis procedures, and machine condition monitoring, are presented in Chapter 10. Similarly, all the numerical integration methods applicable to single and multi-degree of freedom systems, as well as continuous systems, are unified in Chapter 11.

Specific features include the following:

  • More than 200 illustrative examples accompanying most topics.
  • More than 900 review questions to help students in reviewing and testing their understanding of the text material.
  • More than 1000 problems, with solutions in the instructor's manual.
  • More than 30 design project type problems at the ends of various chapters.
  • More than 70 MATLAB, C++, and Fortran computer programs to aid students in the numerical implementation of the methods discussed in the text.
  • Biographical information about scientists and engineers who contributed to the development of the theory of vibrations are presented on the opening pages of chapters and appendixes.
  • The MATLAB, C++, and FORTRAN programs given in the book, answers to problems, and solutions to review questions can be found at the Web site for this book,
Notation and Units

Both the SI and the English system of units have been used in the examples and problems. A list of symbols, along with the associated units in SI and English systems, appears after the Acknowledgments. A brief discussion of SI units as they apply to the field of vibrations is given in Appendix E. Arrows are used over symbols to denote column vectors and square brackets are used to indicate matrices.


Mechanical Vibrations is organized into 14 chapters and 6 appendixes. The material of the book provides flexible options for different types of vibration courses. For a one-semester senior or dual-level course, Chapters 1 through 5, portions of Chapters 6, 7, 8, and 10, and Chapter 9 may be used. The course can be given a computer orientation by including Chapter 11 in place of Chapter 8. Alternatively, with Chapters 12, 13, and 14, the text has sufficient material for a one-year sequence at the senior level. For shorter courses, the instructor can select the topics, depending on the level and orientation of the course. The relative simplicity with which topics are presented also makes the book useful to practicing engineers for purposes of self-study and as a source of references and computer programs.

Chapter 1 starts with a brief discussion of the history and importance of vibrations. The basic concepts and terminology used in vibration analysis are introduced. The free vibration analysis of single degree of freedom undamped translational and torsional systems is given in Chapter 2. The effects of viscous, Coulomb, and hysteretic damping are also discussed. The harmonic response of single degree of freedom systems is considered in Chapter 3. Chapter 4 is concerned with the response of a single degree of freedom system under general forcing functions. The roles of convolution integral, Laplace transformation, and numerical methods are discussed. The concept of response spectrum is also introduced in this chapter. The free and forced vibration of two degree of freedom systems is considered in Chapter 5. The self-excited vibration and stability of the system are discussed. Chapter 6 presents the vibration analysis of multidegree of freedom systems. Matrix methods of analysis are used for the presentation of the theory. The modal analysis procedure is described for the solution of forced vibration problems. Several methods of determining the natural frequencies of discrete systems are outlined in Chapter 7. The methods of Dunkerley, Rayleigh, Holzer, and Jacobi and matrix iteration are also discussed. The vibration analysis of continuous systems, including strings, bars, shafts, beams, and membranes is given in Chapter 8. The Rayleigh and Rayleigh-Ritz methods of fording the approximate natural frequencies are also described. Chapter 9 discusses the various aspects of vibration control, including the problems of elimination, isolation, and absorption. The balancing of rotating and reciprocating machines and the whirling of shafts are also considered. The vibration-measuring instruments, vibration exciters, and signal analysis are the topics of Chapter 10. Chapter 11 presents several numerical integration techniques for finding the dynamic response of discrete and continuous systems. The central difference, Runge-Kutta, Houbolt, Wilson, and Newmark methods are summarized and illustrated. Finite element analysis, with applications involving one-dimensional elements, is discussed in Chapter 12. An introductory treatment of nonlinear vibration, including a discussion of subharmonic and superharmonic oscillations, limit cycles, systems with time-dependent coefficients and chaos, is given in Chapter 13. The random vibration of linear vibration systems is considered in Chapter 14. Appendixes A and B focus on mathematical relationships and deflection of beams and plates, respectively. The basic relations of matrices, Laplace transforms, and SI units are outlined, respectively, in Appendixes C, D, and E. Finally, Appendix F provides an introduction to MATLAB programming.

S.S. Rao

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Table of Contents

List of Symbols
Ch. 1 Fundamentals of Vibration 1
Ch. 2 Free Vibration of Single Degree of Freedom Systems 106
Ch. 3 Harmonically Excited Vibration 219
Ch. 4 Vibration Under General Forcing Conditions 302
Ch. 5 Two Degree of Freedom Systems 381
Ch. 6 Multidegree of Freedom Systems 448
Ch. 7 Determination of Natural Frequencies and Mode Shapes 542
Ch. 8 Continuous Systems 588
Ch. 9 Vibration Control 657
Ch. 10 Vibration Measurement and Applications 741
Ch. 11 Numerical Integration Methods in Vibration Analysis 808
Ch. 12 Finite Element Method 856
Ch. 13 Nonlinear Vibration 901
Ch. 14 Random Vibration 973
App. A Mathematical Relationships 1031
App. B Deflection of Beams and Plates 1034
App. C Matrices 1037
App. D Laplace Transform Pairs 1044
App. E Units 1046
App. F Introduction to MATLAB 1049
Answers to Selected Problems 1059
Index 1071
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  • Anonymous

    Posted February 2, 2004

    Very Good Book

    I go to the school where Rao is a teacher. Good guy likes feedback on his book from everyone who uses it. The book is very good. Lots of examples. Just make sure you keep some references handy, for materials information.

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