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Mechanical Vibrations

In Chapter 3 the section on selfexcitation and stability analysis has been rewritten and expanded.
Two new sections, Using Newton's Second Law to Drive Equations of Motion and Free Vibration of Undamped Systems, have been added to Chapter 6.
The sections on isolation and absorbers have been expanded in Chapter 9.
A section on chaos has been added to Chapter 13.
Two new appendixes, on mathematical relationships and deflection of beams and plates, are now included.
More than 220 new problems have been added at the ends of various chapters.
Each topic in Mechanical Vibrations is selfcontained, with all concepts explained fully and the derivations presented with complete details. The computational aspects are emphasized throughout the book. Several Fortran computer programs, most of them in the form of general purpose subroutines, are included in the diskette accompanying the book. These programs are given for use by the students. Although the programs have been tested, no warranty is implied as to their accuracy. Problems that are based on the use/development of computer programs are given at the end of each chapter and expose students to many important computational and programming details.
Specific features include the following:
More than 50 review questions to help students in reviewing and testing their understanding of the text material.
More than 30 design project type problems at the ends of various chapters.
Biographical information about scientists and engineers who contributed to the development of the theory of vibrations given on the opening pages of chapters and appendixes.
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, is given following the Contents. 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. Contents
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 selfexcited 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 RayleighRitz methods of finding 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 rotting and reciprocating machines and the whirling of shafts are also considered. The vibrationmeasuring 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, RungeKutta, Houbolt, Wilson, and Newmark methods are summarized and illustrated. Finite element analysis, with applications involving onedimensional elements, is discussed in Chapter 12. An introductory treatment of nonlinear vibration, including a discussion of subharmonic and superharmonic oscillations, limit cycles, systems with timedependent 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. Finally, the basic relations of matrices, Laplace transforms, and SI units are outlined, respectively, in Appendixes C, D, and E. Acknowledgments
It has been gratifying to work with the staff of AddisonWesley throughout this revision. In particular, the help of Stuart Johnson, Publishing Partner, has been most valuable. Helen Wythe, Senior Production Supervisor, and Marybeth Mooney, Production Coordinator, handled the task of incorporating my corrections and revisions very efficiently. I would like to thank Purdue University for granting me permission to use the Boilermaker Special in Problem 2.82. Finally, I wish to thank my wife, Kamala, and daughters Sridevi and Shobha without whose patience, encouragement, and support this edition might never have been completed.
S. S. Rao
This text refers to an out of print or unavailable edition of this title.

