[...]... 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 Organization of Material Mechanical Vibrations is organized into 14 chapters and 6 appendixes Chapters 13 and 14 are provided as downloadable files on... urban areas The wheels of some locomotives can rise more than a centimeter off the track at high speeds due to imbalance In turbines, vibrations cause spectacular mechanical failures Engineers have not yet been able to prevent the failures that result from blade and disk vibrations in turbines Naturally, the structures designed to support heavy centrifugal machines, like motors and turbines, or reciprocating... and 107 new illustrations 6 The C++ and Fortran program-based examples and problems given at the end of every chapter in the previous edition have been deleted Features of the Book Each topic in Mechanical Vibrations is self-contained, with all concepts fully explained and the derivations presented in complete detail Computational aspects are emphasized throughout the book MATLAB-based examples as... for helping me write some of the MATLAB programs Finally, I wish to thank my wife, Kamala, without whose patience, encouragement, and support this edition might never have been completed SINGIRESU S RAO srao@miami.edu xv List of Symbols Symbol Meaning English Units SI Units a, a0, a1, a2, Á aij constants, lengths flexibility coefficient in./lb m/N [a] A A, A0, A1, Á b, b1, b2, Á B, B1, B2, Á ! B c,... the propeller shafts of steamships The dynamic vibration absorber, which involves the addition of a secondary spring-mass system to eliminate the vibrations of a main system, was also proposed by Frahm in 1909 Among the modern contributers to the theory of vibrations, the names of Stodola, De Laval, Timoshenko, and Mindlin are notable Aurel Stodola (1859 1943) contributed to the study of vibration of... recognized that many basic problems of mechanics, including those of vibrations, are nonlinear Although the linear treatments commonly adopted are quite satisfactory for most purposes, they are not adequate in all cases In nonlinear systems, phenonmena may occur that are theoretically impossible in linear systems The mathematical theory of nonlinear vibrations began to develop in the works of Poincaré and Lyapunov... undertaken by Duffing and van der Pol brought the first definite solutions into the theory of nonlinear vibrations and drew attention to its importance in engineering In the last 40 years, authors like Minorsky and Stoker have endeavored to collect in monographs the main results concerning nonlinear vibrations Most practical applications of nonlinear vibration involved the use of some type of a perturbation-theory... opened new prospects for progress in the theory of random vibrations Papers by Lin and Rice, published between 1943 and 1945, paved 10 CHAPTER 1 FUNDAMENTALS OF VIBRATION FIGURE 1.6 Finite element idealization of the body of a bus [1.16] (Reprinted with permission © 1974 Society of Automotive Engineers, Inc.) the way for the application of random vibrations to practical engineering problems The monographs... information about 20 scientists and engineers who contributed to the development of the theory of vibrations is presented on the opening pages of chapters and appendixes MATLAB programs given in the book, answers to problems, and answers to review questions can be found at the Companion Website, www.pearsonhighered.com /rao The Solutions Manual with solutions to all problems and hints to design projects is available... kg/m3 lb/in2 sec N/m2 s i th modal vector i th component of j th mode modal matrix r th approximation to a mode shape base displacement amplitude of y (t) relative displacement, x - y amplitude of z (t) mechanical impedance angle, constant angle, constant hysteresis damping constant specific weight logarithmic decrement deflections static deflection Kronecker delta determinant increment in F increment . of these programs. Library of Congress Cataloging-in-Publication Data Rao, S. S. Mechanical vibrations / Singiresu S. Rao. 5th ed. p. cm. Includes index. ISBN 978-0-13-212819-3 (978-0-13-212819-3.