Page 113 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

110 Chapter 1 Fundamentals oF Vibration
In addition, Shock and Vibration Digest, Applied Mechanics Reviews, and Noise and
Vibration Worldwide are monthly abstract journals containing brief discussions of nearly
every published vibration paper. Formulas and solutions in vibration engineering can be
readily found in references [1.40–1.42]. Advanced topics on vibration can be found in the
encyclopedia of vibration [1.51] and an overview of the various aspects of vibration can be
obtained from handbooks on vibration and shock [1.53].

Chapter summary

In this chapter, we presented the fundamental concepts of vibration along with a brief outline of the
history and the importance of the study of vibration. We introduced the concepts of degree of free-
dom, discrete and continuous systems, and the different classes of vibration. We outlined the basic
steps involved in the vibration analysis of a system. We introduced the fundamental type of vibration,
namely harmonic motion, along with the associated terminology. We presented harmonic analysis
and Fourier series representation of periodic functions as well as numerical determination of Fourier
coefficients with examples.
At this point, the reader should be able to achieve the objectives stated at the beginning of the
chapter. To help the reader, review questions in the form of questions requiring brief answers, true
or false statements, fill in the blanks, multiple choices, and matching of statements are given for self
testing with answers available on the Companion Website. Several problems involving different levels
of difficulty in applying the basic concepts presented in the chapter are also given. The answers to
selected problems can be found at the end of the book.

reFerenCes

1.1 D. C. Miller, Anecdotal History of the Science of Sound, Macmillan, New York, 1935.
1.2 N. F. Rieger, “The quest for 2k>m: Notes on the development of vibration analysis, Part I.
genius awakening,” Vibrations, Vol. 3, No. 3/4, December 1987, pp. 3–10.
1.3 Chinese Academy of Sciences (compiler), Ancient China’s Technology and Science, Foreign
Languages Press, Beijing, 1983.
1.4 R. Taton (ed.), Ancient and Medieval Science: From the Beginnings to 1450, A. J. Pomerans
(trans.), Basic Books, New York, 1957.
1.5 S. P. Timoshenko, History of Strength of Materials, McGraw-Hill, New York, 1953.
1.6 R. B. Lindsay, “The story of acoustics,” Journal of the Acoustical Society of America, Vol. 39,
No. 4, 1966, pp. 629–644.
1.7 J. T. Cannon and S. Dostrovsky, The Evolution of Dynamics: Vibration Theory from 1687 to
1742, Springer-Verlag, New York, 1981.
1.8 L. L. Bucciarelli and N. Dworsky, Sophie Germain: An Essay in the History of the Theory of
Elasticity, D. Reidel Publishing, Dordrecht, Holland, 1980.
1.9 J. W. Strutt (Baron Rayleigh), The Theory of Sound, Dover, New York, 1945.
1.10 R. Burton, Vibration and Impact, Addison-Wesley, Reading, MA, 1958.
1.11 A. H. Nayfeh, Perturbation Methods, Wiley, New York, 1973.