Page 21 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

18 PrEFACE
organization of Material
Mechanical Vibrations is organized into 14 chapters and 6 appendices. The reader is assumed to have a basic
knowledge of statics, dynamics, strength of materials, and differential equations. Although some background in
matrix theory and Laplace transform is desirable, an overview of these topics is given in Appendices C and D,
respectively. Chapter 1 starts with a brief discussion of the history and importance of vibrations. The modeling
of practical systems for vibration analysis along with the various steps involved in the vibration analysis are dis-
cussed. A description of the elementary parts of a vibrating system—stiffness, damping, and mass (inertia)—is
given. The basic concepts and terminology used in vibration analysis are introduced. The free vibration analysis of
single-degree-of-freedom undamped and viscously damped translational and torsional systems is given in Chapter
2. The graphical representation of characteristic roots and corresponding solutions, the parameter variations, and
root locus representations are discussed. Although the root locus method is commonly used in control systems,
its use in vibration is illustrated in this chapter. The response under Coulomb and hysteretic damping is also con-
sidered. The undamped and damped responses of single-degree-of-freedom systems to harmonic excitations are
considered in Chapter 3. The concepts of force and displacement transmissibilities and their application in practical
systems are outlined. The transfer function approach, the Laplace transform solution of forced vibration problems,
the frequency response, and Bode diagram are presented.
Chapter 4 is concerned with the response of a single-degree-of-freedom system under general forcing func-
tion. The roles of Fourier series expansion of a periodic function, convolution integral, Laplace transform, and
numerical methods are outlined with illustrative examples. The specification of the response of an underdamped
system in terms of peak time, rise time, and settling time is also discussed. 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. The transfer function approach and the Laplace transform solution of undamped and damped systems
are also presented with illustrative examples. 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 in this chapter. Several methods of determining the natural
frequencies and mode shapes of discrete systems are outlined in Chapter 7. The methods of Dunkerley, Rayleigh,
Holzer, Jacobi, and matrix iteration are discussed with numerical examples.
While the equations of motion of discrete systems are in the form of ordinary differential equations, those of
continuous or distributed systems are in the form of partial differential equations. The vibration analysis of continu-
ous systems, including strings, bars, shafts, beams, and membranes is given in Chapter 8. The method of separation
of variables is presented for the solution of the partial differential equations associated with continuous systems.
The Rayleigh and Rayleigh-Ritz methods of finding the approximate natural frequencies are also described with
examples. Chapter 9 discusses the various aspects of vibration control, including the problems of elimination,
isolation, and absorption. The vibration nomograph and vibration criteria which indicate the acceptable levels of
vibration are also presented. The balancing of rotating and reciprocating machines and the whirling of shafts are
considered. The active control techniques are also outlined for controlling the response of vibrating systems. The
experimental methods used for vibration response measurement are considered in Chapter 10. The hardware used
for vibration measurements and signal analysis techniques are described. The machine condition monitoring and
diagnosis techniques are also presented.
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 dis-
cussed and illustrated. Finite element analysis, with applications involving one-dimensional elements, is discussed
in Chapter 12. Bar, rod, and beam elements are used for the static and dynamic analysis of trusses, rods under
torsion, and beams. The use of consistent and lumped mass matrices in the vibration analysis is also discussed in