Theory of Vibration with ApplicationsThis edition features a new chapter on computational methods that presents the basic principles on which most modern computer programs are developed. It introduces an example on rotor balancing and expands on the section on shock spectrum and isolation. 
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concise, well written, and most important, complete. The best book to study mechanical vibrations. However, previous solid knowledge in mathematics (modelling and analysis) might be compulsory, as the author assumed so and "jumped" over some concepts or modelling techniques.
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Contents
OSCILLATORY MOTION  5 
FREE VIBRATION  17 
HARMONICALLY EXCITED VIBRATION  51 
TRANSIENT VIBRATION  92 
SYSTEMS WITH TWO OR MORE DEGREES  130 
PROPERTIES OF VIBRATING SYSTEMS  171 
LAGRANGES EQUATION  207 
B COMPUTATIONAL METHODS  234 
MODESUMMATION PROCEDURES FOR CONTINUOUS  345 
CLASSICAL METHODS  371 
System  390 
RANDOM VIBRATIONS  419 
NONLINEAR VIBRATIONS  461 
APPENDICES  488 
ANSWERS TO SELECTED PROBLEMS  527 
541  
Common terms and phrases
acceleration amplitude assumed becomes boundary conditions calculation coefficients column constant coordinates curve damper deflection Determine the equation Determine the natural diagonal diagram differential equation disk displacement dynamic eigenvalues eigenvalues and eigenvectors eigenvectors equal equation of motion equilibrium position Example excitation Figure force Fourier Fourier series free vibration frequencies and mode function fundamental frequency harmonic motion inertia initial conditions iteration kinetic energy Lagrange's equation length linear load mass matrix mean square value method mode shapes moment of inertia natural frequencies nonlinear normal modes obtain orthogonal oscillation pendulum phase plane plot potential energy preceding equation Prob problem procedure ratio resonance rotation RungeKutta method shaft shown in Fig shows solution solved spectral density spring springmass system static stiffness matrix structure Substituting system of Fig system shown torque torsional system transform unbalance undamped uniform beam vector velocity virtual virtual displacement viscous damping zero