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vibration of mechanical systems pdf

In Chapter 3, the techniques to compute the response of an SDOF
system to a periodic excitation are presented via the Fourier series
expansion. Then it is shown how the response to an arbitrary excitation is obtained via the convolution integral and the unit impulse response. Last, the Laplace transform technique is presented. The concepts of transfer function, poles, zeros, and frequency response
function are also introduced.

In Chapter 4, mass matrix, stiffness matrix, damping matrix, and
forcing vector are defined. Then the method to compute the natural
frequencies and the mode shapes is provided. Next, free and forced
vibration of both undamped and damped two-degree-of-freedom systems are analyzed. Last, the techniques to design undamped and damped vibration absorbers are presented.

In Chapter 5, the computation of the natural frequencies and the  mode shapes of discrete multi-degree-of-freedom and continuous systems is illustrated. Then the orthogonality of the mode shapes is shown. The method of modal decomposition is presented for the computation of both free and forced responses. The following cases of continuous systems are considered:

transverse vibration of a string, longitudinal vibration of a bar, torsional vibration of a circular shaft,
and transverse vibration of a beam. Last, the finite element method is
introduced via examples of the longitudinal vibration of a bar and the
transverse vibration of a beam.