Theoretical analysis of the effects of internal and boundary damping on the forced vibrations of a uniform bar is carried out using perturbation techniques. A first order correction to the poles of the response function is obtained and the dependence upon frequency noted. It turns out that the real part (damping factor) will in general vary with frequency and hence mode number. In the case of internal damping it varies as approximately n2 where n is the mode number. In the case of a low boundary damping parameter, the damping constant varies as n^ while for high boundary damping it has roughly an n4 dependence. These results virtually insure that the response functions (displacement, moment, strain) for random excitation obtained using a generalized Fourier analysis will converge for Brownian motion type excitation. Relationships showing the mode shape corrections for finite boundary impendances are obtained from the perturbation theory. Several experimental studies are suggested which would contribute to our understanding of these damping mechanisms and their relative importance in studies involving random excitation of bars and plates.
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