An energy method similar to Rayleigh’s method is employed to analyze a nonhomogeneous, damped beam composed of an elastic (metal) layer and an unconstrained viscoelastic layer. This analysis is limited to the case of thin free-free beams vibrating freely in the fundamental mode. The theory developed enables one to predict the damped natural frequency and the rate of decay (in terms of logarithmic decrement) of the transverse vibrations of a composite beam of given dimensions and composed of two particular materials. Experimental measurements bear out the fact that theoretical predictions are indeed accurate. Beams with two symmetric elastic coatings are also considered and their damping effects are compared to those of coating applied to one side only.

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