Significant damping of structural vibration can be attained by coupling to the structure a low-density medium (such as a powder or foam) in which the speed of sound propagation is relatively low. We describe a set of experiments in which flexural vibration of aluminum beams over a broad frequency range is damped by introduction of a layer of lossy low-wave-speed foam. At frequencies high enough to set up standing waves through the thickness of the foam, loss factors as high as 0.05 can be obtained with a foam layer whose mass is 3.9% of that of the beam. In our prior studies [1,2], we modeled the foam as a continuum in which waves of dilatation and distortion can propagate and obtained approximate solutions for the frequency response of the system by means of a modal expansion. However, these modal expansion models are cumbersome for design and quick calculation. In this paper, we develop a simple approximation for the system loss factor based on the complex wavenumber associated with wave propagation, and find that the damping estimates are in close agreement with measured responses and those predicted by modal expansion methods and strain energy approximations. Finally, we extend this approach to longitudinal vibration in a bar coupled to foam and obtain estimates for the system loss factor.

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