Heavy structures (such as machine-tool bases) are sometimes filled with granular materials (such as sand, gravel, or lead shot) to increase their damping. Traditionally, relatively dense granular fills have been selected for such applications in order to obtain strong coupling between the structure and the granular material. But recent experiments indicate that a low-density granular fill can provide high damping of structural vibration if the speed of sound in the fill is sufficiently low. We describe a set of experiments in which aluminum beams are filled with a granular material whose total mass is three per cent of that of the unfilled beam and damping coefficients as high as 0.04 are obtained. The experiments indicate that the damping at high frequencies is essentially a linear phenomenon. We present a simple model that qualitatively explains the essentially linear high-frequency damping observed in the experiments.

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Significant damping can be introduced to a closed structure by filling the structure with a moderately lossy, low-wave-speed medium, such as a foam or a low-density powder. In this paper, we study the damping in long, thin-walled, cylindrical tubes filled with a low-density powder. Experimental results show that significant damping can be attained in tube bending (n=1) modes as well as shell bending (n=2 and higher) modes. To predict the damping in such systems, we develop a model based on three-dimensional shell equations including shear deformation and in-plane inertia, and treat the powder as a compressible fluid with a complex speed of sound. By studying the spatial decay of steady harmonic motion in an infinitely long tube, we obtain estimates for the loss factor of vibration for various numbers of circumferential nodes as a function of driving frequency.

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