Vibration damping in cylindrical shells filled with low-density low-wave-speed media

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.