Prediction of acoustical behavior of granular material stacks as measured in a standing wave tube by using a Biot theory-based model

The acoustical behavior of granular materials, such as activated carbon and silica gel, has drawn attention in recent studies, due to their favorable properties such as good low frequency sound absorption. Like other more traditional porous materials, granular materials can also be tested in a standing wave tube for a convenient assessment of their acoustical properties. However, the behavior of granular materials stacked in a standing tube is more complex than that of traditional materials. For example, the response of lightweight glass bubbles reveals a clear dependence on the sound pressure level of the input signal. Also, when tested in standing wave tubes of different diameters, the same type of granular materials displays differences in their behavior. The apparent stiffness of granule pack is also related to the depth of the stack. In the present work, a model based on Biot theory is proposed, together with a consideration of the effect of the change of boundary conditions and the granule stack stiffness in different test configurations. The model is realized by using a finite difference method, and the simulation results are compared with measurements of different types of granular materials.