A poro-elastic model of sound propagation in granular materials

The dynamics of granular materials have been studied for many years, however, they have recently drawn attention for their unique response to acoustic excitation, and thus their potential applications in acoustics and noise and vibration control. For example, porous granules like zeolite and activated carbon have been applied to enhance the performance of loudspeakers at low frequencies. The reliable prediction of the acoustic behavior of these materials requires accurate characterization, which can be accomplished from a practical point -of -view by making standing wave tube measurements. But, to help with the interpretation of those types of measurements, in this article, the Biot poro-elastic theory is applied to describe the sound propagation in granules stacked in a cylindrical sample holder, as in a standing wave tube. The originality of the present work is the extension of the Biot model to accommodate materials like granular activated carbon (GAC) that are porous at multiple levels, and a finite difference (FD) implementation that incorporates the depth -dependent stiffness of the granular materials predicted by the Janssen's model and Hertzian contact theory. The model predictions are compared with measurements of GAC and light -weight glass bubble stacks, with the simulation results accurately matching the measured features of material absorption.