A finite difference approach for predicting acoustic behavior of the poro-elastic particle stacks

Abstract

The physical properties of particle stacks have been of interest for a long time, and the acoustic properties of such materials have been actively investigated in recent times. Traditional acoustic theories, such as the Biot theory, can serve as a guide for determining the general properties of the stacks, but they do not allow the identification of the differences between the particle stacks and traditional acoustic materials, which are usually modeled as homogeneous continua. Recent research suggests that the Biot theory, combined with depth-dependent stiffness and equivalent density, can be used to model such materials. In this work, a finite difference (FD) scheme based on the Biot theory has been developed based on the idea that the apparent stiffness of the particle stack varies with depth within of the stack. This FD scheme is two-dimensional in cylindrical coordinates with an axisymmetric condition imposed at the axis of the cylinder. This approach is thus suitable for modeling common scenarios in which particle stacks are tested in a cylindrical standing wave tube. The results of several example cases are shown in this paper.