A Finite Difference Approach to Study the Impact of Boundary Conditions on the Acoustical Behavior of Particle Stacks

The responses of particle stacks to incident sound waves show interesting features that are very different from those of a homogeneous continuum. Further studies of the acoustical performance of particle stacks can help both to discover potential noise control applications of these types of materials, and to help provide better insight into the internal status of the particle stacks. In the current study, a finite difference (FD) model for a particle stack was built based on the Biot poro-elastic theory. The intention in developing this model is to describe the acoustical behavior of particle stacks with consideration of not only the finite stiffness of the particles, but also the influence of gravity and friction between the particles and the inner wall of their enclosure: i.e., the cylindrical sample holder of a standing wave tube, in this work. The derivation of governing equations and boundary conditions is introduced, together with acoustic measurement results of particles stacks consisting of micron-scale glass bubbles, including absorption coefficients and surface impedances that are compared with the theoretical predictions. The possible application scenarios of such materials, and potential developments that will further improve the FD model will also be discussed