The impact of boundary conditions on the acoustical behavior of lightweight granular particle stacks

The acoustical behavior of air-saturated granular stacks can differ significantly from that of more traditional sound absorbing materials such as fibrous webs and foams when tested in a standing wave tube. The latter materials can often be modeled as equivalent fluids by using one-dimensional theory, with the further assumption that their behavior does not depend on the input signal level. In contrast, level dependence of the response of lightweight granular materials such as glass bubbles has been consistently observed in previous studies. At low input levels, the absorption coefficient of glass bubble stacks shows solid-like behavior with multiple peaks associated with radial modes of the solid phase of the edge-constrained stack: i.e., the response is two-dimensional. In contrast, at high input levels, glass bubble stacks show one-dimensional fluid-like behavior, with the quarter wave depth resonance dominating the response. It is hypothesized here that at high input levels the particles slip axially at the circumferential boundary, thus showing a one-dimensional response, while at low levels, the particles are constrained to have zero axial velocity, thus creating a two-dimensional response. It is shown here that a two-dimensional finite difference implementation of the poro-elastic Biot theory can accurately reproduce the observed level-dependent behavior.