Experimental study and modeling of the level-dependent acoustical behavior of granular particle stacks

Abstract

Researchers have previously observed elastic modulus softening and increased damping when granular particle stacks are exposed to progressively increasing acoustical excitation levels. However, the level-dependent behavior of granular particle stacks is not well understood, and there are no comprehensive approaches to modeling those effects. Earlier, the authors measured the absorption coefficient of a stack of one type of granular activated carbon stack by using signals having different bandwidths and levels. In the present work, five more types of granular particle stacks were studied to validate and generalize the previous conclusions: i.e., both the modulus softening, and increased damping can be characterized by the total RMS fluid displacement at the sample surface. Therefore, a strain-dependent modulus and damping formula from the literature (based on cyclic loading tests on sand particles) was converted into a total RMS fluid displacement-dependent formula (based on acoustic measurements). In addition, a multi-layered model based on this displacement-dependent formula has been developed to iteratively update each layer’s modulus, damping, and total RMS fluid displacement to solve for the particle stack’s acoustic properties. This approach allows modeling of the particle stack’s acoustical behavior by using a single set of parameters, even for different level and bandwidth test signals.