A modal reduction technique for the finite-element formulation of Biot’s poroelasticity equations in acoustics

Abstract

Recently, finite-element models based on displacement–displacement and pressure–displacement formulations of Biot’s poroelasticity equations have been extensively used to predict the acoustical and structural behavior of multilayer structures. These models, while accurate, lead to large frequency-dependent matrices for large finite-element models and spectral analyses problems necessitating important setup time, computer storage, and solution time. Lately, some authors have established criteria for low-frequency approximations of viscous and thermal effects that allow for a linearization of the poroelastic eigenvalue problem. Complex modes for the damped system or real modes for the undamped system can then be found and used to solve the forced problem. However, this method is not general since it requires assumptions on the porous material physical properties to meet these criteria. It is proposed in this talk to investigate another modal reduction technique. The technique, referred to as selective modal analysis uses a dual basis associated with the skeleton in vacuo and the equivalent fluid in the rigid skeleton limit, respectively. The theory behind the technique will be presented together with numerical examples illustrating its performance.