LOW-FREQUENCY APPROXIMATIONS FOR ACOUSTIC POROUS MATERIALS: LINEARISATION OF THE POROELASTIC EIGENVALUE PROBLEM

Abstract

Recently in acoustics, it was shown that a finite element discretisation of Biot’s dynamic equations — for poroelastic media — leads to a non-linear eigenvalue problem. This non-linearity comes from the complex dissipation mechanisms of the elastic and acoustic waves prevailing within the poroelastic material. These complex dissipation mechanisms are related to viscous and thermal effects. The main drawback of the non-linear eigenvalue problem is that it prevents the use of classical modal analysis techniques for efficient solution of the corresponding matrix system. Since the finite element method is mostly used at low-freuqencies, the objective of this paper is to derive low-frequency approximations on the viscous and thermal disssipation mechanisms that will be used to linearise the poroelastic eigenvalue problem. To achieve the linearisation, it will be shown that the first Lamé coefficient of the poroelastic medium can be considered frequency-independent for most acoustic porous materials.