Evaluation of weveguide modal approximation applied to acoustic absorption analysis of poroelastic materials

Abstract

In order to analyze and design insulation systems, numerical methods, such as the finite element method and the boundary element method, are intensively used. In particular, for poroelastic materials models based on the Biot-Allard theory, mathematical relations in a mixed formulation were developed using the structural displacement u and the fluid pressure p as state variables. In this work, the simulation of the absorbing performance of poroelastic samples, as if placed in impedance tube, is carried out using coupled poroelastic and acoustic finite element models. The goal is to evaluate two methodologies in order to obtain the acoustic absorption response of foam materials found on typical insulating systems. For the first procedure, the porous material model is coupled to a waveguide using a modal expansion technique. For the second procedure, the full acoustic domain is solved using acoustic finite elements and the acoustic absorption function is determined by evaluation of the acoustic pressure field. A systematic comparison of the influence of waveguide modes on the absorption response in the frequency domain was made and the validity of the modal approximation in coupled acoustic-poroelastic analysis is discussed.