Unified Analysis with Mixed Finite Element Formulation for Acoustic-Porous-Structure Multiphysics System

Abstract

This research aims to develop a novel unified analysis method for an acoustic-porous-structure multiphysics interaction system when the porous medium is modeled by the empirical Delany–Bazley formulation. Multiphysics analysis of acoustic structure interaction is commonly performed by solving the linear elasticity and Helmholtz equations separately and enforcing a mutual coupling boundary condition. If the pressure attenuation from a porous material is additionally considered, the multiphysics analysis becomes highly intricate, because three different media (acoustic, porous, and elastic structures) with different governing equations and interaction boundary conditions should be properly formulated. To overcome this difficulty, this paper proposes the application of a novel mixed formulation to consider the mutual coupling effects among the acoustic, fibrous (porous), and elastic structure media. By combining the mixed finite element formulation with the Delany–Bazley formulation, a multiphysics simulation of sound propagation considering the coupling effects among the three media can be easily conducted. To show the validity of the present unified approach, several benchmark problems are considered.