Abstract
In this paper we propose a new method to derive macroscopic equivalent properties of sound absorbing poroelastic material using the homogenization method. Assuming that the microscopic geometry of the poroelastic material is periodic, this method directly provides a macroscopic elastic tensor for the solid phase, an equivalent density and a bulk modulus for the fluid phase. In the derivation of the macroscopic properties, we perform multiphysics analysis of several phenomena arising in the sound absorption by the poroelastic material, namely, elastic motion of the solid phase, compressible viscous fluid flow in the fluid phase, temperature distribution in the fluid phase, and coupled effects between solid and fluid phases. The equivalent density is obtained by averaging the characteristic function of the fluid flow, and the equivalent bulk modulus is calculated by averaging the characteristic function of the temperature distribution. Several numerical models with simple microscopic geometries are employed to compare the macroscopic properties represented in the numerical solutions obtained using the proposed method with solutions obtained analytically. We demonstrate that the proposed method can provide solutions with sufficient accuracy and that the solutions converge to analytically obtained solutions as the value of the discretization parameter used in the numerical models is made smaller.
