Comparison of finite element models for predicting sound absorption coefficients of infinitely periodical slit resonators

Abstract

Two finite element models have recently been utilized to predict the sound absorption coefficient of periodically arranged slit resonators. One is based on the linearized Navier–Stokes equation, entropy conservation law, and mass conservation law. The other is based on the Helmholtz equation with the visco-thermal boundary layer boundary condition. This paper clarifies a condition under which the latter model gives a reasonable approximation. A transition frequency is derived from Johnson–Allard’s effective density of porous media as a criterion. Calculation results demonstrate that the resonator’s resonance frequency must be higher than the transition frequency to obtain a reasonable prediction using the boundary condition model.