Predicting absorption characteristics of single-leaf permeable membrane absorbers using finite element method in a time domain

Abstract

Permeable membranes (PMs), which are air-permeable thin woven fabrics or non-woven fabrics, are attractive sound-absorbing materials used to control acoustics in buildings. Although the absorption characteristics of various PM absorbers have been studied extensively, it has not been established how to incorporate PMs into a wave-based acoustic simulation method known as the time-domain finite element method (TD-FEM). This paper presents a numerical model of limp PMs for TD-FEM as well as a computationally efficient TD-FEM for predicting sound fields including PMs. The limp PM model incorporates effects of both sound-induced vibration of PMs and the air permeability of PMs. Consequently, two material parameters are considered: the surface density and flow resistance of PMs. Verification of the limp PM model and efficiency evaluation of TD-FEM were first performed with an impedance tube problem. Then, reverberation absorption coefficients of single-leaf PM absorbers with a non-locally reacting rigid backed air cavity were predicted through simulation of a reverberation absorption coefficient measurement using the present TD-FEM at frequencies of 100 Hz to 2.5 kHz. The predicted results were compared with measured and theoretical values. To demonstrate the applicability of present TD-FEM, eight PMs, each with different flow resistance and surface density, were considered for comparison. Results revealed that the present TD-FEM with the limp PM model can predict the magnitude relation of absorption characteristics of single-leaf PM absorbers attributable to differences of material properties of PMs.