Application of transfer matrix method, Green's function, and variational technique to predict diffuse absorption with edge effect

Abstract

Acoustic calculations utilizing the Transfer Matrix Method (TMM) occasionally underestimate the sound absorption performance of multi-layered porous material when compared to experimentally obtained data. This is particularly true when experimental data pertains to reverberant (Diffuse-Sabine) absorption. When there is a large impedance mismatch between the reverberant wall and the porous specimen, experimental data indicates Absorption Coefficients greater than 1, which defies the law of conservation of energy. It is hypothesized that the extra absorption is due to the diffraction of waves occurring at the edge of the tested materials, thus increasing the area where energy is absorbed. This contradiction of the law of energy is often referred to as the “edge effect”. This study aims in creating a tool to predict and further understand the edge effect phenomena within reverberation and anechoic rooms and to determine the true absorption performance of the multi-layered porous material by using the TMM, Green’s function, and the variational technique. A plate-foam system is used as a test bed; computation results are compared to experimental absorption data. The outcome of the research will support automobile, aerospace, and architectural companies in reaching sound and vibration targets required for new vehicle/building models.

Model for Frequency Dependence of Thermal Permeability in Order to Quantify the Effects of Thermal Exchange on Wave Propagation in Multi Layered Porous Medium

“…The dl is a segment of the perimeter of the tube and Method with finite size correction via Green's functions techniques (FTMM) [16]. The parameters to this study are listed in Table 1 in [1].…”