An investigation of acoustic propagation through porous rigid materials applying spatial Fourier transform and Johnson-Champoux-Allard model with angle dependent tortuosity

Theoretical, computational, and experimental investigations were conducted on the acoustical properties of the materials that comprises recycled polyurethane glass-beads set in a matrix of epoxy resin core to evaluate their suitability for the applications in construction and building industry, and in noisy environment. The spatial Fourier transform method which is based on determining the complex pressure distributions on two parallel surfaces and decomposing them into plane-wave components by using two-dimensional spatial Fourier transform so that this could be applied to separate the incident and reflected plane wave components. This will lead to determining the absorption and reflection coefficients, which are two important parameters to understand the capacity of the materials to store acoustical energy. The Johnson-Champoux-Allard model with a heuristic angle dependant tortuosity was used to predict effective density and bulk modulus of the material, which were used to calculate wave number and characteristic impedance. Consequently, they are used to determine absorption and reflection coefficient of the porous materials at oblique angles of incidence. Experiments were carried out on two recycled structure samples in a full anechoic chamber to measure their absorption coefficient. A porous matrix model was used with “pressure acoustics” and “solid mechanics” modules together to perform computational simulation using COMSOL Multiphysics software in order to compute the absorption and reflection coefficients of the material. A comparison of the results obtained from COMSOL simulations, measurements, and analytical solution was carried out. The results obtained from three theoretical, data and computational investigation are in a good agreement.