Nonlinear wave propagation through rigid porous materials. II: Approximate analytical solutions

Abstract

A wave perturbation method of analyzing the internal propagation and surface admittance characteristic of highly porous acoustic materials with rigid frames at high particle velocities is presented. It is an iterative method whose implementation is based on experimental observations. Numerical results for an open-cell foam material are compared with both experiments and exact numerical solutions of the fundamental equations of nonlinear motion. Most of the salient features of the surface admittance of a bulk material are predicted analytically with the accuracy increasing as the frequency of excitation is increased. The method is restricted to pure-tone excitation. PACS numbers' 43.25.Ba, 43.25.Ed, 43.55.Ev

Numerical and analytical solutions for sound propagation and absorption in porous media at high sound pressure levels

“…Good agreements between the predictions and experiments were obtained for many types of air-saturated fibrous porous materials. 14 Further studies [15][16][17] showed that there are two flow regimes for air in rigid porous materials: at low velocities, the resistance coefficient increases with the square of the fluid velocity; at high velocities, the resistance coefficient increases linearly with the fluid velocity. It was suggested that similar regimes also exist in the mass coefficient.…”

“…11 The sound propagation and absorption properties of porous media under high sound pressure level conditions have been studied by a number of authors. [12][13][14][15][16][17][18][19][20] Zorumski and Parrott 12 introduced the concept of temporal impedance, which contains resistance and reactance, in their theoretical and experimental studies on the acoustic nonlinearity in rigid porous materials. The instantaneous resistance of rigid porous materials was found to be independent of the testing frequency and equal to the flow resistance of the materials, and the instantaneous reactance is a function of the acoustic fluid velocity.…”

Sound absorption of porous metals at high sound pressure levels

“…It is noted that the nonlinear thermal effect is insignificant in porous materials. Wilson and Lambert et al 5,7 also introduced a numerical as well as a wave perturbation method to solve sound propagation inside porous materials, especially attenuation and surface admittance at high intensities. With a different set of parameters, such as viscous and thermal characteristic lengths but still based on Forchheimer's correction to Darcy's law, Umnova et al 8 introduced another model to deal with high-intensity sound propagation through hard-backed rigid-porous layers.…”

Response of multiple rigid porous layers to high levels of continuous acoustic excitation

“…Particular attention has been paid to Forchheimer's nonlinearity, i.e., a linear variation of flow resistivity with flow velocity, [6][7][8] which is valid in the range of moderate flow velocities. Forchheimer's nonlinearity has been combined with the Johnson/Allard equivalent fluid model for rigid porous materials [9][10][11] in previous publications.…”