Forchheimer-type nonlinearities for high-intensity propagation of pure tones in air-saturated porous media

Abstract

A linear rigid frame, cylindrical capillary theory of sound propagation in porous media is extended to include nonlinear effects of the Forchheimer type, by making a particle velocity-dependent correction to the complex density. This type of nonlinearity becomes important at incident sound-pressure levels above approximately 120 dB re: 20 μPa for highly porous fibrous materials. Data from three experiments on air-saturated porous media and foams, at levels up to 170 dB, are compared to the rigid frame theory with Forchheimer-type extension. One of the experiments measured a low-frequency approximation for the complex density directly; the others measured internal attenuation and surface admittance (inverse impedance). The generally good agreement found between predictions based on the Forchheimer-type nonlinear theory and each of the experiments suggests that this type of nonlinearity is the dominant one for propagation in many types of air-saturated fibrous porous media. Some interesting surface absorption characteristics are predicted at incident sound-pressure levels above 140 dB, especially at lower frequencies.