NONLINEAR-WAVE PROPAGATION THROUGH RIGID POROUS MATERIALS .1. NONLINEAR PARAMETRIZATION AND NUMERICAL-SOLUTIONS

It is well known that the flow resistance, as defined by Darcy's law, becomes a function of the fluid velocity when the fluid velocity becomes sufficiently large. For porous materials in air, there appears to be two separate nonlinear flow regimes: For low velocities, the resistance coefficient increases with the square of the fluid velocity; and, for high velocities, the resistance coefficient increases linearly with the magnitude of the fluid velocity. Similar regimes also exist for the mass coefficient; however, the mass coefficient is observed to decrease with increasing fluid velocity. (For pure-tone excitation, it is shown that these relationships then hold for the complex magnitude of the particle velocity.) In this paper, the two nonlinear flow regimes are parametrized for several porous materials. Nonlinear corrections are made to linear wave theory, and numerical solutions for pure tones are obtained that are then used to predict surface admittance and internal pressures of finite length sample. A simple surface pressure criterion is put fourth based upon the materials nonlinear parameters that gives an approximate maximum surface pressure that a porous material could be exposed to before nonlinear phenomena become important in describing the material's characteristics. © 1990, Acoustical Society of America. All rights reserved.