Interaction of Finite-Amplitude Sound with Air-Filled Porous Materials

摘要

This investigation studied the propagation of high intensity sound waves through an air-filled porous material. The material is assumed to be rigid, incompressible, and homogeneous; and (2) adequately described by two properties: resistivity r and porosity Omega. The resistivity was measured as a function of velocity for static flows and found to follow the empirical relation r=r sub 1 + r sub 2 u(sgn(u). This relation is assumed to apply for acoustic signals as well. Ordinary hydrodynamic nonlinearity (which leads to shock formation) is neglected. The resulting wave equation is still nonlinear, however, because of the u sgn(u) term in the resistivity. The equation is solved in the frequency domain as an infinite set of coupled inhomogeneous Helmhholtz equations, one for each harmonic. An approximate first integral formulation of these equations gives relations for progressive waves. The source wave considered is a slightly distorted intense tone, that is, a finite- amplitude fundamental accompanied by weak higher harmonics. An approximate but analytical solution leads to predictions of excess attenuation, saturation, and phase speed reduction for the fundamental component. A more general numerical solution is used to calculate the propagation curves for the higher harmonics. The u sgn(u) nonlinearity produces a cubic distortion pattern; when the input signal is a pure tone, only odd harmonic distortion products are generated. Quantitative experiments were performed on batted Kevlar 29 having porosities in the range Omega = 0.94 to 0.98. An ad hoc model is presented to illustrate the gross nonlinear effects on absorption.