Abstract
A theory for the non-linear acoustic behavior of porous materials with an elastic frame composed of incompressible grains or fibers has been derived. Johnson’s expression for complex flow resistivity [D. L. Johnson et al., J. Fluid. Mech. 176, 379–402 (1987)] has been combined with the dependence of dc flow resistivity on the amplitude of particle velocity (Forchheimer’s nonlinearity). The frame compressibility has been assumed to be linear. The system of coupled nonlinear equations for slow and fast planar compressional modes propagating in the material has been solved approximately by method of slow varying amplitudes. As a result of calculations the dependence of surface impedance on the amplitude of sound wave has been obtained for either fixed or moving surfaces. For all of the parameter values considered so far, it is predicted that the amplitude of the reflection coefficient increases with the incident sound intensity. This approach has been extended to allow for waves reflected from rigid backing of a layer of material. The influence of nonlinearity on the impedance of a sample of finite thickness has been estimated. [Work supported by USARSDG (UK), Contract No. R7D 8901-EN-01.]
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