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

Abstract

A model has been developed for the response of a rigid-porous hard-backed medium containing an arbitrary number of layers to high amplitude sound. Nonlinearity is introduced by means of a velocity-dependent flow resistivity in Johnson's equivalent fluid model for the complex tortuosity of each layer. Numerical solution of the resulting system of algebraic equations allows prediction of the dependence of surface impedance and reflection coefficient on the incident pressure amplitude. Measurements have been made of the surface impedance of various triple layers, made from different diameters of spherical lead shot and double layers consisting of gravel with different mean particle size, subject to high-intensity continuous sound. Good agreement between the model predictions and data for these multiple-granular layers is demonstrated. Moreover it is shown both theoretically and experimentally that the layer configuration giving optimum performance at low sound intensities may not continue to do so as the incident sound level is increased and the response becomes increasingly nonlinear. It is shown also that the nonlinear behavior depends strongly on layering and that, in some cases, the behavior is changed simply by changing the top layer thickness.

Influence of Forchheimer's nonlinearity and transient effects on pulse propagation in air saturated rigid granular materials

“…Typical values of Forchheimer's nonlinearity parameter n are in the range {0, 10} s/m. 2,14 For materials with n ( 1 s/m (such as mineral wool or granular material with very small particles, e.g., sand), the three effects are comparable in strength only at high level of excitation. For instance, for n ¼ 0:1 s/m acoustic pulse amplitude predicted by Eq.…”

Nonlinear Biot waves in porous media with application to unconsolidated granular media

“…[10][11][12][13][14][15][16] As a consequence, in the present case, we neglect Forchheimer's nonlinearity, which has been shown to play a role in some air-saturated porous media at high acoustic levels in the context of a rigid solid frame ͑equivalent fluid approximation͒. 26 A way to consider nonlinear terms in the constitutive laws has been described by Biot 44 and Donskoy et al 45 and consists in introducing a nonlinear potential H defined by…”

“…24,22,25 Nonlinear effects have been investigated in this equivalent fluid model approximation in the case of intense sound waves. 26 For shorter wavelengths, becoming of the order of the bead diameter, scattering occurs and its modeling for such close scatterers is a hard task even if the geometry is well-known. 27 In water, owing to the lower acoustic energy dissipation than in air, several pioneering experiments have been carried out on the acoustic energy diffusion process and showed that most of the energy transports through water and that the associated waves are multiply scattered by the glass beads.…”

Nonlinear effects on tonal sound in lined ducts

“…Beginning in the United Kingdom in the 2000s, a shift in emphasis occurred from the fibrous materials previously studied to granular materials and porous metals. The theory was extended to include complex compressibility and boundary slip, 18,19 multilayer and double-porosity materials, 20,21 and time-domain solutions and pulse propagation. 22,23 Recent work on porous metals continues in China.…”