Analytical method for the ultrasonic characterization of homogeneous rigid porous materials from transmitted and reflected coefficients

Abstract

A frequency domain method dedicated to the analytic recovery of the four relevant parameters of macroscopically homogeneous rigid frame porous materials, e.g., plastic foams, at the high frequency range of the Johnson-Champoux-Allard model is developed and presented. The reconstructions appeal to experimental data concerning time domain measurements of the ultrasonic fields reflected and transmitted by a plate of the material at normal incidence. The effective density and bulk modulus of the material are first reconstructed from the frequency domain reflection and transmission coefficients. From the latter, the porosity, tortuosity, and thermal and viscous characteristic lengths are recovered. In a sense, the method presented herein is quite similar in the ultrasonic range, but also quite complementary, to the method developed by Panneton and Olny [J. Acoust. Soc. Am. 119, 2027-2040 (2006); 123, 814-824 (2008)] at low frequency, which appeal to experimental data measured in an impedance tube.