Inverse characterization of the frequency-dependent acoustic and elastic parameters of porous materials by surface-normal impedance method.

Abstract

A method for characterizing the frequency-dependent acoustic and elastic parameters of porous materials is proposed and validated in the paper, based on the Biot theory. The parameters include the characteristic impedance, propagation coefficient (also denoted as complex wave number), and longitudinal modulus. The first two are the macroscopic acoustic properties of pore fluid, while the last one is the elastic property of frame. A system related to the three parameters is constructed through the normal surface impedance of three samples with different thickness, based on the transfer matrix theory. With the measured surface impedance and appropriate initial values, an iterative procedure based on the Newton-Raphson method is used to solve the system. The three parameters are identified simultaneously, and then validated by two experimental methods, respectively, i.e., a modified two cavity method for the acoustic parameters and a quasi-static mechanical method for the elastic parameter. The parameters identified from the proposed method are consistent with the results of the two methods except for the imaginary part of the longitudinal modulus. It is shown that the proposed method would have a better performance if the discrepancy of frame displacements among different samples is moderate, corresponding to a reasonable selection of the thickness.