An explicit formula for the coherent SH waves' attenuation coefficient in random porous materials with low porosities

In this paper, the attenuation coefficient of coherent SH waves in random porous material with uniformly randomly distributed elliptical cavities of different aspect ratios is studied. Based on an analysis of the mechanism for attenuation, a simple macro model for the attenuation coefficient is proposed. The macro model says that the attenuation coefficient can be expressed as a function of the mean scattering cross section and the number density of cavities at low porosities. Then, large-scale numerical simulations using the pre-corrected Fast Fourier Transform (pFFT) algorithm accelerated Boundary Element Method (BEM) are conducted to specify this macro model. Finally, this macro model is compared with four theoretical models derived for composite/porous materials with circular inclusions at the porosity p = 3.17% and 5%. Results show this macro model agree well with three of them. Compared to the existing theoretical models, the form of this macro model is simple and has a clear physical meaning. In addition, it is applicable to cases with relatively complex cavities.