Elastic wave propagation in a porous composite with gradient porosity

Wave propagation in gradient porous composite exhibits more complex dynamic behavior than its propagation in non-gradient porous composite due to the spatial variation of mechanical properties. There is a lack of adequate theoretical model that can be used to provide efficient and accurate analyses of the wave propagation in a gradient porous composite. To address this issue, this paper develops a novel analytical technique to study the propagation of one-dimensional elastic wave with relatively low frequency components in a gradient porous composite. The governing wave equation considering the scattering effect caused by cavities is employed to describe the wave propagation in a porous composite. In order to consider the porosity gradient of the composite, a segmented model is constructed to formulate the wave propagation in porous composite by combining the reverberation matrix method and stress wave solution with considering the wave scattering in Rayleigh scattering region. Meso-scale finite element simulations are conducted to validate the proposed method and investigate the effect of the randomness of cavity's spatial distribution. The valid conditions of wavelength and porosity for the present method are determined by quantitative comparison and qualitative analysis, which provides a better understanding about the basis of macroscopic wave propagation. Finally, a parametric analysis is carried out to investigate the effects of porosity gradient on the wave propagation behavior.