Acoustic properties study of porous materials with orthotropic symmetry and specific pore shapes - I. Analytical calculations

Artificially prepared porous materials are usually highly anisotropic, which could affect the performance of porous materials-based ultrasonic devices. In a previous work, the elastic moduli of the porous silicon skeleton have been evaluated by FEM simulations based on five typical pore shapes with orthotropic symmetry. To study on their acoustic properties, in this article, the compliance tensor Sps for orthotropic porous materials (OPMs) is derived instead of getting directly the stiffness tensor Cps, through the "Gedanken experiments" proposed by Biot, for its easier relation to the measurable elastic moduli of skeleton. Cps for orthotropic porous skeleton is consequently acquired by the inversion ofSps. Besides, the 3-D wave equations for OPMs are derived using Biot's theory and the Christoffel's equations. Four propagating wave modes are therefore obtained from their analytic solutions. Numerical and experimental results for porous silicon are used to validate the proposed methodology. A wave modes distinction method is proposed by using the derivative of the wave velocity with respect to the porosity. The results are compared with literature and good agreements have been observed.