Transient Acoustic Wave Propagation in Non-Integer-Dimensional Rigid Porous Media

Abstract

This study concerns the ultrasonic wave propagation in fractional dimensional rigid porous media. A Biot equivalent fluid model with a non-integer dimensional space is developed using the Stillinger-Palmer-Staravinou formalism. A generalized lossy wave equation is derived and solved analytically in time domain. The coefficients of the propagation equation are constant and depend only on the fractional dimension and the acoustical parameters of the porous material. As in the integer dimension case, the obtained propagation equation contains fractional derivative terms that describe viscous and thermal interactions between the solid and the fluid. The dynamic response of the material is obtained using the Laplace transform method.