Solution in time domain of ultrasonic propagation equation in a porous material

Fellah, Wave motion 2 This paper provides an analytical solution in time domain for the propagation of transient ultrasonic waves in a homogeneous isotropic porous material having a rigid frame. The coefficient of this propagation equation are constants and depend only of the acoustical parameters of the porous material. This propagation equation contains a fractional derivatives terms in order to describe the viscous and thermal interactions between the two phases of the porous medium. The dynamic response of the medium is obtained using the Laplace transform method. An experimental application to porous plastic foams is given to validate the solution of this propagation equation