A uniform formalism for acoustic wave propagation in a mixed liquid-solid-porous viscoelastic multilayered structure

Abstract

To deepen the understanding of the ultrasonic behaviour of human multi-layered bone tissues, cortical bone for example, the reflection and transmission of ultrasonic wave at such a structure consisting of a combination of liquid-solid-porous layers was studied. A mathematical model for the plane wave propagation in the layered media was developed using the stable stiffness matrix technique, and taking into account the boundary conditions at each type of interface. First, a recursive algorithm was developed to compute the global stiffness matrix of a multi-layered structure whose layers could be of any type of the classical media (liquid, isotropic solid, or isotropic poroelastic medium), based on the assumption that all layer interfaces are perfect which implies the continuity of displacement and stress. The multi-layered structure being merged into a single layer, the reflection and transmission coefficients were calculated considering that the whole structure is bounded by fluids. Then, a back-recursive algorithm was developed to compute the displacement vectors amplitudes in each layer, which allows the calculation of acoustic field in every layer based on the angular spectrum approach. As an application, the reflection and transmission coefficients as a function of incident angle and frequency were obtained for a five layers configuration bounded by fluid.