Wave Propagation in Porous Piezoelectric Media

A mathematical model is presented in this work that describes the behavior of porous piezoelectric materials subjected to mechanical load and electric field. The model combines Biot's theory of poroelasticity and the classical theory of piezoelectric material wherein it is assumed that piezoelectric coupling exists only with the solid phase of the porous medium. This model is used to analyze the stress and electric wave generated in bone and porous Lead-Zirconate-Titanate (PZT) due to high frequency pulse loading. The governing partial differential equations are solved in the frequency domain by transforming them into a polynomial eigenvalue structure. This approach permits an exact solution for elastic material properties. The material domain is assumed to be in the form of a layered medium where periodic boundary conditions are enforced in the longer direction. The frequency domain based formulation also helps in describing the frequency dependent material properties. The work presents analytical solutions for various essential and natural boundary conditions. The propagating nature of the elastic and electric wave in bone and porous PZT is investigated in detail. It is expected that this model will be instrumental in providing valuable insight into the mechanism of bone regeneration.