Scattering of transverse surface waves by a piezoelectric fiber in a piezoelectric half-space with exponentially varying electromechanical properties

In the present work, an analytical solution is presented for the scattering of transverse surface waves by a homogeneous piezoelectric fiber contained in a functionally graded piezoelectric half-space with exponential variation. The boundary value problem of interest is solved by constructing an appropriate set of multipole functions which satisfy: (a) the electromechanical field equations in the half-space, (b) the boundary conditions along its free surface, and (c) the far-filed radiation conditions. It is shown that the simple poles of these functions are related to the roots of the pertinent dispersion relation. For the case of electrically short condition along the free surface of the inhomogeneous half-space, the analytical expressions for the scattered electromechanical fields are derived. In the given numerical examples, the effects of such parameters as the frequency, the distance of the fiber to the substrate's free surface, and the coefficient in the exponent, indicating the variation of the electromechanical properties of the substrate on the scattered fields are addressed in detail. It is seen that these physical parameters have considerable effect on the dynamic response of the medium.