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Scattering of acoustoelectric waves on a cylindrical inhomogeneity in the transversely isotropic piezoelectric medium

The scattering of acoustoelectric waves on a continuous cylindrical fiber embedded in a piezoelectric medium of hexagonal (transversely isotropic) symmetry is considered. It is assumed that both the matrix and the fiber has hexagonal symmetry with different material characteristics but with the same axis of symmetry which coincides with the cylinder axis of the fiber. Expressions for scattering amplitudes of the acoustoelectric waves follow from a system of integral equations for the electroelastic fields in the medium containing an inhomogeneity. This system is obtained in terms of Green's function of the coupled dynamic electroelastic problem. Explicit expressions are obtained for the components of the Green's function and scattering amplitudes for the quasiplane dynamic problem in the transversely isotropic piezoelectric medium. General formulae are derived for the total scattering cross-section of acoustoelectric waves propagating in the direction normal to the fiber axis. Finally, explicit expressions are obtained for the scattering amplitudes and scattering cross-sections of three acoustoelectric waves in the long wave limit. The results may be useful for future applications to various acoustoelectric inhomogeneity problems in piezoelectric media with hexagonal symmetry.