Plane waves and Green's functions in piezoelectric space under moving oscillating sources

Abstract

The problems of harmonic concentrated point source motion with constant velocity in unbounded homogeneous piezoelectric (electroelastic) three-dimensional medium are considered. The properties of plane waves and their characteristic surfaces such as phase velocity, slowness and ray or group velocity are established in a moving coordinate system. The use of the principle of limiting absorption, Fourier integral transform techniques and the properties of plane waves was enabled to obtain an explicit representation for harmonic piezoelectric Green's tensor for all behaviors of the source motion as a sum of the integrals over the surface of a unit sphere. The quasistatic and dynamic components of the Green's tensor are also extracted. The multidimensional stationary phase method is employed to derive an asymptotic approximation at the far field. Simple formulae for the Poynting energy flux vectors for moving and stationary observers are also presented. It was noted that in far zone the wave fields are subdivided into separate spherical waves under kinematics and energy. It is shown that motion brings some difference in the far field properties, exemplified by the modification of the wave propagation zones and the change in their number, emergence of fast and slow waves under trans- and superseismic motions and etc. It is noted that, as in other problems with trans- and superseismic moving sources, the slow waves in the piezoelectric space transfer the negative energy, measured by moving observer.