Moving Oscillating Loads in 2D Anisotropic Elastic Medium: Plane Waves and Fundamental Solutions

The paper considers a concentrated point force moving with constant velocity and oscillating with constant frequency in an unbounded homogeneous anisotropic elastic 2D medium. Such problems come from the problems of a source that acts along the line in the corresponding three-dimensional anisotropic medium. Fundamental solutions for two-dimensional problems with moving oscillating sources lay the foundation for constructing solutions for more complicated problems and applying the boundary integral equation method. The properties of plane waves, their phase, slowness and ray or group velocity curves are determined in a moving coordinate system. The use of Fourier integral transform techniques and the properties of plane waves enables to obtain an explicit representation for elastodynamic Green's tensor for all types of the source motion as a sum of integrals over a finite interval. The quasistatic and dynamic components of the Green's tensor are obtained. The stationary phase method is employed to derive an asymptotic approximation of the far wave field. Simple formulae for the Poynting energy flux vectors for moving and stationary observers are also presented. It is noted that in far zones the wave fields are subdivided into separate cylindrical 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 motion and etc.