Fundamental Solutions in Plane Problem for Anisotropic Elastic Medium Under Moving Oscillating Source

TL;DR

This paper derives explicit solutions for wave propagation in anisotropic elastic media with moving oscillating sources, analyzing wave fields, velocities, and energy flux, highlighting effects of source motion on wave behavior.

Contribution

It provides the first explicit Green's tensor representations for moving oscillating sources in anisotropic elastic media, including asymptotic far-field approximations.

Findings

Wave properties depend on source motion and anisotropy.

Far-field wave zones are modified by source velocity.

Distinct wave types emerge under different motion regimes.

Abstract

In present article we consider the problems of concentrated point force which is moving with constant velocity and oscillating with cyclic frequency in unbounded homogeneous anisotropic elastic two-dimensional medium. The properties of plane waves and their phase, slowness and ray or group velocity curves for 2D problem in moving coordinate system are described. By using the Fourier integral transform techniques and established the properties of the plane waves, the explicit representation of the elastodynamic Green's tensor is obtained for all types of source motion as a sum of the integrals over the finite interval. The dynamic components of the Green's tensor are extracted. The stationary phase method is applied to derive an asymptotic approximation of the far wave field. The simple formulae for Poynting energy flux vectors for moving and fixed observers are presented too. It is noted that in the far zones the cylindrical waves are separated under kinematics and energy. It is shown that the motion bring some differences in the far field properties. They are modification of the wave propagation zones and their number, fast and slow waves appearance under trans- and superseismic motion and so on.