The elastodynamic Liénard–Wiechert potentials and elastic fields of non-uniformly moving point and line forces

Abstract

The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and of line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Liénard–Wiechert potentials. The exact closed-form solutions of the displacement field and of the elastic fields produced by the point force and the line forces are calculated. The displacement fields can be identified with the elastodynamic Liénard–Wiechert tensor potentials. For a non-uniformly moving point force, we decompose the elastic fields into a radiation part and a non-radiation part. We show that the solution of a non-uniformly moving point force is the generalization of the Stokes solution towards the non-uniform motion. For line forces, the mathematical solutions are given in the form of time integrals and, therefore, their motion depends on the history.