An application of the dynamic Betti-Rayleigh reciprocal theorem to moving-point loads in elastic media

Two problems connected with the transient motion of an elastic body acted upon by a moving-point force are solved by an application of the dynamic BettiRayleigh reciprocal theorem. This theorem, which is the analogue of Green's theorem for the scalar wave equation, permits the solution to be written as a single expression, irrespective of the value of the (constant) moving-force velocity v. In particular, the displacement field in an infinite elastic body, due to a transient-point body force moving in a straight line, is given in a simple form. Next the surface motion of an elastic halfspace acted upon by a transient pressure spot moving in a straight line is analyzed for a material for which Poisson's ratio is one-fourth. The normal displacement is expressed in a simple manner, but the tangential displacement is quite complicated and is not fully expressible in terms of elementary functions. Singularities of the displacement fields are identified and discussed.