Elastic Wave Propagation in a Semi-Infinite Solid Medium

Abstract

Plane waves possessing complex angles of propagation play an important role in the theory of elastic wave radiation. A simple physical picture is given of these waves and their utility illustrated by employing them in the study of continuous sinusoidal wave propagation in the neighborhood of an unstressed, plane boundary in a semi-infinite, homogeneous, and isotropic solid medium. The Rayleigh wave and the von Schmidt, or Head wave are particular features of the study. A simpler solution than Sauter's [Z. angew Math. Mech. (1950)] has been found for the displacement field radiated by an impulsive force acting at a line in the surface. By reciprocity this gives the surface displacement due to an internal line force. An equivalent problem is provided by an impulsive force acting at the edge and in the plane of a semi-infinite thin sheet, provided that the bulk dilatation wave velocity is replaced by the thin sheet dilatation wave velocity. This has been simulated experimentally by detonating small explosive charges at the edge of an aluminum sheet, 0.5 mm thick. Displacements detected by a novel condenser microphone technique are in excellent agreement with those determined theoretically.