Transition radiation of elastic waves at the interface of two elastic half-planes

Abstract

Radiation of elastic waves is studied that is emitted by a point load that crosses the interface of two elastic half-planes. It is assumed that the load has a constant magnitude, moves along a straight line normal to the interface, and has a constant speed that is smaller than the minimum shear wave speed in the half-planes. In this case the mechanism of excitation of elastic waves is conventionally referred to as transition radiation. The adopted model allows to obtain an analytical expression for the elastic field excited by the load in the frequency–wavenumber domain. Using this expression, the energy of transition radiation is derived in a closed form. It is shown that transition radiation of the body waves occurs at any non-zero velocity of the load. Additionally, transition radiation of interface waves may occur provided that parameters of the half-planes allow existence of Stoneley waves. A parametric analysis of the directivity diagram of radiated body waves is accomplished focusing on dependence of the diagram on the load speed, load direction, and parameters of the half-planes. Using parameters that allow radiation of interface waves, the energy of this radiation is compared to that of the body waves. It is shown that the energy of the interface waves is greater unless the load velocity is close to the lowest body wave velocity.