THE PROPAGATION OF LONGITUDINAL ELASTIC WAVES AROUND RIGHT-ANGLED CORNERS IN RODS OF SQUARE CROSS-SECTION

Abstract

In the experiments reported below it was demonstrated that longitudinal elastic waves in rods of square cross-section are transmitted in part around right-angled corners. This behaviour, which would not be predicted on the basis of a filament approximation in which the effects of the cross-section dimensions were neglected completely, is analyzed theoretically on the assumption that the filament approximation is valid everywhere except in the vicinity of the corner. In this region (more precisely, the region comprising the cube of material which forms the corner), the material is assumed to behave as a rigid body. The resulting set of equations predict transmitted wave amplitudes of the correct sign, and of magnitude and shape in good agreement with the experimental observations.