REFLECTION AND TRANSMISSION OF THE ENERGY OF TRANSIENT ELASTIC EXTENSIONAL WAVES IN A BENT BAR

Abstract

Reflection and transmission of the energy of a transient elastic extensional wave at a sharp or smooth bend of a bar are studied theoretically and experimentally, with the principal aim being to validate the model used by Wu and Lundberg in a parallel study of harmonic elastic waves. In this model effects of rotary inertia and shear deformation are neglected, and in the straight sections before and after the bend the motion is assumed to be governed by the one-dimensional wave equation for extensional waves and the Euler –Bernoulli equation for flexural waves. Interest is focused on extensional waves mainly because there is a simple way to evaluate the energy of such waves from measurements of strains. Good agreement is obtained between experimental and theoretical results for energy transmission and reflection coefficients as well as for wave forms when (i) the incident wave is long relative to the transverse dimensions of the bar and (ii) the radius of curvature is either large relative to the transverse dimensions of the bar or small relative of the length of the incident wave.