Solution of impact-induced flexural waves in a circular ring by the method of characteristics

Abstract

A study of elastic wave propagation in a curved beam (circular ring) is presented. The governing equations of motion are formulated in two forms based on Timoshenko beam theory. Solutions are obtained using the method of characteristics, whereby a numerical scheme employing higher-order interpolation is proposed for the finite difference equations. Results obtained are verified by experiments; it is found that use of the higher-order numerical scheme improves correlation with experimental results. Comparison of the relative accuracy between the two mathematical formulations - one in terms of generalized forces and velocities and the other in terms of generalized displacements - shows the former to be mathematically simpler and to yield more accurate results.