Reverberation-ray analysis of moving or distributive loads on a non-uniform elastic bar

Abstract

The method of reverberation-ray matrix has been developed and successfully applied to analyze the wave propagation in a multibranched framed structure or in a layered medium. However, the formulation is confined to the case of external concentrated loads applied at the junctions. This paper aims to extend the formulation of reverberation-ray matrix to cases of continuously distributed loads and point moving loads. To this end, a non-uniform bar subjected to these new types of loads is considered for illustration. The difference lies largely in the exact solutions, which include the particular parts due to the loads considered in this paper. The compatibility between displacements in the dual coordinates for a single member is utilized to derive the phase relations. For several types of loadings, numerical results are given and compared with the exact solutions or those obtained by other available method. Exact agreement is observed, thereby validating the present approach. The commonly adopted method that transforms distributed load to equivalent nodal forces is also discussed.