Dynamic substructure analysis of stress waves generated by impacts on non-uniform rod structures

The dynamic substructure method (DSM) has high computational efficiency, and has been successfully applied in analyzing the modal responses of complex flexible bodies and in computing the dynamic responses of flexible bodies undergoing strong motion. However, the use of this method to analyze the propagation of stress waves generated by impacts has yet to be validated. The object of this paper is to propose a dynamic substructure computational procedure for the analysis of impact-induced stress waves in a non-uniform flexible structure. The procedure is established based on fixed-interface modal synthesis theory, finite element theory and a local contact model. The application of the procedure is demonstrated using composite rods subjected to longitudinal impacts. The governing equations during the contact and separation phases are solved by the Newmark-β method, and then the stress waveforms are obtained. In order to verify the accuracy of the procedure, the numerical solutions are compared with the analytical solutions obtained by method of characteristics. Furthermore, the 'succession collision' phenomenon resulting from the elastic wave effect is captured. All investigations showed that DSM was sufficiently accurate to analyze wave motion problems in complicated mechanical structures.