Analytical solutions of the impact problems of conical rod structures with a spring

Analytical solutions for the impact problems of conical rod structures with supporting spring are provided. The target rod and the impactor are considered as a integrated system during the vibration. The nondimensional variables are defined to simplify the mathematical model. The wave propagation and impacted end responses of the conical rod are analyzed with illustrative examples. The effects of mass parameter and inclination of the conical rod on the wave propagation are also discussed. The longitudinal impact solutions of conical rod structures linked with a spring are presented and the results are compared with the corresponding results of uniform rod structures.