Finite element analysis of longitudinal impact waves in conical rods

In this paper, a finite element formulation for the impact-induced waves in a variable cross-section rod that collides with a rigid mass is provided. The rod has either fixed, free, or deformable support conditions. The analysis is based on St. Venant's contact theory. The effects of boundary conditions, mass ratios, and geometrical shape of the rod upon stress wave propagation, contact force, displacement, and velocity are thoroughly analyzed by illustrative examples. The proposed finite element formulation considers the rod and the struck mass as one system during the contact period to eliminate the discontinuity at the arrival of the impact wave to the contact end, which gives accurate results. Excellent agreement is found between the finite element results and analytical solution using the mode superposition method for the fixed support boundary condition. The results show that the presented formulation can be used to model many systems with variable cross-section rods that are subjected to longitudinal impact. For instance, it can be used as a basis for modeling nanostructures under impact loads, as benchmark templates for crack detection, and for validating approximate analytical solutions.