Dynamic modeling and analysis of discontinuous wave propagation in a rod

The wave propagation in an impacting rod is instant and nearly discontinuous, which remains a challenging problem for both dynamic modeling and experimental test. This paper presents an Enriched Finite Element Method (Enriched FEM) with controllable dispersion error to accurately and efficiently model the discontinuous wave propagation. The Enriched FEM approximates the displacement solutions based on a linear interpolation enriched with a series of harmonic functions. The paper focuses on the dispersion error of the enriched finite element from spatial-temporal discretization and the sampling theorem of the enriched finite element with different cutoff numbers, and then gives a simple quantitative criterion on the interdependent relationship between the size of mesh and time step so as to reduce the numerical dispersion error. In addition, the paper presents the experimental study on the wave propagation of an elastic rod colliding with a rigid wall. The experimental results explicitly show the incidence and reflection of the stress wave in the rod in the contact duration. They also indicate that the amplitude of the strain almost does not decay with the wave propagation along the rod. The numerical results based on the Hertzian contact model are in good agreement with the experimental observations, especially at wave interfaces.