Dynamics of rod under axial impact by a body

Abstract

A longitudinal elastic impact a body makes on a thin rod is considered. The results of theoretical, finite element and experimental approaches to the solution of the problem are compared. The theoretical approach takes into account both the propagation of longitudinal waves in the rod and the local deformation due to the Hertz model. This approach leads to a differential equation with a delayed argument. A three-dimensional dynamic problem is considered within the framework of finite-element approach, in which the wave propagation and local deformation are automatically taken into account. A benchmark of these two approaches showed a complete qualitative and satisfactory quantitative agreement of the results in the contact force and the impact time. In the experiment, only the impact time was determined. Comparison of the measured impact time with the theoretical and finite-element results was satisfactory. Due to the fact that the tested rod was relatively short, an approximate model with two degrees of freedom was also developed to calculate the impact time. The problem of excitation of transverse oscillations after the impactor rebound off the rod is solved. For parametric resonance, the motion has the character of beats at which the energy of longitudinal oscillation is transferred into the energy of transverse oscillation and vice versa. An estimate for the maximum possible amplitude of transverse oscillation is obtained. Refs 12. Figs 6. Table 1.