Effects of key parameters on energy distribution and kinetic characteristics in collision of bar and beam

Abstract

Elastic-collision problems are the foundations of all collision problems, and a bar and a beam can represent a typical and simple structure. However, the elastic collision of a bar and a beam is a complicated phenomenon. The purpose of this research is to clarify the relationship between the principal parameter and the kinetic characteristics that influence this complicated elastic collision phenomenon, and to explain these on the basis of an impact force waveform, the apparent coefficient of restitution, and energy distribution. We employed an analysis method in which the impact force assumes an exponential function for the basic equation of the one-dimensional elastic vibration corresponding to the longitudinal vibration of the bar and the lateral vibration of the beam, and in which the force satisfies the condition of continuity of the displacement. In the experiment, assuming flat-surface contact, we directly detected collision phenomenon electrically using PZT pasted onto the end surface of the collision bar. On the basis of this study, the key parameter in the above-mentioned collision phenomenon is clarified, and an energy distribution situation and the influence of each parameter can now be considered for arbitrary combinations of the bar and beam. Furthermore, it is assumed that there is a correlation among the energy state after collision between a bar and a beam, the restitution state and the sound generated when a beam and a bar collide. Therefore, it is important to analytically study the effect of key parameters on various energy states. Thus, as our principal result, the complicated motion of a system involving an intermittent collision phenomenon namely, an elastic bar and an elastic beam supported at both ends, was clarified theoretically and experimentally.