Propagation of Impact-Induced Longitudinal Waves in Mechanical Systems With Variable Kinematic Structure

Abstract

In previous publications by the authors of this paper it was shown that elastic media become dispersive as the result of the coupling between the finite rotation and the elastic deformation. Impact-induced harmonic waves no longer travel, in a rotating rod, with the same phase velocity and consequently the group velocity becomes dependent on the wave number. In this investigation, the propagation of impact-induced longitudinal waves in mechanical systems with variable kinematic structure is examined. The configuration of the mechanical system is identified using two different sets of modes. The first set describes the system configuration before the change in the system topology, while the second set describes the configuration of the system after the topology changes. In the analysis presented in this investigation, it is assumed that collision between the system components occurs first, followed by a change in the system topology. Both events are assumed to occur in a very short-lived interval of time such that the system configuration does not appreciably change. By using the first set of modes, the jump discontinuity in the system velocities is predicted using the algebraic generalized impulse momentum equations. The propagation of the impact-induced wave motion after the change in the system topology is described using the Fourier method. The series solution obtained is used to examine the effect of the topology change on the propagation of longitudinal elastic waves in constrained mechanical systems. It is shown that, while, for a nonrotating rod, mass capture or mass release has no effect on the phase and group velocities, in rotating rods the phase and group velocities depend on the change in the system topology. In particular the phase velocities of low harmonic longitudinal waves are more affected by the change in the system topology as compared to high frequency harmonic waves.