Transverse wave motion in mechanical systems with variable kinematic structure

In this investigation, the effect of the change in the system topology on the propagation of impact-induced transverse waves is examined. A simple system that consists of a rotating beam which is impacted transversely by a rigid mass is used to investigate numerically the effect of mass capture on the propagation of the transverse waves in constrained mechanical systems. The nonlinear equations of motion of the rotating beam that account for the geometric stiffening are first derived using the principle of virtual work in dynamics. The effect of the geometric stiffening on the dynamics of the beam is first examined in order to determine the conditions under which the linearization of the dynamic equations of the beam is valid. Using the results of this preliminary study, a simple model for the rotating beam is derived and used in the analysis of the impact-induced transverse waves.; The dispersive nature of the impact-induced transverse waves in mechanical systems with variable kinematic structure is also examined in this investigation. The effect of the mass capture on the phase and the group velocities of the dispersive transverse waves is demonstrated using a simple model that consists of a rotating beam impacted transversely by a rigid mass. The results obtained in this investigation indicate that the change in the system topology has more significant effects on the wave velocities of low frequency transverse waves as compared to high frequency waves. Furthermore, the change in these velocities is more significant in rotating beams as compared to nonrotating beams.