Effect of Mass Capture on the Propagation of Transverse Waves in Rotating Beams

摘要

The dispersive nature of the impact induced transverse waves in mechanicalsystems with variable kinematic structure is examined in this investigation. 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. In particular, the effect of the centrifugal geometric stiffening due to the distributed inertia of the beam is compared with the effect of the centrifugal geometric stiffening due to the inertia of a mass concentrated at the end of the beam. 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 jump discontinuity in the system velocities as the result of impact is predicted using the generalized impulse momentum equations that involve the restitution conditions. The effect of the mass capture on the phase and the group velocities of the dispersive transverse waves is demonstrated using the simple model that consists of a rotating beam impacted transversely by a rigid mass.