Effect of mass capture on the propogation of transverse waves in rotating beams

Abstract

The dispersive nature of the impact-induced transvers waves in mechanical systems with variable kinematic structure is examined in this investigation. The non-linear equations of motion of the rotatinf 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 impact0induced transverse waves. The jump discontinuity in the system velocities as the result of impact is predicted using the generalized impulse momentum equations that involove 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 rotatinf 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 non-rotating beams. A dimensionless rotation wave number is defined and is used to measure the significance of the effect of the angular velocity on the velocity of wave propagation.