Calculation of Vibro-Impact Dynamics of Loosely Supported Rods

Abstract

Vibro-impact dynamics of a loosely-supported rod subject to harmonic and random forces are analyzed. A rod constrained by unilateral contact against springs at contact sites located at different positions is modeled. The beam equations of motion for the rod, with appropriate boundary conditions, are discretized in space by finite element method and in time. The contact forces are computed from the displacements. The model has been used to simulate one span of a rod fixed at one end and loose at the other end. Impact forces, and displacements are calculated as a function of time for different friction coefficients when the rod at one end is subject to sinusoidal or random forces. Lissajous figures and phase plane maps for the system are plotted. Further, the wear rate of the rod is predicted. Some of the predictions are compared with experiments and the results are satisfactory.