Residual vibration response spectra for a servomotor-driven flexible beam

Abstract

In this paper residual vibration response spectra for a servomotor-driven flexible beam are discussed. The dynamic model consists of a flexible beam, which is modelled as a Euler-Bernoulli beam. The beam is rotated by a servomotor. The rotational trajectory is assumed to be a triangular velocity (bang-bang) trajectory. The equations governing the vibration of the rotating flexible beam are derived. For the solution, a summation of the orthogonal modes technique is used. Equations are solved numerically. Simulation results show that the maximum amplitude of the residual vibration changes with the change of the frequency ratio. Here the frequency ratio is defined as the first natural frequency of the flexible beam divided by the rotational frequency of the servomotor. When frequency ratios are even numbers like 2, 4, 6, etc., the maximum residual vibration amplitudes are minimized. When frequency ratios are odd numbers like 3, 5, 7, etc., then the maximum residual vibration amplitudes are maximized. The simulation results are also verified by experiment.