VIBRATION EIGENFREQUENCY ANALYSIS OF A SINGLE-LINK FLEXIBLE MANIPULATOR

Abstract We analyse the vibration eigenfrequencies of a flexible slewing beam with a payload attached at one end. A wave propagation method (WPM) is used. There are four types of waves which propagate along a beam—two dispersive waves travelling in opposite directions, and two evanescent waves near the endpoints. We add a fifth time-harmonic function corresponding to oscillation of the beam at the payload end. We show that the large frequencies are asymptotically identical to those for the clamped–free beam, independent of the payload. For small eigenfrequencies, we incorporate WPM with a perturbation iteration procedure, the results of which agree well with “exact” values which result from solving a transcendental equation cited elsewhere in the literature.