Vibration eigenfrequency analysis of a single-link flexible manipulator

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. (C) 1998 Academic Press Limited.