VIBRATION OF A ROTATING DISCONTINUOUS SHAFT BY THE DISTRIBUTED TRANSFER-FUNCTION METHOD

A systematic method is presented for analyzing the vibration of a rota ting, geometrically discontinuous shaft with general boundary conditio ns. Both the Rayleigh and Timoshenko beam models are considered in the analysis. Exact, closed form solutions for the free and forced respon ses are obtained by the distributed transfer function method and a gen eralized displacement formulation. Numerical results of the natural fr equencies, mode shapes and steady state response of a rotating, steppe d two-span shaft are presented. Effects of system parameters such as t he slenderness ratio and diameter ratio of the shaft on the free respo nse are examined and discussed. It is shown that, with different combi nations of boundary conditions, the forward and backward precision mod es have different shapes even for the simply-simply supported shaft. M oreover, the difference between the forward and backward mode shapes i ncreases with the rotation speed of the shaft.