Vibration of a rotating discontinuous shaft by the distributed transfer function method

Abstract

A systematic method is presented for analyzing the vibration of a rotating, geometrically discontinuous shaft with general boundary conditions. Both the Rayleigh and Timoshenko beam models are considered in the analysis. Exact, closed form solutions for the free and forced responses are obtained by the distributed transfer function method and a generalized displacement formulation. Numerical results of the natural frequencies, mode shapes and steady state response of a rotating, stepped two-span shaft are presented. Effects of system parameters such as the slenderness ratio and diameter ratio of the shaft on the free response are examined and discussed. It is shown that, with different combinations of boundary conditions, the forward and backward precision modes have different shapes even for the simply-simply supported shaft. Moreover, the difference between the forward and backward mode shapes increases with the rotation speed of the shaft.