Abstract
In this paper, the distributed transfer function formulation is used to investigate the dynamic characteristics of a rotating stepped beam. The Rayleigh beam model with general boundary conditions is considered. Exact closed-form solutions are obtained for the free and forced responses. Results for the natural frequencies and mode shapes of the stepped beam are presented. For the purpose of illustration, three sets of boundary conditions are considered: simply-simply supported, clamped-clamped, and clamped-simply supported. Effects of system parameters such as the length ratio and diameter ratio of the beam on the free and forced responses are examined and discussed. It is shown that for different combinations of boundary conditions, the pair of natural frequencies for the forward and backward precession modes are associated with different mode shapes except for the simply-simply supported beam. Moreover, the difference between the forward and backward mode shapes increases with the rotation speed of the beam.
