Transverse buckling of a rotating Timoshenko beam

Abstract

This work considers a group of problems associated with rotating Timoshenko beams. The beam is not assumed to be hubclamped, i.e. the axis of rotation does not necessarily pass through the beam's clamped end. Cases of physical interest involving off-clamped beams include wobbling rotors, impellor blades, and turbine blades. For clamped-free boundary conditions, we seek solutions of the governing equations which correspond to transverse buckling. For the rotor, it is known that Euler-Bernoulli beams do not have buckled modes. By contrast, the Timoshenko beam will have an infinite number of buckled modes. In the impellor blade case, both Euler-Bernoulli and Timoshenko beams will have an infinite number of buckled modes. However, the Timoshenko beam will buckle at a lower eigenrotation speed. This is also true for the case of a rotating Timoshenko beam with clamped-clamped boundary conditions, e.g. a turbine blade clamped at both the rim and hub of a rotating platform. Analytic results for both the clamped-free and clamped-clamped cases are augmented by results obtained from numerical solution of the corresponding boundary value problems.