Dynamic stability of spinning Timoshenko shafts with a time-dependent spin rate

Abstract

The equations of motion of a spinning Timoshenko shaft with time-dependent spin rate are formulated using Hamilton's principle and the assumed mode method. The deformations of the shaft are expressed in terms of an inertial reference frame. The time-dependent spin rate is assumed to be a steady state average value superimposed by sinusoidal perturbations. The resulting governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The periodic functions are embedded in both the gyroscopic and stiffness coefficient matrices. By the use of the multiple scales method, the regions of instability due to parametric excitations are determined. Numerical results for a simply supported spinning shaft are presented. © 1997 Academic Press Limited.