DYNAMIC STABILITY OF SPINNING TIMOSHENKO SHAFTS WITH A TIME-DEPENDENTSPIN RATE

The equations of motion of a spinning Timoshenko shaft with time-depen dent spin rate are formulated using Hamilton's principle and the assum ed mode method. The deformations of the shaft are expressed in terms o f an inertial reference frame. The time-dependent spin rate is assumed to be a steady state average value superimposed by sinusoidal perturb ations. The resulting governing equations of motion involve periodic c oefficients, which are not in the form of standard Mathieu-Hill equati ons. The periodic functions are embedded in both the gyroscopic and st iffness coefficient matrices. By the use of the multiple scales method , the regions of instability due to parametric excitations are determi ned. Numerical results for a simply supported spinning shaft are prese nted. (C) 1997 Academic Press Limited.