On the mechanisms of instability of a circular plate under a rotating spring-mass-dashpot system

The response of a stationary, undamped, asymmetric, classical, circular plate subjected to a rotating spring-mass-dashpot system is formulated in a co-ordinate system fixed to the plate. Use of an eigenfunction expansion reduces the equation of motion to a set of coupled Hill's equations. Techniques for analytical solution of the Hill's equations are illustrated on axisymmetric plates. It is found that a spring rotating at supercritical speed will parametrically excite the plate to single mode and combination resonances. A rotating mass will destabilize the plate above a speed greater than the critical speed at which the inertia force of the rotating mass exceeds the elastic restoring force of the plate. A viscous dashpot destabilizes the plate when it rotates at supercritical speed by negatively damping the backward-travelling wave components of the plate eigenmodes.