Abstract
This paper analyzes the nonlinear transverse vibrations of a clamped-free, uniform, flexible, annular disc, spinning about its axis with a constant angular velocity, and subjected to transverse loading from a pre-compressed spring. This is representative of a large class of loadings in rotating disc systems including air jet and electromagnetic excitation. Such loading can induce a simultaneous critical speed resonance and parametric instability. The disc is modelled by the Von Karman field equations, which are then discretized by a Galerkin projection onto a pair of 1-1 internally resonant modes. First order averaging is used to predict the dynamics of the forward and backward travelling waves (FTW and BTW). Equilibrium branches of the BTW amplitude and phase equations and their stability are studied for various combinations of parameters. The response is substantially different from that arising from a critical speed resonance or of a parametric instability alone. As many as five equilibrium solutions can coexist. Two distinct regimes of large amplitude response appear to exist depending on the relationship between the strength of the parametric excitation and the damping. The existence of these regimes underscores the subtle competition between critical speed resonance and parametric instability in such systems.
