Non-linear dynamics of a thin rotating disc with aerial forces

Abstract

Abstract

This article presents a non-linear model of a thin rotating disc with aerial interaction. The disc, having an annular geometry, is modelled as a von Karman plate with perfectly clamped inner boundary and free outer boundary. The aerial force in the transverse direction is assumed to be produced by two effects: first, the resistance to transverse motion of the disc, and second, the viscous drag of the fluid. Non-linear dynamic analysis without and with external forces has been carried out. Using perturbation analysis, the frequency-amplitude relation is first determined, and the wave mode instabilities are clearly brought out. It is shown that the ratio of the coefficients of the two aerial force terms decides the stable spin speed region. Next, the response of the disc to small constant point force is studied. The linear stability of the solutions close to a critical speed is studied using solution perturbation method.