Bifurcation analysis of an accelerating disc immersed in a bounded compressible medium near principal parametric resonance

Abstract

This paper investigates the effect of low frequency parametric excitations on the coupled dynamics of a spinning disc bounded in a compressible fluid filled enclosure. Specifically, the effect of principal parametric resonance due to disc accelerations is studied. The angular acceleration of the disc results in the governing equations being represented as nonlinearly coupled non-autonomous gyroscopic system. Investigations into the bifurcation behaviour is first studied using Floquet theory on the linearised equations; the stable and unstable regions of the trivial solution are obtained in the amplitude–frequency parameter space corresponding to the acceleration, for various damping configurations. A codimension-two bifurcation is observed when two control parameters are considered in the bifurcation analysis. The bifurcation behaviour subsequently investigated through direct numerical integration of the governing equations, reveals that the coupled system exhibits a two-period quasi periodic oscillation in the post bifurcation regime.