Dynamic Stability of Disks With Periodically Varying Spin Rates Subjected to Stationary In-Plane Edge Loads

Abstract

This paper presents an analysis of dynamic stability of an annular plate with a periodically varying spin rate subjected to a stationary in-plane edge load. The spin rate of the plate is characterized as the sum of a constant speed and a small, periodic perturbation. Due to this periodically varying spin rate, the plate may bring about parametric instability. In this work, the initial stress distributions caused by the periodically varying spin rate and the in-plane edge load are analyzed first. The finite element method is applied then to yield the discretized equations of motion. Finally, the method of multiple scales is adopted to determine the stability boundaries of the system. Numerical results show that combination resonances take place only between modes of the same nodal diameter if the stationary in-plane edge load is absent. However, there are additional combination resonances between modes of different nodal diameters if the stationary in-plane edge load is present.