Transverse vibration and stability of an eccentric rotating circular plate

A thin circular plate rotating at constant angular speed around the axis perpendicular to the plane of the plate is investigated in this paper. The axis of rotation is parallel to the plate's axis of symmetry and the distance between them is the plate's eccentricity. The outer edge of the plate is attached to a rigid body rotating together with the plate. The stresses and displacements in the plate's middle plane are determined in the paper. The natural frequencies of the transverse vibration with respect to angular speed and eccentricity are determined using Galerkin's method. The mode shapes for the certain frequencies are shown. Due to the plate's eccentricity and rotation, the mode shapes are deformed in comparison with the plate without eccentricity. It is shown that frequencies split for the asymmetric mode shapes, so that there are two different frequencies in those cases. The critical angular speed which results in stability loss in the first mode is determined.