Impact of mounting with an overlap on vibration and stability of a rotating annular plate

In this paper, we investigate a thin annular plate, whose inner edge has a smaller radius before mounting onto a rigid shaft then the radius of the shaft itself. After mounting onto the shaft forcefully, the overlap appears on the plate where it touches the shaft. The plate spins together with the shaft at a constant angular speed. Two possible cases of supporting the outer edge of the plate have been examined—when the edge is clamped and when it is free. The paper presents the determined frequencies of small transversal vibration with respect to the size of the overlap and angular speed. When determining the frequencies, the Galerkin method has been used. Based on these data, plate stability was examined and the critical value of the angular speed was determined using the dynamic criterion. For the special case of a non-rotating plate, the critical value of the overlap at which the plate loses stability was determined. ity of a rotating plate with an overlap was also examined using nonlinear Karmanʹs equations analysis applying the Ljapunov–Schmidt method. The analytical solution of the linearised equations system was obtained using the standard procedure. After that, the bifurcation equation was obtained and signs of the bifurcation coefficients were determined. Consequently, we came to the conclusions regarding the bifurcation type. nclusions of the bifurcation type have been corroborated by numerical integration of the differential equations system and certain stability loss cases have been presented on drawings.