Free Vibration of Circular Plate Elastically Supported at Some Points

Abstract

This paper studies the free vibration of a circular plate whose deflection, rotation and torsion are elastically supported at some points located inside the plate or on the circumference. Regarding the reactive forces and moments at all points as unknown harmonic exciting loads, the stationary response of the plate to these loads is derived. The natural frequencies and the mode shapes of the plate are calculated by determining the unknown quantities with use of constraint conditions at the supports. Applying the method to a circular plate supported at some equispaced points of equal radii, the natural frequencies and the mode shapes are calculated numerically. From the result of this study, it is concluded that the natural frequencies of the plate become larger with an increase in the stiffness and the number of supports, but they do not vary monotonously according to the location of the supports.