Modal Analysis Of Circular Plates With A Free Edge And Three Simple Interior Supports

Abstract

The Green function for the free vibration of a circular plate with a free edge is determined by modal analysis and used to derive the characteristic equation and mode shapes for a circular plate with a free edge and interior, simple supports. The inclusion of the effect of elasticity at the support or a concentrated mass, rather than a point support, on the form of the characteristic equation is discussed. The method is investigated by determining the natural frequencies of a circular plate with a free edge and a central, elastic, simple support or a central, concentrated mass and results are compared with previously published values. The method is then applied to determining the natural frequencies and mode shapes of a circular plate with a free edge and three interior, simple supports on a circle concentric with the plate center. Natural frequencies for many values of the support radius are tabulated and the mode shapes for a particular case illustrated.