Analysis of Free Vibration of Annular Plate of Variable Thickness by Use of a Spline Technique Method

Abstract

The free vibration of an annular plate of radially varying thickness is analyzed by use of a spline technique method. For this purpose, with the plate divided into small ring-shaped elements, the transverse deflection of each element is expressed by a quintic spline function with unknown coefficients. These coefficients are determined and also a frequency equation of motion of the plate at each dividing circle and also satisfies the boundary conditions at both edges. The method is applied to annular plates with linearly, parabolically and exponentially varying thickness ; the natural frequencies and the mode shapes of the plates are calculated numerically and the effects of the varying thickness on them are discussed.