Free Vibration of an Orthotropic Elliptical Plate with a Similar Hole

Abstract

This paper studies free vibration of an orthotropic elliptical plate with a similar hole at the center by means of the Ritz method using a spline function as an admissible function. For this purpose, the plate is transformed into an annular plate of unit outer radius, the transverse deflection of the plate is written in a series of the products of deflection function of a sectorial beam and trigonometric function of angular co-ordinate, and the frequency equation is derived by the Ritz method. The deflection of the sectorial beam is expressed approximately as a quintic spline polynomial, which satisfies the equation governing the flexural vibration of the beam at all the knots dividing it into small elements and also satisfies the boundary conditions at both ends. The present method is applied to orthotropic annular plates and elliptical plates with a similar hole at the center, the natural frequencies and the mode shapes being calculated numerically with high accuracies.