Free Vibration of Polar-Orthotropic Sector Plates Resting on Point Supports

Abstract

An accurate Ritz solution for the free vibration of point-supported annular sector plates of polar orthotropy is presented. A double power series function is used to represent deflection of the plate, with Lagrange multipliers to impose the constraint conditions. To establish accuracy of the approach, the frequency parameters of a sector plate with some supporting points distributed along the boundary are compared to those of a uniformly simply supported plate. The natural frequencies and mode shapes are presented for wide ranges of the opening angle, radius ratio, and orthotropic parameters.