Accurate natural frequencies of transversely isotropic moderately thick annular sector plates

Abstract

This article introduces an analytical method for free vibration analysis of transversely isotropic moderately thick annular sector plates. The plate has simply supported radial edges and arbitrary conditions along the circular edges. The displacement field of Mindlin's first-order shear deformation plate theory is considered and, based on this, the governing equations of motion are obtained. By using a function, which will be referred to as the boundary layer function, the three coupled governing equations of motion have been converted into two uncoupled equations. The general solutions of these equations contain integer and non-integer order Bessel and/or modified Bessel functions of the first and second kinds. By applying the boundary conditions at the inner and outer radii, an eigenvalue problem for finding the natural frequencies is obtained. The nine distinct cases considered involve all possible combinations of boundary conditions along the circular edges. An accurate non-dimensional frequency parameter is presented for a wide range of sector angles, some thickness—radius ratios and different inner-to-outer radius ratios. Three mode shapes of an annular sector plate with a sector angle of 60° are also presented. Finally, the effects of sector angle, thickness—radius ratio, boundary conditions, and inner-to-outer radius ratio on the frequency parameter are discussed.