Three-dimensional free vibration analysis of thick laminated annular sector plates using a hybrid method

An accurate and efficient solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of thick laminated annular sector plates is presented. Plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. In order to accurately model the variation of material properties across the thickness, the layerwise theory is used to approximate the displacement components in this direction. Then, employing the Hamilton’s principle together with the modal analysis, through-the-thickness and circumferential discretized form of the equations of motion and the related boundary conditions are obtained. Finally, the differential quadrature method (DQM) as an efficient and accurate numerical method is applied to discretize the resulting variable coefficients differential equations in the radial direction. The fast rate of convergence of the method is demonstrated and to show its high accuracy, comparison studies with the available results in the literature are made. Finally, some new results are prepared, which can be used as benchmark solutions for future works.