Modifications and improvements to conventional state space differential quadrature method are proposed for free vibration analysis of thick, soft-core sandwich panels with arbitrary edge boundary conditions, using an exact two-dimensional elasticity model. The modifications are based on a systematic procedure to implement all possible combinations of edge boundary conditions including simply supported, clamped, free and guided edges. Natural frequencies and mode shapes are obtained and compared with exact elasticity solutions from state space method and approximate solution from finite element simulations; demonstrating the high numerical accuracy and rapid convergence of the modified method. Further, the proposed framework is compared to the conventional implementation of the state space differential quadrature method for thick cantilever sandwich panels and is shown to give results with better accuracy and faster convergence.
A novel procedure, within the framework of the state space method in linear elasticity, is proposed for three-dimensional analysis of simply supported, multi-layered plates including any number of arbitrary graded layers at arbitrary locations along the transverse coordinate. First, the conventional state space method used for single layer exponentially graded plates is extended to multi-layered plates including any number of exponentially graded layers. This is achieved by incorporating additional matrices for implementing continuity of the state variables at interfaces involving at least one exponentially graded layer. Further, a piece-wise exponential model is used to extend the procedure to plates that include any number of layers whose material properties vary as arbitrary smooth functions along the transverse coordinate. Comparisons with existing elasticity and approximate solutions show that the method is capable of providing numerical results with better accuracy for all the cases studied. New results are obtained for three-dimensional deformation analysis of sandwich plates with graded face sheets and graded soft core, including a detailed parametric study.
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