Stability and vibration of shear deformable plates––first order and higher order analyses |
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| Institution: | 1. State Key Laboratory of Ocean Engineering, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;2. Department of Architecture and Civil Engineering, City University of Hong Kong, Kawloon, Hong Kong, China;1. School of Engineering, Indian Institute of Technology Mandi, Himachal Pradesh 175005, India;2. Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, W.B 721302, India;1. College of Information Technology, Shanghai Ocean University, Shanghai 201306, China;2. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong Special Administrative Region;3. School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China;4. City University of Hong Kong Shenzhen Research Institute Building, Shenzhen Hi-Tech Industrial Park, Nanshan District, Shenzhen, China |
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| Abstract: | This work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions. The Reissener–Mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of Reddy have been applied to the plate’s analysis. The governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy. The solution is obtained by the extended Kantorovich method. This approach is combined with the exact element method for the vibration and stability analysis of compressed members, which provides for the derivation of the exact dynamic stiffness matrix including the effect of in-plane and inertia forces. The large number of numerical examples demonstrates the applicability and versatility of the present method. The results obtained by both shear deformation theories are compared with those obtained by the classical thin plate’s theory and with published results. Many new results are given too. |
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