DSC-Ritz element method for vibration analysis of rectangular Mindlin plates with mixed edge supports |
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| Authors: | Y Xiang SK Lai L Zhou CW Lim |
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| Institution: | 1. School of Engineering, University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW 1797, Australia;2. Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, PR China;1. Wright State University, Dayton, OH, 45435, USA;2. Moscow Institute of Physics and Technology, Moscow, 141700, Russia;3. Institute for Problems in Mechanics, 119526, Russia;1. Department of Mechanical Engineering, SSTC,SSGI, Bhilai, C.G., India;2. Department of Mechanical Engineering, National Institute of Technology, Raipur, C.G., India;3. Department of Civil Engineering, National Institute of Technology, Raipur, C.G., India;1. National Research Tomsk Polytechnic University, Tomsk, Russian Federation;2. Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation;1. State Key Laboratory of Coastal and Offshore Engineering, Department of Civil Engineering, Dalian University of Technology, Dalian, China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China;3. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, USA |
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| Abstract: | Based on Mindlin's first-order shear deformable plate theory, a DSC-Ritz element method is developed for the free vibration analysis of moderately thick rectangular plates with mixed supporting edges. The rationale of the present approach is not only to apply the discrete singular convolution (DSC) delta type wavelet kernel as a trial function with the Ritz method, but also to incorporate the method in finite elements in order to handle the mixed boundary constraints. The approach is novel and flexible as it passes through a bottleneck of the global DSC-Ritz method in treating the kinematic supporting edges with assorted discontinuities. A series of numerical simulations for rectangular Mindlin plates with various edge support discontinuities, plate thicknesses and aspect ratios are presented. For verification, the vibration frequencies thus established are directly compared with those reported in the open literature. New sets of numerical results for several other cases of moderately thick plates with mixed simply supported, clamped and free edges are presented and discussed in detail. |
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