Hamiltonian system-based new analytic free vibration solutions of cylindrical shell panels |
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| Institution: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, PR China;2. Mathematics Science College, Inner Mongolia Normal University, Hohhot 010022, PR China;1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, China;2. School of Chemical Machinery and Safety, Dalian University of Technology, Dalian 116024, China;3. Studienbereich Mechanik, Technische Universität Darmstadt, Darmstadt 64289, Germany;1. Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, PR China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Center for Computational Mechanics, Dalian University of Technology, Dalian 116023, PR China;1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, China;2. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China |
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| Abstract: | This paper deals with the classical challenging free vibration problems of non-Lévy-type cylindrical shell panels, i.e., those without two opposite edges simply supported, by a Hamiltonian system-based symplectic superposition method. The governing equations of a vibrating cylindrical panel are formulated within the Hamiltonian system framework such that the symplectic eigen problems are constructed, which yield analytic solutions of two types of fundamental problems. By the equivalence between the superposition of the fundamental problems and the original problem, new analytic frequency and mode shape solutions of the panels with four different combinations of boundary conditions are derived. Comprehensive benchmark results are tabulated and plotted, which are useful for validation of other numerical/approximate methods. The primary advantage of the developed approach that no pre-determination of solution forms is needed enables one to pursue more analytic solutions of intractable shell problems. |
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