Global Dynamics of a Parametrically and Externally Excited Thin Plate |
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Authors: | Zhang Wei Liu Zhaomiao Yu Pei |
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Institution: | (1) College of Mechanical Engineering, Beijing Polytechnic University, Beijing, 100022, P. R. China;(2) Department of Applied Mathematics, The University of Western Ontario, Ontario, Canada, N6A 5B7 |
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Abstract: | Both the local and global bifurcations of a parametrically andexternally excited simply supported rectangular thin plate are analyzed.The formulas of the thin plate are derived from the vonKármán equation and Galerkin's method. The method ofmultiple scales is used to find the averaged equations. The numericalsimulation of local bifurcation is given. The theory of normal form,based on the averaged equations, is used to obtain the explicitexpressions of normal form associated with a double zero and a pair ofpurely imaginary eigenvalues from the Maple program. On the basis of thenormal form, global bifurcation analysis of a parametrically andexternally excited rectangular thin plate is given by the globalperturbation method developed by Kovacic and Wiggins. The chaotic motionof the thin plate is found by numerical simulation. |
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Keywords: | rectangular thin plate local and global bifurcations normal form chaos |
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