Analysis of global dynamics in a parametrically excited thin plate |
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Authors: | Zhang Wei |
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Institution: | (1) College of Mechanical Engineering, Beijing Polytechnic University, 100022 Beijing, China |
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Abstract: | The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The
formulas of the thin plate are derived by von Karman type equation and Galerkin's approach. The method of multiple scales
is used to obtain the averaged equations. Based on the averaged equations, the theory of the normal form is used to give the
explicit expressions of the normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple program.
On the basis of the normal form, a global bifurcation analysis of the parametrically excited rectangular thin plate is given
by the global perturbation method developed by Kovacic and Wiggins. The chaotic motion of thin plate is also found by numerical
simulation.
The project supported by the National Natural Science Foundation of China (10072004) and by the Natural Science Foundation
of Beijing (3992004) |
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Keywords: | rectangular thin plate global bifurcations normal form chaos |
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