Dynamical analysis of axially moving plate by finite difference method |
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Authors: | Xiao-Dong Yang Wei Zhang Li-Qun Chen Ming-Hui Yao |
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Institution: | (1) College of Naval Architecture and Power, Naval University of Engineering, Wuhan, 430033, People’s Republic of China |
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Abstract: | The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially
moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion
of the plate is derived by Newton’s second law. The finite difference method in spatial field is applied to the differential
equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal
field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear
forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation
amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion,
and then the periodic motion becomes chaotic motion by period-doubling bifurcation. |
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Keywords: | |
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