Abstract
The primary aim of this paper is to study the chaotic motion of a large deflection plate. Considered here is a buckled plate, which is simply supported and subjected to a lateral harmonic excitation. At first, the partial differential equation governing the transverse vibration of the plate is derived. Then, by means of the Galerkin approach, the partial differential equation is simplified into a set of two ordinary differential equations. It is proved that the double mode model is identical with the single mode model. The Melnikov method is used to give the approximate excitation thresholds for the occurrence of the chaotic vibration. Finally numerical computation is carried out.
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Baran D D. Mathematical models used in studying the chaotic vibration of buckled beams [J].Mechanics Research Communications, 1994,21(2):189–196
Poddar B, Moon F C, Mukherjee S. Chaotic motion of an elastic-plastic beam [J].J Appl Mech, 1988,55(1): 185–189
Keragiozov V, Keoagiozova D. Chaotic phenomena in the dynamic buckling of elasticplastic column under an impact [J].Nonlinear Dynamics, 1995,13(7): 1–16
Holms P, Marsden J. A partial differential equation with infinitely many periodic orbits: chaotic oscillation of a forced beam [J].Arch Rat Mech Analysis, 1981,76(2): 135–165
Lee J Y, Symonds J Y. Extended energy approach to chaotic elastic-plastic response to impulsive loading [J].Int J Mech Sci, 1992,34(2): 165–177
Moon F C, Shaw S W. Chaotic vibration of a beam with nonlinear boundary conditions [J].Nonlinear Mech, 1983,18(6): 465–477
Symonds P S, Yu T X. Counterintuitive behavior in a problem of elastic-plastic beam dynamics [J].J Appl Mech, 1985,52(3): 517–522
Lepik U. Vibration of elastic-plastic fully clamped beams and arches under impulsive loading [J].Int J Nonlinear Mech, 1994,29(4): 67–80
Dai Decheng,Nonlinear Vibration [M]. Nanjing: Southeast University Press, 1993 (in Chinese)
Moon F C.Chaotic and Fractal Dynamics [M]. New York: John Wiley & Sons, Inc, 1992
Thompson J M T, Stewart H B.Nonlinear Dynamics and Chaos, Geometrical Methods for Engineers and Scientists [M]. New York: John Wiley & Sons, 1986
Han Qiang. The dynamic buckling, bifurcation and chaotic motion of several structures [D], Doctor's thesis. Taiyuan: Taiyuan University of Technology, 1996
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Project supported by the National Natural Science Foundation of China (19672038) and the Natural Science Foundation of Shanxi Province (981006)
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Xuefeng, S., Qiang, H. & Guitong, Y. The double mode model of the chaotic motion for a large deflection plate. Appl Math Mech 20, 360–364 (1999). https://doi.org/10.1007/BF02458561
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DOI: https://doi.org/10.1007/BF02458561