Shu Xuefeng, Han Qiang, Yang Guitong. The Double Mode Model of the Chaotic Motion for a Large Deflection Plate[J]. Applied Mathematics and Mechanics, 1999, 20(4): 346-350.
Citation: Shu Xuefeng, Han Qiang, Yang Guitong. The Double Mode Model of the Chaotic Motion for a Large Deflection Plate[J]. Applied Mathematics and Mechanics, 1999, 20(4): 346-350.

The Double Mode Model of the Chaotic Motion for a Large Deflection Plate

  • Received Date: 1998-01-06
  • Rev Recd Date: 1998-09-15
  • Publish Date: 1999-04-15
  • 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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  • [1]
    Baran D D.Mathematical models used in studying the chaotic vibration of buckled beams[J].Mechanics Research Communications,1994,21(2):189~196.
    [2]
    B Poddar,F C Moon,S Mukherjee.Chaotic motion of an elastic-piastic beam[J].J Appl Mech,1988,55(1):185~189.
    [3]
    Keragiozov V,Keoagiozova D.Chaotic phenomena in the dynamic buckling of elastic-plastic column under an impact[J].Nonlinear Dynamics,1995,13(7):1~16.
    [4]
    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.
    [5]
    Lee J Y,Symonds.Extended energy approach to chaotic elastic-plastic response to impulsive loading[J].Int J Mech Sci,1992,34(2):165~177.
    [6]
    Moon F C,Shaw S W.Chaotic vibration of a beam with nonlinear boundary conditions[J].Non~Linear Mech,1983,18(6):465~477.
    [7]
    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.
    [8]
    Lepik U.Vibration of elastic-plastic fully clamped beams and arches under impulsive loading[J].Int J Non-Linear Mech,1994,29(4):67~80.
    [9]
    戴德成.非线性振动[M].南京:东南大学出版社,1993.
    [10]
    Moon F C.Chaotic and Fractal Dynamics[M].New York:John Wiley & Sons,Inc,1992.
    [11]
    Thompson J M T,Stewart H B.Nonlinear Dynamics and Chaos,Geometrical Methods for Engineers and Scientists[M].New York:John Wiley & Sons,1986.
    [12]
    韩强,几类结构的动力屈曲、分叉与混沌问题研究[D]:[学位论文].太原:太原工业大学,1996.
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