大挠度板混沌运动的双模态分析

树学锋; 韩强; 杨桂通

大挠度板混沌运动的双模态分析

太原工业大学应用力学研究所, 太原 030024

基金项目: 国家自然科学基金资助课题(19672038);山西省自然科学基金资助课题(981006)

详细信息

作者简介:
树学锋(1964~ ),男,副教授,博士.

中图分类号: O34
计量
- 文章访问数: 2010
- HTML全文浏览量: 126
- PDF下载量: 568
- 被引次数: 0
出版历程
- 收稿日期: 1998-01-06
- 修回日期: 1998-09-15
- 刊出日期: 1999-04-15

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

Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P R China

摘要

摘要: 研究了大挠度矩形薄板受迫振动时的混沌运动,导出了矩形薄板的非线性控制方程;利用Galerkin原理,将其化为二自由度的常微分方程组,从理论上证明了在讨论其混沌运动时可以归结为一个单模态问题;利用Melnikov函数法给出了发生混沌运动的临界条件,揭示出在此类新的非线性动力系统中,同样存在着发生混沌的可能.
- 屈曲板 /
- 混沌 /
- Poincaré映射
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.
- buckled plate /
- chaos /
- Poincaré section

HTML全文

参考文献(12)

[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.