非线性粘弹性柱的稳定性和混沌运动

陈立群; 程昌钧

非线性粘弹性柱的稳定性和混沌运动

陈立群^1,2,
程昌钧^1,2

1.
上海市应用数学和力学研究所, 上海200072;
2.
上海大学力学系, 上海201800

基金项目: 国家自然科学基金资助资助(19727027);中国博士后科学基金资助;上海科技发展基金资助(98JC14032;98SHB1417)

详细信息

作者简介:
陈立群(1963- ),上海市人,博士,教授;程昌钧(1937- ),女,重庆市人,教授,博导.研究方向:非线性固体力学,已发表论文100余篇;多次获得省部级以上各种奖励,1998年获教育部科技进步(甲类)一等奖.

中图分类号: O322
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- 文章访问数: 3141
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- 被引次数: 0
出版历程
- 收稿日期: 1999-06-25
- 修回日期: 2000-05-25
- 刊出日期: 2000-09-15

Stability and Chaotic Motion in Columns of Nonlinear Viscoelastic Material

CHEN Li-qun^1,2,
CHENG Chang-jun^1,2

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;
2.
Department of Mechanics, Shanghai Univesity, Shanghai 201800, P R China

摘要

摘要: 研究了受轴向周期力作用的各向同性简支柱的动力学稳定性。假定粘弹性材料满足Lea-derman非线性本构关系。导出运动方程为非线性偏微分-积分方程,并利用Galerkin方法简化为非线性微分-积分方程。应用平均法进行了稳定性分析,并用数值结果进行验证。数值结果还表明系统可能存在混沌运动。
- 稳定性 /
- 混沌 /
- 平均法 /
- Galerkin方法 /
- 粘弹性柱
Abstract: The dynamical stability of a homogeneous,simple supported column,subjected to a periodic axial force,is investigated.The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive ralation.The equation of motion was derived as a nonlinear integro-partial-differential equation,and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis.Numerical results are presented to compare with the analytical ones.Numerical results also indicate that chaotic motion appears.
- stability /
- chaos /
- averaging method /
- Galerkin method /
- viscoelastic column

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参考文献(18)

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[2]	Stevens K K. On the parametric excitation of a viscoelastic column[J]. AIAA J,1966,12(10):2111-2116.
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[4]	Gluckner P G, Szyskowski W. On the stability of column made of time dependent materials[J]. Encyc Civ Eng Prac Tech,1987,23(4):577-626.
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[7]	Smart J, Williams J G. A comparison of single integral non-linear viscoelasticity theories[J]. J Mech Phys Solids,1972,20(2):313-324.
[8]	Leaderman H. Large longitudinal retareded elastic deformation of rubberlike network polymers[J]. Polymer Trans Soc Rheol,1962,6(4):361-382.
[9]	Nayfef A H, Mook D T. Nonlinear Oscillations[M]. New York: Wiley,1979.
[10]	Sanders J A, Verhulst F. Averaging Methods in Nonlinear Dynamical Systems[M]. Berlin: Springer-Verlag,1985.
[11]	Touati D, Cederbaum G. Dynamic stability of nonlinear viscoelastic plates[J]. Int J Solids Struct,1994,31(18):2367-2376.
[12]	Suire G, Cederbaum G. Periodic and chaotic behavior of viscoelastic nonlinear(elastica)bars under harmonic excitations[J]. Int J Mech Sci,1995,37(5):753-772.
[13]	Touati D, Cederbaum G. Influence of large deflections on the dynamic stability of nonlinear viscoelastic plates[J]. Acta Mech,1995,113(2):215-231.
[14]	Argyris J. Chaotic vibrations of a nonlinear viscoelastic beam[J]. Chaos Solitons, Fractals,1996,7(1):151-163.
[15]	ZHANG Neng-hui, CHENG Chang-jun. Chaos behavior of viscoelastic plates in supersonic flow[A]. In: CHIEN Wei-zang, CHENG Chang-jun, DAI Shi-qiang, LIU Yu-lu, Eds.Proc 3rd Inter Conf Nonlinear Mech[C]. Shanghai: Shanghai University Press,1998,432-436.
[16]	ZHU Yan-yan, ZHANG Neng-hui, Miura F. Dynamical behavior of viscoelastic rectangular plates[A]. In: CHIEN Wei-zang, CHENG Chang-jun, DAI Shi-qiang, LIU Yu-lu, Eds. Proc 3rd Inter Conf Nonlinear Mech[C]. Shanghai: Shanghai University Press,1998,445-450.
[17]	程昌钧,张能辉. 粘弹性矩形板的混沌和超混沌行为[J]. 力学学报,1998,30(6):690-699.
[18]	陈立群,程昌钧. 用输出变量反馈线性化方法控制粘弹性板的混沌振动[J]. 应用数学和力学,1999,20(12):1229-1234.

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文章访问数: 3141
HTML全文浏览量: 289
PDF下载量: 608
被引次数: 0

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非线性粘弹性柱的稳定性和混沌运动

作者简介:
陈立群(1963- ),上海市人,博士,教授;程昌钧(1937- ),女,重庆市人,教授,博导.研究方向:非线性固体力学,已发表论文100余篇;多次获得省部级以上各种奖励,1998年获教育部科技进步(甲类)一等奖.

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Stability and Chaotic Motion in Columns of Nonlinear Viscoelastic Material

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留言板

非线性粘弹性柱的稳定性和混沌运动

作者简介: 陈立群(1963- ),上海市人,博士,教授;程昌钧(1937- ),女,重庆市人,教授,博导.研究方向:非线性固体力学,已发表论文100余篇;多次获得省部级以上各种奖励,1998年获教育部科技进步(甲类)一等奖.

计量

出版历程

Stability and Chaotic Motion in Columns of Nonlinear Viscoelastic Material

计量

出版历程

目录

作者简介:
陈立群(1963- ),上海市人,博士,教授;程昌钧(1937- ),女,重庆市人,教授,博导.研究方向:非线性固体力学,已发表论文100余篇;多次获得省部级以上各种奖励,1998年获教育部科技进步(甲类)一等奖.