粘弹性浅拱的非线性动力学行为

易壮鹏; 王连华; 赵跃宇

doi:10.3879/j.issn.1000-0887.2009.06.011

粘弹性浅拱的非线性动力学行为

doi: 10.3879/j.issn.1000-0887.2009.06.011

1.
长沙理工大学土木与建筑学院,长沙 410114;2.湖南大学土木工程学院,长沙 410082

基金项目: 国家自然科学基金资助项目(10502020;10772065)

详细信息

作者简介:
易壮鹏(1979- ),男,湖南望城人,讲师,博士(联系人.E-mail:yizhuangpeng@163.com).

中图分类号: U311.2
计量
- 文章访问数: 1679
- HTML全文浏览量: 159
- PDF下载量: 795
- 被引次数: 0
出版历程
- 收稿日期: 2008-08-22
- 修回日期: 2009-02-25
- 刊出日期: 2009-06-15

Nonlinear Dynamic Behaviors of Viscoelastic Shallow Arches

1.
School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410114, P. R. China;

摘要

摘要: 研究了外荷载作用下粘弹性浅拱的非线性动力行为．通过d’Alembert原理和Euler-Bernoulli假定建立了浅拱的控制方程，其中非线性粘弹性材料采用Leaderman本构关系．运用Galerkin法和数值积分研究粘弹性浅拱的非线性动力特性．并分析了矢高、材料参数、激励幅值和频率等参数的影响，结果表明一定条件下粘弹性浅拱可出现混沌运动．
- 粘弹性浅拱 /
- Leaderman本构关系 /
- Galerkin法 /
- 分岔 /
- 混沌
Abstract: The nonlinear dynamic of nonlinear viscoelastic shallow arches subjected to the external excitation is investigated.Based on the d.Alembert principle and the Euler-Bernoulli assumption,the governing equation of shallow arch was obtained,where the Leaderman constitutive relation was applied.The Galerkin method and numerical integration were used to study the nonlinear dynamic properties of the viscoelastic shallow arches.Moreover,the effects of the rise,the material parameter and excitation on the nonlinear dynamic of shallow arch were investigated.The results show that viscoelastic shallow arches may have chaotic motion for certain condition.
- viscoelastic shallowarch /
- Leaderman constitutive relation /
- Galerkin method /
- bifurcation /
- chaos

HTML全文

参考文献(17)

[1]	陈立群,程昌钧.基于Galerkin截断的粘弹性结构动力学行为研究综述[J].自然杂志,1999,21(1):1-4.
[2]	陈立群,程昌钧.非线性粘弹性梁的动力学行为[J].应用数学和力学2000,21(9):897-902.
[3]	陈立群，程昌钧，张能辉.具有几何和物理非线性粘弹性梁的混沌运动[J].工程力学，2001,18(1):1-6.
[4]	Chen L Q,Cheng C J.Dynamical behavior of nonlinear viscoelastic columns based on 2-order Galerkin truncation[J].Mechanics Research Communications,2000,27(4):413-419. doi: 10.1016/S0093-6413(00)00112-9
[5]	陈立群，程昌钧.非线性粘弹性柱的稳定性和混沌运动[J].应用数学和力学,2000,21(9):890-896.
[6]	程昌钧，盛冬发，李晶晶.损伤粘弹性Timoshenko梁的拟静态力学行为分析[J].应用数学和力学，2006,27(3):267-274.
[7]	Argyris J,Belubekian V,Ovakimyan N,et al.Chaotic vibrations of a nonlinear viscoelastic beam[J].Chaos Solitons & Fractals,1996,7(2):151-163.
[8]	李根国，朱正佑，程昌钧.非线性粘弹性Timoshenko梁动力学行为的分析[J].力学季刊，2001,22(3):346-351.
[9]	程昌钧，盛冬发，杨骁.损伤粘弹性桩基的非线性动力学行为[J].振动与冲击，2006,25(1):18-24.
[10]	冯振宇，王忠民，樊丽俭.粘弹性点支承粘弹性桩的动力稳定性分析[J].中国公路学报，2006,19(1):67-70.
[11]	张能辉，程昌钧.粘弹性板动力稳定性分析中的两模态Galerkin逼近[J].应用数学和力学，2003,24(3):221-228.
[12]	程昌钧，张能辉.轴压作用下粘弹性柱壳的动力学行为[J].应用数学和力学，2001,22(1):1-8.
[13]	张能辉，王建军，程昌钧.轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法[J].应用数学和力学，2007,28(1):1-8.
[14]	Huang N C,Nachbar W.Dynamic snap-through of imperfect viscoelastic shallow arches[J].Journal of Applied Mechanics,ASME,1968,35:289-296. doi: 10.1115/1.3601194
[15]	Leaderman H.Large longitudinal retarded elastic deformation of rubber like network polymers[J].Polymer Trans Soc Rheol,1962,6(4):361-382.
[16]	Potapov V D,Marasanov A Y.The investigation of the stability of elastic and viscoelastic rods under a stochastic excitation[J].International Journal of Solids and Structure,1997,34(9):1367-1377. doi: 10.1016/S0020-7683(96)00128-X
[17]	Bi Q,Dai H H.Analysis of non-linear dynamics and bifurcations of a shallow arch subjected to periodic excitation with internal resonance[J].Journal of Sound and Vibration,2000,233(4):553-567. doi: 10.1006/jsvi.1999.2813