粘弹性板动力稳定性分析中的两模态Galerkin逼近

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

张能辉^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.
上海市应用数学和力学研究所上海 200436

基金项目: 上海市高等学校青年科学基金资助项目(01QN70);上海市重点学科资助项目

详细信息

作者简介:
张能辉(1970- ),男,河北人,副教授,博士(E-mail:nhzhang@mail.shu.edu.cn).

中图分类号: O345
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出版历程
- 收稿日期: 2001-09-04
- 修回日期: 2002-12-16
- 刊出日期: 2003-03-15

Two-Mode Galerkin Approach in Dynamic Stability Analysis of Viscoelastic Plates

ZHANG Neng-hui^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 University, Shanghai 200436, P. R. China

摘要

摘要: 利用最大Liapunov指数分析法以及其它数值和解析的动力学方法,研究了大挠度粘弹性薄板的动力稳定性。材料的行为由Boltzmann叠加原理描述。采用Galerkin方法将原积分-偏微分模型简化为两模态的近似积分模型,而通过引进新变量,该近似积分模型可进一步化为一个常微分模型。数值比较了1-模态和2-模态截断系统的动力学性质,讨论了面内周期激励下材料的粘弹性性质、加载的幅度和初值对板动力学行为的影响。
- 粘弹性板 /
- 动力稳定性 /
- von Kürmün假设 /
- Galerkin方法 /
- 混沌 /
- Hopf分叉
Abstract: The dynamic stability of viscoelastic thin plates with large deflections was investigated by using the largest Liapunov exponent analysis and other mumerical and analytical dynamic methods.The material behavior was described in terms of the Boltzmann superposition principle.The Galerkin method was used to simplify the original integro-partial-differential model into a two-mode approximate integral model, which further reduced to an ordinary differential model by introducing new variables.The dynamic properties of one-mode and two-mode truncated systems were numerically compared.The influence of viscoelastic properties of the material, the loading amplitude and the initial values on the dynamic behavior of the plate under in-plane periodic excitations was discussed.
- viscoelastic plate /
- dynamic stability /
- von Kûrmûn.shypothesis /
- Galerkin method /
- chaos /
- Hopf bifurcation

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参考文献(11)

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