## 留言板

 引用本文: 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.
ZHANG Neng-hui, CHENG Chang-jun. Two-Mode Galerkin Approach in Dynamic Stability Analysis of Viscoelastic Plates[J]. Applied Mathematics and Mechanics, 2003, 24(3): 221-228.
 Citation: ZHANG Neng-hui, CHENG Chang-jun. Two-Mode Galerkin Approach in Dynamic Stability Analysis of Viscoelastic Plates[J]. Applied Mathematics and Mechanics, 2003, 24(3): 221-228.

• 中图分类号: O345

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

• 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。
•  [1] Bolotin V V.The Dynamic Stability of Elastic System[M].San Francisco:Holden Day,1964. [2] 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. [3] ZHANG Neng-hui,CHENG Chang-jun.Chaotic behavior of viscoelastic plates in supersonic flow[A].In:CHIEN Wei-zang,CHENG Chang-jun,DAI Shi-qiang,et al Eds.Proc 3rd Inter Conf on Nonlinear Mech[C].Shanghai:Shanghai University Press,1998,432-436. [4] ZHU Yuan-yuan,ZHANG Neng-hui,Miura F.Dynamical behavior of viscoelastic rectangular plates[A].In:CHIEN Wei-zang,CHENG Chang-jun,DAI Shi-qiang,et al Eds.Proc 3rd Inter Conf on Nonlinear Mech[C].Shanghai:Shanghai University Press,1998,445-450. [5] 张能辉,程昌钧.面内周期激励下粘弹性矩形板的混沌和周期行为[J].固体力学学报,2000,21(增刊):160-164. [6] 陈立群,程昌钧.粘弹性板混沌振动的输出变量反馈线性化控制[J].应用数学和力学,1999,20(12):1229-1234. [7] Aboudi J,Cederbaum G,Elishakoff I.Dynamic stability analysis of viscoelastic plates by Liapunov exponents[J].J Sound Vib,1990,139(3):459-467. [8] Touati D,Cederbaum G.Dynamic stability of nonlinear viscoelastic plates[J].Int J Solids Struct,1994,31(17):2367-2376. [9] Wojciech S,Klosowicz M.Nonlinear vibration of a simply supported viscoelastic inextensible beam and comparison of methods[J].Acta Mechanica,1990,85(1):43-54. [10] CHEN Li-qun,CHENG Chang-jun.Dynamical behavior of nonlinear viscoelastic columns based on 2-order Galerkin truncation[J].Mech Res Comm,2000,27(4):413-419. [11] ZHANG Neng-hui,CHENG Chang-jun.Non-linear mathematical model of viscoelastic thin plates with its applications[J].Comput Methods Appl Mech Engng,1998,165(4):307-319.

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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

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