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。
-
关键词:
- 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.-
Key words:
- viscoelastic plate /
- dynamic stability /
- von Kûrmûn.shypothesis /
- Galerkin method /
- chaos /
- Hopf bifurcation
-
[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.
点击查看大图
计量
- 文章访问数: 2530
- HTML全文浏览量: 90
- PDF下载量: 673
- 被引次数: 0