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叶敏, 吕敬, 丁千, 张伟. 复合材料层合板1:1参数共振的分岔研究[J]. 力学学报, 2004, 36(1). DOI: 10.6052/0459-1879-2004-1-2003-024
引用本文: 叶敏, 吕敬, 丁千, 张伟. 复合材料层合板1:1参数共振的分岔研究[J]. 力学学报, 2004, 36(1). DOI: 10.6052/0459-1879-2004-1-2003-024
THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(1). DOI: 10.6052/0459-1879-2004-1-2003-024
Citation: THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(1). DOI: 10.6052/0459-1879-2004-1-2003-024

复合材料层合板1:1参数共振的分岔研究

THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE

  • 摘要: 针对复合材料对称铺设各向异性矩形层合板的物理模型,在同时考虑了材料、阻尼和几何等非线性因素后,建立了二自由度非线性参数振动系统动力学控制方程,并应用多尺度法求得基本参数共振下的近似解析解,利用数值模拟分析了系统的分岔和混沌运动. 指出了伽辽金截断对系统动力学分析的影响,以及系统进入混沌的途径.

     

    Abstract: A simply supported rectangular symmetric cross-plylaminated composite plate with parametric excitation is considered. Thegoverning equations of motion for the laminated composite plate arederived by means of von K\'arm\'an equation. The material nonlinearity,geometric nonlinearity and nonlinear damping are included in thegoverning equations of motion. The Galerkin's approach is used toobtain a two-degree-of-freedom nonlinear system under parametricexcitation. The method of multiple scales is utilized to transform thesecond-order non-autonomous differential equations to first-orderaveraged equations. The averaged equations are numerically solved toobtain the bifurcation responses and to analyze the stability for thelaminated composite plate. Under certain conditions the laminatedcomposite plate may occur two non-steady-state bifurcation solutionsand jumping phenomena. The bifurcation and chaotic motion of therectangular symmetric cross-ply laminated composite plate is simulatednumerically. The effect of the Galerkin's truncation to nonlineardynamic analysis is presented. The way of the system going into chaosis also investigated and explained.

     

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