| 叠层板在两项简谐激励作用下的组合共振分析 |
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| 引用本文： | 胡宇达,吕书锋,李佰洲.叠层板在两项简谐激励作用下的组合共振分析[J].工程力学,2010(6). |
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| 作者姓名： | 胡宇达 吕书锋 李佰洲 |
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| 作者单位： | 燕山大学建筑工程与力学学院; |
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| 摘 要： | 研究了在四边简支的边界条件下,正交各向异性矩形叠层板在两项横向简谐激励作用下的非线性组合共振及其稳定性问题。在给出了正交各向异性叠层板的振动微分方程的基础上,利用伽辽金法导出了相应的无量纲化达芬型非线性强迫振动方程。应用多尺度法对组合共振问题进行求解,得到了系统在稳态运动下的幅频响应方程。基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件。通过数值算例,对几种复合材料薄板的共振特性进行了分析,分别给出了不同条件下系统运动的响应图、幅频图和动相平面图,讨论了不同参数对系统非线性动力学行为的影响。
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| 关 键 词： | 叠层板 各向异性 组合共振 稳定性 多尺度法 |
NONLINEAR COMBINATION RESONANCES OF ORTHOTROPIC LAMINATED PLATE UNDER TWO-TERM HARMONIC EXCITATION |
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| HU Yu-da,LU Shu-feng,LI Bai-zhou.NONLINEAR COMBINATION RESONANCES OF ORTHOTROPIC LAMINATED PLATE UNDER TWO-TERM HARMONIC EXCITATION[J].Engineering Mechanics,2010(6). |
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| Authors: | HU Yu-da LU Shu-feng LI Bai-zhou |
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| Affiliation: | HU Yu-da,LU Shu-feng,LI Bai-zhou(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao,Hebei 066004,China) |
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| Abstract: | The stability and nonlinear combination resonance of a rectangular orthotropic laminated thin plate excited by two-term harmonic forces are studied under the boundary condition simply supported on four sides.Based on the vibration differential equation of orthotropic laminated plates,the nondimensional Duffing nonlinear forced vibration equation is deduced by using Galerkin method.The amplitude frequency response equation of system steady motion under combination resonance is obtained by the method of Multi... |
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| Keywords: | laminated plate orthotropic combination resonance stability multiple scales method |
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