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扁拱的面内非线性稳定与突变分析

Nonlinear in-plane stability and catastrophe analysis of shallow arches
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摘要 通过位移、应变能突变分析扁拱结构受简谐荷载作用特性。采用谐波平衡法由扁拱非线性振动方程获得位移、频率关系尖点突变模型,据位移突变判别式分析扁拱非线性响应;用系统能量原理及有限元软件,借助突变理论导出结构失稳的应变能突变准则,并比较位移与应变能突变判别方式差异。结果表明,扁拱受简谐荷载作用的位移或应变能会发生突变,跨度、矢高及荷载对突变均有影响;用位移、应变能突变判别式计算结果基本一致,且各有优势及不足。 The catastrophe properties of shallow arches under harmonic load were analyzed by adopting the catastrophe criteria of displacement and strain energy respectively. A cusp catastrophe model that expresses the relationship between displacement and frequency was obtained from the nonlinear vibration equation by the harmonic balance method and the nonlinear responses of shallow arches were analyzed according to the criterion of displacement catastrophe. The strain energy catastrophe guideline of instability was obtained according to catastrophe theory by using the system energy principle and finite element software. The differences between the results by the two catastrophe criteria were discussed. The results show that the displacement or strain energy of shallow arches both can have a sudden change. Span, rise and load have impact on catastrophe. The results are almost the same, calculated according to either of the two catastrophe criteria, each has advantages and disadvantages.
出处 《振动与冲击》 EI CSCD 北大核心 2016年第6期47-51,74,共6页 Journal of Vibration and Shock
基金 江苏高校优势学科建设工程资助项目
关键词 扁拱 突变理论 稳定 位移突变 应变能突变 shallow arch catastrophe theory stability displacement catastrophe strain energy catastrophe
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参考文献12

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