扁拱的面内非线性稳定与突变分析

朱晓蕾,孙敦本

振动与冲击 ›› 2016, Vol. 35 ›› Issue (6) : 47-51.

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (6) : 47-51.
论文

扁拱的面内非线性稳定与突变分析

  • 朱晓蕾,孙敦本
作者信息 +

The in-plane nonlinear stability and catastrophe analysis of shallow arches

  • ZHU Xiao-lei,SUN Dun-ben
Author information +
文章历史 +

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。
 

Abstract

The catastrophe properties of shallow arches were analyzed by displacement and strain energy catastrophe under harmonic load. The cusp catastrophe model that expressed the relationship between displacement and frequency was obtained from the nonlinear vibration equation by the harmonic balance method, the nonlinear response of shallow arches were analyzed according to the criterion of displacement catastrophe. The strain energy catastrophe guideline of instability was obtained with catastrophe theory by system energy principle and finite element software, the differences of both judgment methods were compared between the displacement and strain energy catastrophe. The results show that the displacement or strain energy of shallow arches could have a sudden change. Span, rise and load have impact on catastrophe. The results are almost the same that calculated from the catastrophe criterion of displacement and strain energy, each has advantages and disadvantages.

关键词

扁拱 / 突变理论 / 稳定 / 位移突变 / 应变能突变

Key words

shallow arch / catastrophe theory / stable / displacement catastrophe / strain energy catastrophe

引用本文

导出引用
朱晓蕾,孙敦本 . 扁拱的面内非线性稳定与突变分析[J]. 振动与冲击, 2016, 35(6): 47-51
ZHU Xiao-lei,SUN Dun-ben. The in-plane nonlinear stability and catastrophe analysis of shallow arches[J]. Journal of Vibration and Shock, 2016, 35(6): 47-51

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