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

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (6) : 47-51.

ZHU Xiao-lei，SUN Dun-ben

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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.

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

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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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