考虑剪切变形的圆弧深拱参数共振稳定性分析

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (2) : 119-122.

论文

考虑剪切变形的圆弧深拱参数共振稳定性分析

赵洪金1; 刘超1,2; 董宁娟3; 吴敏哲1

作者信息 +

Analysis of stability for parametric resonance of circular deep arch considering influence of shear deformation

ZHAO Hong-jin1; LIU Chao1 2; DONG Ning-juan3; WU Min-zhe1

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文章历史 +

摘要

基于结构弹性稳定理论，根据能量法推导出以位移为基本未知量的圆弧深拱总势能，从Hamilton原理出发,建立了考虑剪切变形的圆弧深拱的动力稳定微分方程。利用Galerkin方法将该方程转化为二阶常微分Mathieu型参数共振方程，推导出圆弧深拱主参数共振的临界频率方程式，从而求得周期解所包围的动力不稳定区域。通过分析剪切变形、圆弧半径、圆心角等参数对圆弧深拱动力稳定性的影响，探讨了圆弧深拱发生参数共振的动力稳定性问题，为拱型结构动力分析与设计提供参考依据。

Abstract

Based on the theory of elastic stability of structure, the total potential energy of circular deep arch for unknown variables with displacement was obtained according to energy method, dynamic stability differential equation of circular deep arch subject to under distributing radial periodic load was established through applying the energy method and Hamilton principle. Galerkin’s method was used to convert the partial differential equations into the ordinary differential Mathieu equations, so as to deduce the critical frequency equations of primary parameter resonance of deep arch, and then dynamic instability regions surrounded by periodic solutions were obtained. Dynamic stability problems of parametric vibration was discussed about circular deep arch，through analyzing the influences of shear deformation, radius of circle and central angle etc. on the dynamic stabilities, which provides reference basis for dynamic analysis and design in structure engineering.

导出引用

赵洪金;刘超;董宁娟;吴敏哲. 考虑剪切变形的圆弧深拱参数共振稳定性分析[J]. 振动与冲击, 2012, 31(2): 119-122

ZHAO Hong-jin;LIU Chao;DONG Ning-juan;WU Min-zhe. Analysis of stability for parametric resonance of circular deep arch considering influence of shear deformation[J]. Journal of Vibration and Shock, 2012, 31(2): 119-122