考虑剪切变形的圆弧深拱参数共振稳定性分析

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。

Stability analysis for parametric resonance of a circular deep arch considering influence of shear deformation

Based on the theory of elastic stability of structure,the total potential energy of a circular deep arch with displacements as basis unknown variables was deduced according to the energy method,the dynamic stability differential equation of the circular deep arch under distributed radial periodic load was established using the energy method and Hamilton principle.Galerkin’s method was used to convert the partial differential equation into the ordinary differential Mathieu equations,so as to derive the critical frequency equations of the main parameter resonance of the deep arch,and then the dynamic instability regions surrounded by periodic solutions were obtained.Through analyzing the influences of shear deformation,radius of circle arch and circular central angle etc.on the dynamic stability of the deep arch,the dynamic stability problems of parametric resonance of the circular deep arch were studied.The results provided a reference basis for dynamic analysis and design of arch types of structure.