闭口薄壁截面圆弧拱空间动力稳定性分析

摘要

Applying the energy method and Hamilton principle, the differential equations for spatial dynamic stability analysis of a thin-walled circular arch with closed section subject to radial periodically-distributed load were established. Galerkin 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, the dynamic instability regions surrounded by periodic solutions were obtained. Spatial dynamic stability problems of parametric vibration of the thin-walled circular arch with closed section were discussed. The influences of dead load, radius of circle and central angle etc. on the dynamic stability were analyzed. This work provides some reference basis for dynamic analysis and design for engineering structures.%　　通过能量法和Hamilton原理，建立径向均布周期荷载作用下闭口薄壁截面圆弧拱动力稳定偏微分方程，利用Galerkin方法将其转化为2阶常微分Mathieu-Hill型参数振动方程，求得周期解所包围的动力不稳定区域，探讨了闭口截面圆弧拱发生空间参数振动的动力稳定性问题，分析了恒载系数、圆弧半径以及圆心角等参数对空间动力不稳定区域的影响，为工程结构动力设计提供参考依据。