周期荷载作用下几何缺陷拱的动力稳定性

分析了周期荷载作用下几何缺陷对拱的动力性能的影响.首先将结构有限元节点坐标偏差视为随机变量,通过建立拱的条件相关矩阵,分解得出几何缺陷的分布方式及缺陷幅值标准差.在考虑动力荷载作用下结构的稳定性能时,由Lyapunov稳定性原理出发,推导出了反应结构长期动力性能的运动稳定方程,基于此方程求解Lyapunov指数.对比分析了几何缺陷拱与完善拱的动力稳定性能,研究了周期荷载作用的频率与几何缺陷的大小对拱动力稳定性能的影响.结果表明与静力屈曲模态相似的几何缺陷分布方式对拱的动力稳定性影响最大;同时存在使拱发生动力失稳的激励频率区域.

Dynamic Stability of Arch with the Geometrical Imperfection Subject to the Periodic Load

This paper investigated the dynamic stability of arch with the geometrical imperfection subject to the external excitation.First,considering the coordinate deviations of finite element nodes as the random variables,the conditional covariance matrix was derived,which was decomposed to obtain the distribution shapes and imperfection amplitude variance of geometrical imperfection.To determine the dynamic stability and reflect the long-term dynamic behavior of the arch structures,the motion stability equation was obtained with the Lyapunov theory,which was used to determine the maximum Lyapunov exponent of the arch.Then,the dynamic stability of the arch with geometrical imperfect and the perfect arch were studied.At last,the effects of the frequencies of the periodic load and the amplitude of the geometrical imperfection on the dynamic stability of the arch were investigated.The results have shown that the geometrical imperfection with the static buckling mode shape is susceptible to the dynamic stability of the arch.