几何缺陷对拱结构动力稳定性的影响

The effects of geometrical imperfections on dynamic stability of arch structures

分析了外激励下几何缺陷对拱结构动力稳定性的影响。推导了拱结构边界确定而结构本身节点坐标偏差随机且指数相关时的条件相关矩阵,分解得到几何缺陷的分布方式和大小。从非线性运动方程出发,分别得出了周期荷载作用下非线性刚度矩阵可线性化,非周期荷载作用下同时考虑几何、材料非线性的Lyapunov指数计算方法。最后以一圆弧拱为例分别对周期荷载、阶跃荷载、脉冲荷载及地震荷载作用下几何缺陷的影响进行了数值分析。结果表明周期激励作用下拱结构存在动力失稳频域;在不同分布方式几何缺陷中动力稳定性对与屈曲模态相似的缺陷最为敏感。

This paper is concerned with the effects of geometrical imperfections on the dynamic stability of arch structure under external load. The conditional covariance matrix of stochastic arch structure, whose node coordinate deviations are exponentially correlative, is determined by deterministic boundary conditions, and through the decomposition of the matrix the distribution shapes and amplitude of geometrical imperfections are obtained. From the nonlinear motion equation, the top Lyapunov exponents for periodic load, in which the nonlinear stiffness matrix can be linearized, and for non-periodic load, where both geometrical and material nonlinearities are taken into account, are determined respectively. And a circular arch is taken as an example to investigate the effects of geometrical imperfections under periodic load, step load, impulsive load and earthquake load. The results show that the buckling frequency regions exist under periodic excitation and the dynamic stability is most sensitive to the geometrical imperfection that is similar to the static buckling mode.