桅杆的非线性随机研究

Theoretical Study on the Chaos of Guyed Masts

通过引入微小白噪声摄动 ,将桅杆的非线性动力方程转变成 Ito随机微分方程的形式 ,采用路径积分推导出该噪声模型响应概率密度函数的形式解 ,根据该函数的分布特征和平均 Poincaré图研究桅杆响应特性受激励参数的影响和混沌现象。算例分析表明 :桅杆响应特性依赖于激励的频率及其强度 ,而与激励方向基本无关 ;共振频率附近激励强度的增长将导致桅杆出现混沌运动 ,结构在水平面内各方向上产生大幅振荡 ,这是造成结构疲劳损伤累积的重要起因。

By introducing tiny perturbations of white noise, the equation of motion of guyed masts has a stochastic form of Ito's. The joint probability density function of the state vector associated with such a model can be formularized with path integral method. The applicability of the probability density function for predicting the chaos of guyed masts is then investigated. Numerical results demonstrate that characteristics of the structural behaviors depend on both intensity and frequency of the excitation. Chaotic motion is induced when the excitation intensity near the resonant frequency strengthens and it is a key factor for fatigue of structures.