行道树随机结构风振响应分析与动力可靠度评价

Wind-Induced Vibration Analysis and Dynamic Reliability Assessment of Stochastic Urban Trees

建立了行道树风振响应分析的简化理论模型,根据有限元理论,分析了影响行道树动力学特征的材料物理参数,即密度和弹性模量.将风荷载模拟为Davenport谱,提出了基于虚拟激励法的行道树风振响应分析方法.考虑材料物理参数的随机性,利用概率密度演化理论,给出了行道树随机结构风振响应分析的基本步骤,提出了与行道树主干抗弯强度相关的失效风速概念和动力可靠度评价方法.以上海地区城市行道树为例进行了分析,揭示了树种材料参数不确定性对行道树随机动力学响应的影响,计算了不同风速水平下行道树结构的破坏概率,在风险意义上定义了行道树的失效风速.

A simplified theoretical model for wind-induced vibration analysis of urban trees is built up. By virtue of finite element method, two critical parameters influencing the dynamic responses of urban trees, i.e. density and elastic modulus, are analyzed. Using Davenport spectrum to model the wind loading, a numerical scheme based on the pseudo excitation method for analyzing the wind-induced response of stochastic urban trees is suggested. The basic steps of stochastic response analysis of urban trees are provided utilizing the probability density evolution method. The concept of failure wind velocity related to the trunk anti-moment strength of urban trees is proposed, and the method of its probability assessment is given. For illustrative purposes, the typical urban trees in Shanghai area are analyzed. Numerical results indicate that the randomness inherent in the tree material parameters has a significant influence upon the stochastic dynamics of urban trees. The failure probabilities of urban trees subjected to wind loads of different levels are calculated that helps the definition of the failure wind velocity of urban trees in the sense of risks.