结构随机动力稳定性的定量分析方法

李杰; 徐军

doi:10.6052/0459-1879-15-304

结构随机动力稳定性的定量分析方法

doi: 10.6052/0459-1879-15-304

李杰^1,2, ,,
徐军¹

1.
同济大学土木工程学院, 上海 200092
2. 土木工程防灾国家重点实验室, 上海 200092

基金项目: 国家自然科学基金资助项目(51261120374,9131530.

详细信息

通讯作者:
李杰,教授,主要研究方向:随机动力系统分析、混凝土随机损伤力学与生命线工程抗灾.E-mail:lijie@tongji.edu.cn

中图分类号: O317⁺3
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- 被引次数: 0
出版历程
- 收稿日期: 2015-08-05
- 修回日期: 2015-12-02
- 刊出日期: 2016-05-18

A QUANTITATIVE APPROACH TO STOCHASTIC DYNAMIC STABILITY OF STRUCTURES

Li Jie^{1,2
, ,},
Xu Jun¹

1.
School of Civil Engineering, Tongji University, Shanghai 200092, China
2. State Key Laboratory of Disaster Reduction in Civil Engineering, Shanghai 200092, China

摘要

摘要: 提出了结构随机动力稳定性的定量分析方法,讨论了经典的随机动力稳定性概念,指出结构动力稳定性不仅与结构参数有关,也与作用在结构上的外部载荷密切相关,据此引入了一种判定结构动力稳定性的新准则,明确了结构随机动力稳定性的基本涵义.在概率守恒原理基础上,推导了概率耗散系统的广义概率密度演化方程.引入结构动力失稳的物理机制作为引起概率耗散的驱动力,利用概率耗散系统概率密度演化方程、可以方便获得结构响应的概率密度演化过程,从而定量求解结构的动力稳定概率.据此,可以定量评价结构系统依概率为1或依给定概率意义上的结构随机动力稳定性.采用本文所建议方法对典型结构动力系统进行了随机动力稳定性分析,并与蒙特卡洛方法计算结果进行对比.数值结果表明了所建议方法的有效性.
- 随机动力稳定 /
- 定量方法 /
- 概率耗散系统 /
- 概率密度演化方程
Abstract: A quantitative approach is proposed for stochastic dynamic stability analysis of structures. The classical concept of stochastic dynamic stability is firstly revisited. It is pointed that the dynamic stability of structures not only depends on structural parameters, but also relates to the applied external excitations. A new criterion for identifying dynamic stability of structures is introduced and the definition of stochastic dynamic stability of structures is therefore formulated based on the criterion. According to the principle of preservation of probability, the generalized density evolution equation for probability-preserved system is introduced firstly and then the equation for probability-dissipated system is derived. On the basis, the probability of stability/instability can be obtained via solving the equation for probability-dissipated system by introducing the physical mechanism of dynamic instability of structures as the triggering force of probability dissipation. Numerical algorithms for solving the generalized density evolution equation for probability-dissipated system are provided. According to the obtained probability, it is readily applicable to quantitatively evaluate stochastic dynamic stability of structures in the sense of stability in probability 1 or a given probability. Stochastic dynamic stability analyses of typical structural dynamic systems are carried out by the proposed approach, where the results by Monte Carlo simulations are employed for comparisons. The numerical results verify the e ectiveness of the proposed approach.
- stochastic dynamic stability /
- quantitative approach /
- probability-dissipated system /
- probability density evolution equation

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