非线性随机动力系统响应概率密度函数分布模式研究

项目名称： 非线性随机动力系统响应概率密度函数分布模式研究

项目编号： No.51478311

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 建筑科学

项目作者： 朱海涛

作者单位： 天津大学

项目金额： 83万元

中文摘要： 工程结构在风、海浪或地震作用下的动力响应常呈现非线性特性，从而引起结构响应概率密度函数多样性的分布形态,对结构动力失效概率影响很大。本项目拟采用理论分析、数值模拟与模型试验相结合的研究方法，针对非线性随机动力系统响应概率密度函数分布模式展开系统的研究。通过研究基于FPK方程的指数多项式闭合法和状态空间分裂法的标准化求解方法及其扩展求解方法，获得系统的稳态概率密度近似函数表达式；结合蒙特卡罗模拟方法和试验方法，通过分析典型非线性系统动力响应，验证标准化求解方法的有效性，确定影响标准化求解方法有效性的系统类型、控制参数及参数取值范围；研究非线性坐标变换和概率传递法则将标准化求解方法可解范围进行扩展；以工程领域中梁的非线性随机振动问题为重点，运用所建立的方法系统地开展在不同系统类型和激励方式影响下系统响应概率密度函数不同形态的形成机理和分布模式研究，为准确评估工程结构动力失效概率提供参考和建议。

中文关键词： 计算力学；结构可靠度；非线性分析；设计理论；结构分析

英文摘要： Some engineering structures usually behave in a nonlinear manner under winds, sea waves or seismic actions, leading to different distribution patterns of the probability density function (PDF) of their response. This significantly affects their dynamical failure probability. This investigation combines analytical approaches, numerical simulation and model tests to systematically study the PDF distribution patterns of nonlinear stochastic dynamical systems.Cooperated with the exponential-polynomial closure method and state-space-split method, a standard FPK-equation-based solution procedure and its generalized procedure are developed for the stationary approximate PDF solutions. Monte Carlo simulation and experiments are also employed to investigate the PDF solutions of some conventional dynamical systems for evaluating the effectiveness of the developed procedure, in which the applicable system types, critical factors and effective ranges are also determined. The developed procedure is extended by using nonlinear coordinate transformation and probability transfer. Mostly aiming at the random vibration of beams, the project adopts the established method and considers different nonlinear system types and excitation patterns to systematically investigate different PDF distribution patterns and their formulation mechanisms. The research outcome will give references and suggestions for accurately estimating the dynamical failure probability of engineering structures.

英文关键词： computational mechanics;structural reliability;nonlinear analysis;design theory;structural analysis