【作者】 张旭方；

【导师】 张义民；

【作者基本信息】 东北大学 ， 机械电子工程， 2008， 硕士

【摘要】 滞回系统是实际工程结构中普遍存在的典型非线性系统之一。构件由于大幅变形进入塑性区或者由于干摩擦等原因导致在周期运动中正向运动与反向运动时位移与非线性恢复力形成滞回环,使系统瞬时恢复力不仅依赖于该瞬时位移,而且取决于该时刻速度方向,从而表现为非线性。工程结构由于制造、安装误差等原因使描述结构的参数具有随机性。安全性设计是结构设计的主要目标。正确衡量随机参数对系统响应等各方面影响,对于系统分析和安全评估具有重要作用。本文以Bouc-Wen滞回模型为研究对象,基于首次穿越模型,对具有随机滞回环参数的一类非线性随机滞回系统可靠性分析问题进行研究。主要包括一下三部分内容：1.在系统各阶失效模式相互独立的前提下,应用四阶矩技术和Edgeworth级数逼近技术,解决了由滞回环本身随机性引起的非线性随机系统可靠性分析问题。在随机参数前四阶矩已知的情况下,获得了极限状态方程的前四阶矩；利用Edgeworth级数技术,将极限状态方程近似展开为标准正态分布的函数,发展了系统可靠性分析的经验修正公式。2.应用概率摄动技术确定系统不同失效模式之间相关性；利用随机结构灵敏度分析的梯度算法,确定失效模式之间相关性强弱与随机参数之间的动态关系。数值算例中讨论了系统随机参数对系统失效模式相关性的参数动态灵敏度。依据系统动力修改的灵敏度分析准则,对系统结构参数进行修改。动力修改后系统失效模式性相关性较修改前有明显改善。3.在随机参数联合概率密度函数未知的情况下,提出了具有相关失效模式的多自由度随机滞回结构振动系统可靠性分析的数值方法。应用Gram-Charlier级数,逼近出系统各阶极限状态方程的边缘概率密度函数；采用不完全概率信息技术给出了可靠性状态函数的联合概率密度函数,从而对相关失效模式多自由度随机滞回环参数系统的可靠性分析问题进行探讨。更多还原

【Abstract】 Hysteretic system is one of the most typical nonlinear systems in engineering. Structural systems under dynamic loading usually exhibit hysteretic behavior, especially when the response becomes inelastic. The effect of hysteretic restoring force exhibits the change of stiffness and energy. Because the restoring force of a hysteretic system depends not only on the instantaneous displacement, but also on its past history. Uncertainties in material properties and structural geometry are due to measurement inaccuracies or structure complexities. Structures with random parameters are complicated to analyze, since the response is statistically correlated to these parameters. The safety of engineering structures is one of the major objectives of structure design. It can help designer to establish acceptable tolerances on structures and determine the fluctuations of the system parameters for safety operations.On the basement of the Bouc-Wen hysteretic model, an numerical method for the reliability analysis of nonlinear stochastic hysteretic system that caused by uncertain hysteretic loop itself is presented, mainly including of following three aspects:1. In the premise of the independent of failure modes, the fourth-moment technique and Edgeworth series approximation theory are employed to develop a reliability analysis method systematically. With known the first-four moment of random parameters, the corresponding statistical characters of limit state equation of system are computed. So the probability distribution of limit state equation can be express by standard normal distribution function from Edgeworth series.2. The probability purterbation method is emloyed to determine the statistical characteristic of failure modes and the correlation between them. The dynamtic sensitivity for correlation of failure modes with respect to random parameters is discussed in time domain. A numerical method of dynamic sensitivity analysis for correlation of failure modes of nonlinear random vibration system is developed. The numeric example is used to verify the present method.3. The theory of incomplete probability information, the statistical fourth-moment technique and Gram-Charlier series approximation theory are employed to develop a reliability analysis method systematically. The numerical example has revealed that in most of cases, though stochastic system is characterized by a set of independent random parameters, the responses are strong correlated and correlated failure modes is main cause of system failure. It has solved the reliability analysis of nonlinear stochastic hysteretic system that caused by uncertain hysteretic loop itself and correlated failure modes更多还原