车桥耦合系统动力相互作用与多点地震响应数值方法研究

发布时间：2018-01-12 16:01

本文关键词：车桥耦合系统动力相互作用与多点地震响应数值方法研究　出处：《大连理工大学》2015年博士论文　论文类型：学位论文

【摘要】：车辆桥梁耦合系统是一个时变的复杂动力学系统。随着车速不断提高,行车密度不断增加,载重量的不断增大,车辆与桥梁耦合系统的动力特性与振动控制越来越受到人们的重视。另外,随着高速公路和高速铁路的迅猛发展,桥梁在线路中所占的比重越来越大,地震发生时车辆在桥梁上的机率大为增加。此时,路面／轨道不平顺以及可能发生的脱离会导致系统内部存在时频非平稳随机性与非线性作用关系,而桥梁高柔性、低阻尼的动力特性使其对地震地面运动随机场的非均匀性和非平稳性更为敏感。车桥耦合系统动力相互作用问题的求解可分为时变方法和迭代方法两种。时变方法将耦合系统作为一个整体,应用逐步积分方法对时变运动方程组直接进行求解。迭代方法将车辆与桥梁分别作为两个独立的子系统,通过他们之间的相互作用关系,经过多次迭代从而得到整个系统的动力响应。迭代方法突出的优点是将车辆和桥梁子系统作为常规的结构动力学问题进行分析,可以避免时变方法中因车桥系统参数差异过大可能引起的系数矩阵病态问题。本文在车桥耦合系统传统迭代方法基础上,提出基于车桥相互作用力预估格式的免迭代方法,在保证计算精度的前提下显著提高了计算效率,并且将车辆与桥梁之间复杂的连接关系与方程的求解相剥离。研究了车辆与桥梁之间力的传递方式,建立了考虑车轮与桥梁脱离及随机路面不平顺的线性互补方法,进一步发展了车桥耦合系统多点非平稳随机地震作用下随机响应分析模型和高效求解方法。具体研究内容包括： 1)针对桥梁在移动力作用下的动力响应分析问题,提出了一种基于有限元模型和Duhamel积分的解析方法。该方法通过构造桥面分段连续形函数,得到了移动力作用下桥梁动力响应的解析表达；在计算中通过对Duhamel积分的分解变换,利用积分的可加性,极大地减少了计算时间,并可方便地获得多个移动力下桥梁的共振和相消条件。 2)提出了一种基于车桥相互作用力预估格式的免迭代方法。该方法兼顾计算精度和效率,对于线性或非线性连接条件,均可通过预测得到当前时刻车辆与桥梁间的相互作用力,采用精细积分方法分别对车辆、桥梁子系统直接进行求解,从而避免了传统迭代方法复杂、耗时的迭代过程,在保证计算精度的前提下显著提高了计算效率 3)通过构造车轮与桥梁之间相对位移和相互作用力间的线性互补关系,建立了考虑车轮与桥梁脱离和路面不平顺的动力学分析模型。无论车轮是否脱离、车辆模型如何复杂,该方法都可以采用统一的运动方程进行描述。在求解中不需要在每一时间步内对接触状态进行判断,避免了一般算法“假设—判断—迭代”的过程。 4)建立了车辆桥梁耦合系统在非平稳多点地震作用下考虑路面不平顺的随机动力响应分析方法。通过将预估免迭代算法与虚拟激励法相结合,建立了同时考虑轨道不平顺和多点地震的行波效应、部分相干效应和场地效应的大型斜拉桥梁车辆耦合系统随机动力响应分析高效分析算法,研究了地震动及其空间效应、路面不平顺和车辆行驶速度等因素对车桥耦合系统随机动力响应的影响,并进一步从随机振动角度研究了地震对车轮与桥梁脱离的影响。
[Abstract]:The vehicle bridge coupling system is a time - varying complex dynamics system . As the vehicle speed is continuously increased , the driving density is continuously increased and the weight of the vehicle is continuously increased , the dynamic characteristics and vibration control of the vehicle and the bridge coupling system are more and more attention . In addition , with the rapid development of the highway and the high - speed railway , the probability of the vehicle on the bridge is greatly increased . The solution of dynamic interaction problem of axle coupling system can be divided into time - varying method and iterative method . The time - varying method applies the coupling system as a whole , and applies the step - by - step integration method to solve the time - varying motion equations . The iterative method takes the vehicle and the bridge as two independent subsystems . Through the interaction between them , the dynamic response of the whole system is obtained through many iterations . The iterative method has the advantage of using the vehicle and the bridge subsystem as the conventional structural dynamics problems . Based on the traditional iterative method of vehicle - bridge coupling system , this paper proposes a non - iterative method based on the vehicle - bridge interaction force prediction format , which improves the computational efficiency significantly on the premise of guaranteeing the calculation precision , and separates the complex connection relationship between the vehicle and the bridge from the solution of the equation . 1 ) According to the dynamic response analysis problem of bridge under the action of displacement , a finite element model and Duhamel integral analysis method are presented . The analytical expression of the dynamic response of the bridge under the action of displacement is obtained by constructing the continuous function of the bridge section . 2 ) A non - iterative method based on vehicle - bridge interaction force prediction format is proposed . The method considers the calculation precision and efficiency , and the interaction force between the vehicle and the bridge can be obtained by predicting the interaction force between the vehicle and the bridge at the current time by predicting the interaction force between the vehicle and the bridge at the current time by means of a fine integration method , thereby avoiding the complicated and time - consuming iterative process of the traditional iterative method , and obviously improving the calculation efficiency under the premise of guaranteeing the calculation accuracy . 3 ) By constructing the linear complementarity between the relative displacement and the interaction force between the wheel and the bridge , a dynamic analysis model considering the detachment of the wheel from the bridge and the irregularity of the road surface is established . Regardless of whether the wheel is disengaged , the vehicle model is complicated , the method can be described using a uniform motion equation . In solving the problem , it is not necessary to judge the contact state every time step , and the general algorithm " hypothesis - determination - iteration " is avoided . 4 ) The stochastic dynamic response analysis method of vehicle bridge coupling system considering road surface irregularity is established under the action of non - stationary multi - point earthquake . By combining the estimated non - iterative algorithm with the virtual excitation method , the influence of ground motion and its spatial effect , surface irregularity and vehicle running speed on the random dynamic response of axle coupling system is studied .

【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U441.3

【参考文献】