移动荷载作用下桥梁的动力学正反问题研究

发布时间：2019-04-03 18:14

【摘要】：桥梁作为交通运输工程中的关键枢纽,移动荷载作用下的振动问题一直以来都是学者们关注的重点。其中一方面主要是分析桥梁受移动荷载作用下的动力响应,它对桥梁设计、行车舒适性评价、使用安全性评估有着重要的理论价值。另一方面基于移动荷载作用下的桥梁振动响应,对桥梁结构损伤及未知移动荷载进行识别,将更有利于桥梁系统的实时健康监测、损伤诊断与评估,具有实际工程应用价值与意义。本文针对移动荷载作用下桥梁动力响应的求解(即动力学正问题)及桥梁结构损伤和移动荷载的同步识别(即动力学反问题)进行了分析,主要研究工作具体包括:(1)针对一般梁桥在移动力作用下的竖向动力响应分析,提出了一种基于有限元模型的半解析方法。本方法不依赖于有限元单元类型或形函数,直接由模态分析得到的离散振型出发;基于信号采样定理,提出了一种结构连续振型的恢复方法;进而推导了一般梁桥竖向动力响应的封闭解。利用等截面简支梁的理论解验证了本方法的准确性,进而以三跨加腋连续梁桥为代表,利用半解析表达式,讨论了移动力作用下的振动规律。重点分析了荷载移动速度、桥梁损伤对结构竖向动力响应的影响,同时还阐明了荷载移动速度变化引起结构共振的机理,并给出了跨中挠度极值对应的荷载临界速度计算公式。(2)针对同时存在未知结构损伤和未知移动荷载激励的情况,利用移动力作用下梁桥结构的强迫振动响应,基于联邦扩展卡尔曼滤波(FEKF)算法,提出了移动力和梁桥结构损伤的同步识别方法;并结合l1范数正则化改善了此反问题求解过程的不适定性。通过简支梁的数值算例分析表明,提出的算法能够准确地完成损伤和移动力的同步识别,且具有良好的鲁棒性。(3)针对考虑多次测量信息融合的结构损伤识别,提出基于l1范数正则化的联邦扩展卡尔曼滤波算法来解决。当测点信息不完整,通过改变传感器在结构上的测量位置,获取不同测点布置下的多组测量数据;并将各组不同的测量信息各自构成FEKF框架里的不同子系统,仅融合公有变量已得到结构损伤的最优估计。采用自由振动下的简支梁和二维框架结构,初步验证了该方法的有效性。此方法还可继续推广到桥梁受移动荷载作用的情况。
[Abstract]:As the key hub of transportation engineering, the vibration of bridge under moving load has always been the focus of scholars. On the one hand, it is mainly to analyze the dynamic response of bridge under moving load, which has important theoretical value for bridge design, evaluation of driving comfort and evaluation of safety in use. On the other hand, based on the vibration response of bridge under moving load, the identification of bridge structure damage and unknown moving load will be more beneficial to the real-time health monitoring, damage diagnosis and evaluation of bridge system. It has practical engineering application value and significance. In this paper, the solution of bridge dynamic response under moving load (i.e. dynamic positive problem) and simultaneous identification of bridge structure damage and moving load (i.e. inverse dynamic problem) are analyzed. The main research work is as follows: (1) A semi-analytical method based on finite element model is proposed to analyze the vertical dynamic response of a general beam bridge under moving dynamic action. This method does not depend on the finite element type or shape function, and starts directly from the discrete mode shape obtained by modal analysis, and based on the signal sampling theorem, a method for restoring the continuous mode shape of the structure is proposed. Furthermore, the closed solution of vertical dynamic response of general beam bridge is derived. The accuracy of the method is verified by the theoretical solution of the simple supported beam with equal section. Then, the vibration law of the three-span continuous beam bridge with axils is discussed by means of semi-analytical expression under the action of moving force. The influence of load moving velocity and bridge damage on the vertical dynamic response of the structure is emphatically analyzed, and the mechanism of structural resonance caused by the change of load moving velocity is also clarified. The calculation formula of critical load velocity corresponding to the extreme value of mid-span deflection is given. (2) in view of the existence of both unknown structural damage and unknown moving load excitation, the forced vibration response of beam bridge structure under the action of moving force is used. Based on the federally extended Kalman filter (FEKF) algorithm, a synchronous identification method for moving force and beam bridge damage is proposed. Combined with L1 norm regularization, the ill-posed process of solving this inverse problem is improved. Numerical examples of simply supported beams show that the proposed algorithm can accurately identify damage and moving forces synchronously, and has good robustness. (3) for the structural damage identification considering multiple measurement information fusion, the proposed algorithm has good robustness. A federated extended Kalman filter (FKF) algorithm based on L1 norm regularization is proposed to solve this problem. When the information of the measuring point is not complete, by changing the measuring position of the sensor in the structure, many groups of measuring data under different layout of the measuring point are obtained. The different measurement information of each group is made up of different subsystems in the framework of FEKF, and only the public variables are fused to obtain the optimal estimation of structural damage. A simple supported beam and a two-dimensional frame structure under free vibration are used to verify the effectiveness of the proposed method. This method can also be extended to the case of bridge subjected to moving loads.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：U441

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