基于有限元-向量式有限元的斜拉桥非线性振动计算方法  

Nonlinear vibration calculation method for cable-stayed bridge based on finite element&vector form finite element method

作　　者：王涛[1] 胡宇鹏[2] 张兴标 刘德贵[1] WANG Tao;HU Yupeng;ZHANG Xingbiao;LIU Degui(School of Civil Engineering and Architecture,Southwest University of Science and Technology,Mianyang 621000,China;Institute of System Engineering,China Academy of Engineering Physics,Mianyang 621999,China)

机构地区：[1]西南科技大学土木工程与建筑学院,四川绵阳621000 [2]中国工程物理研究院总体工程研究所,四川绵阳621999

出　　处：《振动与冲击》2022年第3期129-138,215,共11页Journal of Vibration and Shock

基　　金：国家自然科学基金(51708468);西南科技大学博士基金(20zx7125)。

摘　　要：向量式有限元(VFFE)法本质上是考虑几何非线性的有限元(FE)显式动力时程积分方法。阐述了向量式有限元的基本原理,对比了向量式有限元与基于单元随动坐标系的非线性有限元动力计算方法的相同点与差别,开发了使用杆、梁单元的有限元-向量式有限元统一算法框架的计算程序。使用该程序建立了大跨度斜拉桥计算模型,首先,使用非线性有限元法计算了斜拉桥的静力状态与动力特性,计算了列车-桥梁耦合动力作用下桥梁的振动;然后,使用向量式有限元法计算了斜拉桥在拉索突然断裂状态下的非线性振动;最后,计算了在列车-桥梁耦合动力作用下,拉索发生断裂时,桥梁与列车的振动状态。结果表明:使用向量式有限元可以简单可靠地直接模拟斜拉桥在破坏状态下的非线性振动状态;列车运行至跨中附近时,若斜拉桥跨中最长拉索突然发生断裂,对其他拉索的安全性影响不大,离断裂拉索越远的拉索受到的影响越小,但拉索突然断裂会对桥上行驶中列车的安全性造成威胁。该研究为大跨度斜拉桥在破坏状态下的非线性振动分析提供了新的解决方案。The vector form finite element(VFFE)method is essentially an explicit finite element(FE)dynamic time-history integration method considering geometric nonlinearity.Here,the basic principle of VFFE was described.Similarities and differences between the VFFE method and the nonlinear FE dynamic calculation method based on element follow-up coordinate system were compared,and the calculation program using rod and beam elements was developed in the VFFE unified algorithm framework.Using this program,the calculation model of a long-span cable-stayed bridge was established.Firstly,the static state and dynamic characteristics of a cable-stayed bridge were calculated with the nonlinear FE method,and the bridge vibration under train-bridge coupled dynamic action was calculated.Then,the nonlinear vibration of cable-stayed bridge under the condition of a cable sudden fracture was calculated with the VFFE method.Finally,vibration states of bridge and train during a cable fracture under train-bridge coupled dynamic action was calculated.The results showed that the nonlinear vibration state of cable-stayed bridge under failure state can be simulated simply and reliably by using the VFFE method;when a train passing near bridge mid-span,if the longest cable in mid span of the cable-stayed bridge suddenly breaks,the broken cable has little impact on the safety of other cables,and the farther away from it,the less its affecting on other cables,but its sudden breaking can threaten the safety of the train passing through the bridge;this study can provide a new solving scheme for analyzing nonlinear vibration of a long-span cable-stayed bridge under failure state.

关 键 词：桥梁工程 斜拉桥 向量式有限元(VFFE)法 非线性振动 拉索断裂 

分 类 号：TU311.3[建筑科学—结构工程]