基于改进高斯精细积分法的车桥耦合振动分析框架
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摘要
假定任一时刻的位移可以根据其相邻时间步上的运动状态由Hermite插值函数确定,采用3节点高斯积分方法展开精细积分法中状态方程的Duhamel项,构造了一种改进的高斯精细积分算法用于求解结构非线性问题,在此基础上,提出了适用于车桥耦合振动研究的高效求解分析框架。车桥耦合系统由车辆、桥梁有限元子系统组成,其中车辆子系统引入部件刚体假定,而桥梁子系统借助于振型叠加法缩减自由度数目,两个子系统间的相互作用通过非线性的虚拟力表达。以一节4轴客车匀速通过32m简支梁为研究对象,分别采用所提出的分析框架、传统Newmark-β法进行动力分析。结果表明:相对于Newmark-β法,高斯精细积分方法既能避免求解线性方程组,又可显著提高计算收敛的积分步长,分析框架显示出良好的实用效果。
With the assumption that the displacement of any moment can be determined by the motion of its two adjacent time steps with the help of a Hermite interpolating function,an improved Gauss precise integration method is constructed to solve the structural nonlinear problems,in which the Duhamel term of a state equation of a precise time-integration method is expanded in terms of 3-node Gauss integration method.On the basis of the improved method,an efficient analysis framework for the dynamic interaction analysis of a train-bridge system is proposed.The train-bridge system consists of train subsystems and bridge subsystems,and both of them are established with the finite element method.The rigid component assumption is introduced to the train subsystem,the mode superposition method is applied to the bridge subsystem to reduce the degrees-of-freedom,and the dynamic interaction between two subsystems is expressed with nonlinear virtual forces.A 4-axle vehicle passing through a simply-supported beam with a 32m span at constant speed is taken as a case study.The dynamic analysis of the coupled system is carried out by using the proposed framework and the traditional Newmak-β method,respectively.The numerical results show that the improved Gauss precise integration method not only avoids the solution of linear equations but also improves the time interval of integration,comparing with Newmak-β method,and the framework shows good effectiveness in application.
With the assumption that the displacement of any moment can be determined by the motion of its two adjacent time steps with the help of a Hermite interpolating function,an improved Gauss precise integration method is constructed to solve the structural nonlinear problems,in which the Duhamel term of a state equation of a precise time-integration method is expanded in terms of 3-node Gauss integration method.On the basis of the improved method,an efficient analysis framework for the dynamic interaction analysis of a train-bridge system is proposed.The train-bridge system consists of train subsystems and bridge subsystems,and both of them are established with the finite element method.The rigid component assumption is introduced to the train subsystem,the mode superposition method is applied to the bridge subsystem to reduce the degrees-of-freedom,and the dynamic interaction between two subsystems is expressed with nonlinear virtual forces.A 4-axle vehicle passing through a simply-supported beam with a 32m span at constant speed is taken as a case study.The dynamic analysis of the coupled system is carried out by using the proposed framework and the traditional Newmak-β method,respectively.The numerical results show that the improved Gauss precise integration method not only avoids the solution of linear equations but also improves the time interval of integration,comparing with Newmak-β method,and the framework shows good effectiveness in application.
引文
[1]夏禾,张楠.车辆与结构相互作用[M].北京:科学出版社,2005:1―2.Xia He,Zhang Nan.Dynamic interaction of vehicle and structures[M].Beijing:Science Press,2005:1―2.(in Chinese)
[2]杜宪亭.强地震作用下大跨度桥梁空间动力效应及列车运行安全研究[D].北京:北京交通大学,2011:1―2.Du Xianting.Research on spatial dynamic effect of long-span bridge and running safety of train during strong earthquakes[D].Beijing:Beijing Jiaotong University,2011:1―2.(in Chinese)
[3]翟婉明.车辆-轨道耦合动力学[M].北京:科学出版社,2007:1―8.Zhai Wanming.Vehicle-track coupling dynamics[M].Beijing:Science Press,2007:1―8.(in Chinese)
[4]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,32(2):131―136.Zhong Wanxie.On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,32(2):131―136.(in Chinese)
[5]储德文,王元丰.精细直接积分法的积分方法选择[J].工程力学,2002,19(6):115―119.Chu Dewen,Wang Yuanfeng.Integration formula selection for precise direct integration method[J].Engineering Mechanics,2002,19(6):115―119.(in Chinese)
[6]王梦甫,周锡元.结构动力方程的高斯精细时程积分法[J].工程力学,2004,21(4):13―16.Wang Mengfu,Zhou Xiyuan.Gauss precise time integration of structural dynamic analysis[J].Engineering Mechanics,2004,21(4):13―16.(in Chinese)
[7]潘玉华,王元丰.复阻尼结构动力方程的高斯精细时程积分法[J].工程力学,2012,29(2):16―20.Pan Yuhua,Wang Yuanfeng.Gauss precise time integration of complex damping vibration system[J].Engineering Mechanics,2012,29(2):16―20.(in Chinese)
[8]吕和祥,于洪洁.精细积分的非线性动力学积分方程及其解法[J].固体力学学报,2001,22(3):303―308.LüHexiang,Yu Hongjie.An integral equation of non-linear dynamics and its solution method[J].Acta Mechanic Solid Sinica,2001,22(3):303―308.(in Chinese)
[9]王海波,余志武.非线性动力分析避免状态矩阵求逆的精细积分多步法[J].振动与冲击,2008,27(4):105―107,116,173.Wang Haibo,Yu Zhiwu.Precise integration multi-step method for nonlinear dynamic equation to avoid calculating inverse of state matrix[J].Journal of Vibration and Shock,2008,27(4):105―107,116,173.(in Chinese)
[10]徐萃薇.计算方法引论[M].高等教育出版社,2002:191.Xu Cuiwei.Computing method introduction[M].High Education Press,2002:191.(in Chinese)
[11]钟万勰.子域精细积分及偏微分方程数值解[J].计算结构力学及应用,1995,12(3):253―260.Zhong Wanxie.Subdomain precise integration method and numerical solution of partial differential equations[J].Computational Structural Mechanics and Applications,1995,12(3):253―260.(in Chinese)
[12]Wilson E L.Three-dimensional static and dynamic analysis of structures:A physical approach with emphasis on earthquake engineering[M].Computers and Structures Inc.,Berkley,California,2002:158.
[2]杜宪亭.强地震作用下大跨度桥梁空间动力效应及列车运行安全研究[D].北京:北京交通大学,2011:1―2.Du Xianting.Research on spatial dynamic effect of long-span bridge and running safety of train during strong earthquakes[D].Beijing:Beijing Jiaotong University,2011:1―2.(in Chinese)
[3]翟婉明.车辆-轨道耦合动力学[M].北京:科学出版社,2007:1―8.Zhai Wanming.Vehicle-track coupling dynamics[M].Beijing:Science Press,2007:1―8.(in Chinese)
[4]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,32(2):131―136.Zhong Wanxie.On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,32(2):131―136.(in Chinese)
[5]储德文,王元丰.精细直接积分法的积分方法选择[J].工程力学,2002,19(6):115―119.Chu Dewen,Wang Yuanfeng.Integration formula selection for precise direct integration method[J].Engineering Mechanics,2002,19(6):115―119.(in Chinese)
[6]王梦甫,周锡元.结构动力方程的高斯精细时程积分法[J].工程力学,2004,21(4):13―16.Wang Mengfu,Zhou Xiyuan.Gauss precise time integration of structural dynamic analysis[J].Engineering Mechanics,2004,21(4):13―16.(in Chinese)
[7]潘玉华,王元丰.复阻尼结构动力方程的高斯精细时程积分法[J].工程力学,2012,29(2):16―20.Pan Yuhua,Wang Yuanfeng.Gauss precise time integration of complex damping vibration system[J].Engineering Mechanics,2012,29(2):16―20.(in Chinese)
[8]吕和祥,于洪洁.精细积分的非线性动力学积分方程及其解法[J].固体力学学报,2001,22(3):303―308.LüHexiang,Yu Hongjie.An integral equation of non-linear dynamics and its solution method[J].Acta Mechanic Solid Sinica,2001,22(3):303―308.(in Chinese)
[9]王海波,余志武.非线性动力分析避免状态矩阵求逆的精细积分多步法[J].振动与冲击,2008,27(4):105―107,116,173.Wang Haibo,Yu Zhiwu.Precise integration multi-step method for nonlinear dynamic equation to avoid calculating inverse of state matrix[J].Journal of Vibration and Shock,2008,27(4):105―107,116,173.(in Chinese)
[10]徐萃薇.计算方法引论[M].高等教育出版社,2002:191.Xu Cuiwei.Computing method introduction[M].High Education Press,2002:191.(in Chinese)
[11]钟万勰.子域精细积分及偏微分方程数值解[J].计算结构力学及应用,1995,12(3):253―260.Zhong Wanxie.Subdomain precise integration method and numerical solution of partial differential equations[J].Computational Structural Mechanics and Applications,1995,12(3):253―260.(in Chinese)
[12]Wilson E L.Three-dimensional static and dynamic analysis of structures:A physical approach with emphasis on earthquake engineering[M].Computers and Structures Inc.,Berkley,California,2002:158.
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