基于离散时间传递矩阵法的变截面梁地震时程分析方法研究
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摘要
为提高变截面梁地震动力求解的计算效率,提出了基于离散时间传递矩阵法的时程分析方法。首先,从欧拉梁的偏微分振动方程出发,基于逐步时间积分法的线性化方法并结合张量变换原理,建立了变截面梁的动力时程计算方法;其次,考虑地震动激励的非一致输入效应,采用数值迭代求解的方式建立了变截面梁地震动力时程分析的离散时间传递矩阵算法;最后,编制了数值仿真计算程序,并结合具体算例进行了算法的有效性和高效性验证。算例结果表明:在采用相同计算模型的前提下,离散时间传递矩阵法不仅能够在计算精度方面与有限元法保持一致,同时还拥有更高的计算效率。
In order to improve the computational efficiency of seismic dynamic solution of a beam with variable cross-section,a time-history analysis method based on the discrete time transfer matrix method was proposed.Firstly,based on the partial differential vibration equation of Euler-Bernoulli beam,employing the linearization method of the step-by-step time integration and combining with the tensor transformation principle,the dynamic time-history analysis method of beam with variable cross-section was established.Secondly,considering the inconsistency input effect of ground motion excitation,the discrete time transfer matrix algorithm for seismic dynamic time-history analysis of beam with variable cross-section was established by the numeric iteration method.Finally,by means of computer program,the validity and efficiency of that method were verified.The results are as follows.Compared to the FEM,the proposed method not only has almost the same calculation accuracy but also a higher computational efficiency under the premise of adopting the same calculation model.
In order to improve the computational efficiency of seismic dynamic solution of a beam with variable cross-section,a time-history analysis method based on the discrete time transfer matrix method was proposed.Firstly,based on the partial differential vibration equation of Euler-Bernoulli beam,employing the linearization method of the step-by-step time integration and combining with the tensor transformation principle,the dynamic time-history analysis method of beam with variable cross-section was established.Secondly,considering the inconsistency input effect of ground motion excitation,the discrete time transfer matrix algorithm for seismic dynamic time-history analysis of beam with variable cross-section was established by the numeric iteration method.Finally,by means of computer program,the validity and efficiency of that method were verified.The results are as follows.Compared to the FEM,the proposed method not only has almost the same calculation accuracy but also a higher computational efficiency under the premise of adopting the same calculation model.
引文
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[10]贾宏宇,郑史雄.直接求解多维多点地震动方程的虚拟激励法[J].工程力学,2013,30(3):341-346.JIA Hongyu,ZHENG Shixiong.Pseudo excitation method of direct solving ground motion equation of multi-dimensional[J].Engineering Mechanics,2013,30(3):341-346.(in Chinese)
[11]赵雷,刘宁国.大跨度叠合梁斜拉桥多维多点非平稳随机地震响应分析[J].应用数学和力学,2017,38(1):118-125.ZHAO Lei,LIU Ningguo.Non-stationary random seismic analysis of large-span composite beam cable-stayed bridges under multi-support and multidimentional earthquake excitations[J].Applied Mathematics and Mechanics,2017,38(1):118-125.(in Chinese)
[12]王新敏.有限元工程结构数值分析[M].北京:人民交通出版社,2007:538-540
[2]RUI X T,HE B,LU Y Q,et al.Discrete time transfer matrix method for multi-body system dynamics[J].Multi-body System Dynamics,2005,14(4):317-344.
[3]RUI X T,HE B,RONG B,et al.Discrete time transfer matrix method for multi-rigid-flexible-body system moving in plane[J].Journal of MultiBody Dynamics,2009,223(1):23-42.
[4]何斌,陈树辉.连续梁瞬态振动离散时间精细传递矩阵法[J].振动与冲击,2008,24(4):4-8.HE Bin,CHEN Shuhui.Discrete-time precise transfer matrix method for transient vibration analysis of a continuous beam[J].Journal of Vibration and Shock,2008,24(4):4-8.(in Chinese)
[5]邵俊虎,向天宇,赵人达.考虑二阶效应梁柱瞬态分析的传递矩阵法[J].西南交通大学学报,2014,61(4):631-636.SHAO Junhu,XIANG Tianyu,ZHAO Renda.Transfer matrix method of beam-column transient analysis considering second-order effect[J].Journal of Southwest Jiaotong University,2014,61(4):631-636.(in Chinese)
[6]孙建鹏,李青宁.大跨桥梁地震反应的频域精细传递矩阵法[J].工程力学,2010,27(12):8-13.SUN Jianpeng,LI Qingning.Precise transfer matrix method for seismic response analysis of the long-span bridges in frenquency domain[J].Engineering Mechanics,2010.27(12):8-13.(in Chinese)
[7]芮筱亭.多体系统传递矩阵法及其应用[M].北京:科学出版社,2008:265.
[8]翟婉明,夏禾,等.列车-轨道-桥梁动力相互作用理论与工程应用[M].北京:科学出版社,2011:150-151.ZHAI Wanming,XIA He,et al.Train-track-bridge Dynamic Interaction:Theory and Engineering Application[M].BEIJING:Science Press,2011:150-151.(in Chinese)
[9]石永久,江洋,王元清.直接求解法在结构多点输入地震响应计算中的应用与改进[J].工程力学,2011,28(1):75-81.SHI Yongjiu,JIANG Yang,WANG Yuanqing.Application and improvement of direct solving method in seismic response analysis of structures under multi-support excitations[J].Engineering Mechanics,2011,28(1):75-81.(in Chinese)
[10]贾宏宇,郑史雄.直接求解多维多点地震动方程的虚拟激励法[J].工程力学,2013,30(3):341-346.JIA Hongyu,ZHENG Shixiong.Pseudo excitation method of direct solving ground motion equation of multi-dimensional[J].Engineering Mechanics,2013,30(3):341-346.(in Chinese)
[11]赵雷,刘宁国.大跨度叠合梁斜拉桥多维多点非平稳随机地震响应分析[J].应用数学和力学,2017,38(1):118-125.ZHAO Lei,LIU Ningguo.Non-stationary random seismic analysis of large-span composite beam cable-stayed bridges under multi-support and multidimentional earthquake excitations[J].Applied Mathematics and Mechanics,2017,38(1):118-125.(in Chinese)
[12]王新敏.有限元工程结构数值分析[M].北京:人民交通出版社,2007:538-540