状态空间法分析大跨度桥梁的地震反应
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摘要
大跨度桥梁,作为交通枢纽工程和生命线工程的重要组成部分,如何提高其抗震安全性一直是工程界普遍关注的焦点问题,其中一个主要方面就是地震反应分析方法。状态空间法来源于现代控制论,是现代控制论的标志,借助于电子计算机的发展,研究设计复杂的动力学系统。状态空间法分析大跨度桥梁的地震反应,其实质是时程分析法,通过状态向量把运动基本方程转化成状态空间方程,再把状态空间方程离散化求解。
本论文正是在有限元和状态空间理论上利用MATLAB语言编程分析大跨度桥梁的地震反应,其主要工作内容有;
1.把结构反应的总位移分为拟静态位移和动力相对位移,推导了多点地震激励下大跨度桥梁的基本运动方程,通过状态向量转化成状态空间方程。
2.介绍了状态空间法的基本理论,计算动力响应迭代格式以及状态转换矩阵的算法。在有限元及状态空间法的基础上用MATLAB语言编写了大跨度斜拉桥空间模型地震反应分析程序,并以算例进行了验证。
3.利用分析软件ANSYS,通过适当简化建立大跨度斜拉桥的结构模型,作为进行动力分析的基础,计算斜拉桥的自振特性。
4.利用程序和ANSYS软件对大跨度斜拉桥在一致激励和行波效应下作了地震反应分析,用此检验程序并作比较。同时也用此程序和ANSYS对大跨度斜拉桥进行了一维、二维、三维地震反应分析比较。
As an important part of the traffic key projects and the lifeline engineering, how to improve the seismic safety of long-span bridges is always the focus problem to be paid more attention in the engineering field, in which seismic response analysis method is a main aspect. State space method from the modern cybernetics, as the symbol of the modern cybernetics, recurs to the development of the electronic computer, and studies complicated dynamic system. State space method analyzed the seismic response of long-span bridges in nature is the time history method, and in this method, the motion equations are transformed to state space equations discretely solved by the state vectors.
In this thesis, the finite element method and state space theory were used to solve the seismic response of long-span bridges. This paper is mainly concerned with the following studies:
1. The displacement of the structure response was decomposed to the quasi-static and dynamic displacement, and the equations of motion of long-span bridges, subjected to seismic multi-support excitation, are deduced, which are transformed to the state space equations by the state vectors.
2. The basis theory of state space method, the dynamic iterative method and state transform matrix solution were presented. On the base of the finite element method, 3 dimension seismic response analysis model of the long-space cable-stayed bridge was programmed in MATLAB and was verified by using the numerical example.
3. Using ANSYS, the properly simplified model of the long-space cable-stayed bridge was analyzed and its dynamic properties were calculated.
4. the seismic response analysis of the long-span bridges was calculated under the traveling wave effect and consistent excitation respectively by the MATLAB program and ANSYS. At the same time, the 1-D, 2-D, 3-D seismic response analysis in MATLAB and ANSYS was compared.
本论文正是在有限元和状态空间理论上利用MATLAB语言编程分析大跨度桥梁的地震反应,其主要工作内容有;
1.把结构反应的总位移分为拟静态位移和动力相对位移,推导了多点地震激励下大跨度桥梁的基本运动方程,通过状态向量转化成状态空间方程。
2.介绍了状态空间法的基本理论,计算动力响应迭代格式以及状态转换矩阵的算法。在有限元及状态空间法的基础上用MATLAB语言编写了大跨度斜拉桥空间模型地震反应分析程序,并以算例进行了验证。
3.利用分析软件ANSYS,通过适当简化建立大跨度斜拉桥的结构模型,作为进行动力分析的基础,计算斜拉桥的自振特性。
4.利用程序和ANSYS软件对大跨度斜拉桥在一致激励和行波效应下作了地震反应分析,用此检验程序并作比较。同时也用此程序和ANSYS对大跨度斜拉桥进行了一维、二维、三维地震反应分析比较。
As an important part of the traffic key projects and the lifeline engineering, how to improve the seismic safety of long-span bridges is always the focus problem to be paid more attention in the engineering field, in which seismic response analysis method is a main aspect. State space method from the modern cybernetics, as the symbol of the modern cybernetics, recurs to the development of the electronic computer, and studies complicated dynamic system. State space method analyzed the seismic response of long-span bridges in nature is the time history method, and in this method, the motion equations are transformed to state space equations discretely solved by the state vectors.
In this thesis, the finite element method and state space theory were used to solve the seismic response of long-span bridges. This paper is mainly concerned with the following studies:
1. The displacement of the structure response was decomposed to the quasi-static and dynamic displacement, and the equations of motion of long-span bridges, subjected to seismic multi-support excitation, are deduced, which are transformed to the state space equations by the state vectors.
2. The basis theory of state space method, the dynamic iterative method and state transform matrix solution were presented. On the base of the finite element method, 3 dimension seismic response analysis model of the long-space cable-stayed bridge was programmed in MATLAB and was verified by using the numerical example.
3. Using ANSYS, the properly simplified model of the long-space cable-stayed bridge was analyzed and its dynamic properties were calculated.
4. the seismic response analysis of the long-span bridges was calculated under the traveling wave effect and consistent excitation respectively by the MATLAB program and ANSYS. At the same time, the 1-D, 2-D, 3-D seismic response analysis in MATLAB and ANSYS was compared.
引文
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[10]史志利,李忠献.随机地震动场多点激励下大跨度桥梁抗震分析方法.地震工程与工程振动,2003,23(4):124-130
[11]李忠献,史志利.行波激励下大跨度连续刚构桥的地震反应分析.地震工程与工程振动,2003,23(2):68-76
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[16]屈铁军,王前信.多点输入地震反应分析研究的进展.世界地震工程, 1993(1)
[17]张治勇,孙柏涛,宋天舒.新抗震规范地震动功率谱模型参数的研究.世界地震工程,Vol.16,No.3,2000,33-38
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[19]项海帆.斜张桥在行波作用下的地震反应[J].同济大学学报,1983,(2):1-9
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[22]Nazmy A S,Abdel-GhfforA M.Effect of ground motio spatial variabil ity on the response of cable-stayed bridges[J]EESD,1992,21:120
[23]刘吉柱.大跨度拱桥地震反应的行波效应分析[D].上海:同济大学桥梁工程系,1987
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[25]王前信,伍国,李云林.拱式结构对地震多支点输入的反应[J].地震工程与工程振动,1984,4(2):49-81
[26]陈厚群,侯顺载,王均.拱坝自由场地震输入和反应[J].地震工程和工程振动,1990,10(2):53-64
[27]A Der Kiureghian and A Neuenhofer,Response Spectrum Method for Multi-support Seismic Excitations,Earthquake Eng.Struct.Dyn.1992,vo 1.21:713-740
[28]E H Zavoni,E H Vanmarcke,Seismic Random Vibation Analysisof M ulti-supported Structural Systems,ASCEJ.of Engineering Mechanics.1994,vol.120:1107-1128
[29]Dumanoglu A A,Severn R T,Stochastic response of suspension bfidg es toEarthquakeforces,EarthquakeEngineeringandStructuralDynamics,1990,19:133-152
[30]王君杰,王前信,江近仁.大跨拱桥在空间变化地震动下的响应.振动工程学报,vol.8,No 2,1995,119-126
[31]李建俊,林家浩,张文首.大跨度结构受多点随机地震激励的响应.计算结 构力学及其应用,Vol.12,No.4,1995,445-451
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