大跨度斜拉桥风致抖振响应的非线性时程分析
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摘要
随着我国跨江海大跨度桥梁的兴建,抖振响应问题成为桥梁抗风性能研究的一个重要方面。本文以杭州湾跨海大桥南、北航道斜拉桥施工过程抗风措施研究课题为背景,进行桥梁结构抖振时域非线性分析研究,并提出切实可行的抗风措施。
采用迭代的谐波合成法拟模拟了各态历经的多变量平稳高斯随机过程。引入了频率双索引的概念来保证模拟结果的各态历经性,并综合了FFT技术改善了模拟精度,提高了模拟计算的效率,为在时域中不断变换风速进行抖振计算提供了条件。
抖振风荷载包括静力风荷载、抖振力、自激力三部分。静力风荷载用风洞试验得出的静力三分力系数计算。抖振力按Scanlan的准定常气动力公式计算,并引入Liepmann的近似公式表达的气动导纳修正。在Scanlan提出的钝体气动力公式基础上,研究了自激力时域化问题,提出了等效节点自激力法,将自激力转化为节点位移矢量及速度矢量的函数,引入气动刚度矩阵和气动阻尼矩阵,结合有限元程序实现自激力的时域化。
考虑了结构的几何非线性、由于静风位移引起的有效静力三分力系数、有效气动导数和气动导纳以及风的不同自然攻角等非线性因素,建立了全面的非线性抖振分析方法。基于APDL参数化有限元分析技术对ANSYS进行了二次开发,实现了大跨斜拉桥的非线性抖振响应时域分析。
对杭州湾跨海大桥南、北航道斜拉桥最大双悬臂状态塔底固结时线性时域分析结果与频域反映谱法的结果进行了比较,验证了程序的可靠性。进行了最大双悬臂状态非线性影响因素分析,结果表明,竖向弯曲抖振响应的最大值及均方根大于线性计算值,扭转抖振响应也略有增加。考虑风攻角变化时,抖振响应的最大值呈现增加趋势。
对南、北航道斜拉桥的不同施工控制状态分别进行了抖振响应分析,其结果与恒载内力叠加,在此基础上提出了施工阶段的抗风措施。对南航道斜拉桥最大双悬臂状态增设抗风措施后的效果进行了验算,结果表明,所采用的抗风措施提高了结构的刚度,有利于控制抖振。
The buffeting response of bridge comes to be an important aspect of the wind induced vibration control as the construction of long span bridges, which span the great river or the sea. The nonlinear buffeting analysis in the time-domain was done based on the research subject which was research of wind resistance measure of Hang Zhou bay bridge. Feasible wind resistance measures were given.
The ergodic multi variable Gaussian random process was simulated by the iterative WAWS. The concept of frequency double index was imported to assure the ergodicity of results. The simulating precision was improved by using the technology of FFT. At the same time, the efficiency of simulating calculation was improved. It was convenient for the nonlinear buffeting analysis in the time-domain under different wind speeds.
Buffeting wind load includes static wind force, buffeting force and full coupled auto-excited load. The three-component coefficients were used to calculate static wind force. The buffeting force was calculated by the quasi-steady aerodynamic formula deduced by Scanlan and the approximate formula deduced by Liepmann was used to compute the aerodynamic admittance. Based on the blunt body aerodynamic formula deduced by Scanlan, the full coupled auto-excited load in the time domain was analysis. The equivalent nodal full coupled auto-excited load method was given to translate full coupled auto-excited load to function of nodal displacement vector and velocity vector. To implement the analysis in the time domain of full coupled auto-excited load, the finite element procedure was used by importing the aerodynamic stiffness matrix and aerodynamic damping matrix.
The method of nonlinear buffeting analysis considering the structural geometric nonlinearity, the static 3-component coefficients, effective flutter derivatives, aerodynamic admittance function and angle of wind attack was established. The secondary development of ANSYS was done by the APDL parametric finite element analysis method to implement the nonlinear buffeting analysis in the time domain of the long span cable bridge.
The linear time-domain results of Hang Zhou bay bridge under the double jib condition were compared with that from the response spectrum method in the frequency domain. The compared results showed the finite element analysis result was reliable. The nonlinear influencing factor analysis results showed the maximum of vertical buckling buffeting response and root-mean-square was greater than the linear result. The maximum of buffeting response was presented increment tendency by the change of angle of wind attack.
The buffeting response analysis of the south and North Channel cable bridges was done under different construct condition. The wind resistance measures were given by the analysis result. The North Channel cable bridge was analyzed after taking measures, the results showed the wind resistance measures increased the stiffness of structure and controlled the buffeting of the bridge.
采用迭代的谐波合成法拟模拟了各态历经的多变量平稳高斯随机过程。引入了频率双索引的概念来保证模拟结果的各态历经性,并综合了FFT技术改善了模拟精度,提高了模拟计算的效率,为在时域中不断变换风速进行抖振计算提供了条件。
抖振风荷载包括静力风荷载、抖振力、自激力三部分。静力风荷载用风洞试验得出的静力三分力系数计算。抖振力按Scanlan的准定常气动力公式计算,并引入Liepmann的近似公式表达的气动导纳修正。在Scanlan提出的钝体气动力公式基础上,研究了自激力时域化问题,提出了等效节点自激力法,将自激力转化为节点位移矢量及速度矢量的函数,引入气动刚度矩阵和气动阻尼矩阵,结合有限元程序实现自激力的时域化。
考虑了结构的几何非线性、由于静风位移引起的有效静力三分力系数、有效气动导数和气动导纳以及风的不同自然攻角等非线性因素,建立了全面的非线性抖振分析方法。基于APDL参数化有限元分析技术对ANSYS进行了二次开发,实现了大跨斜拉桥的非线性抖振响应时域分析。
对杭州湾跨海大桥南、北航道斜拉桥最大双悬臂状态塔底固结时线性时域分析结果与频域反映谱法的结果进行了比较,验证了程序的可靠性。进行了最大双悬臂状态非线性影响因素分析,结果表明,竖向弯曲抖振响应的最大值及均方根大于线性计算值,扭转抖振响应也略有增加。考虑风攻角变化时,抖振响应的最大值呈现增加趋势。
对南、北航道斜拉桥的不同施工控制状态分别进行了抖振响应分析,其结果与恒载内力叠加,在此基础上提出了施工阶段的抗风措施。对南航道斜拉桥最大双悬臂状态增设抗风措施后的效果进行了验算,结果表明,所采用的抗风措施提高了结构的刚度,有利于控制抖振。
The buffeting response of bridge comes to be an important aspect of the wind induced vibration control as the construction of long span bridges, which span the great river or the sea. The nonlinear buffeting analysis in the time-domain was done based on the research subject which was research of wind resistance measure of Hang Zhou bay bridge. Feasible wind resistance measures were given.
The ergodic multi variable Gaussian random process was simulated by the iterative WAWS. The concept of frequency double index was imported to assure the ergodicity of results. The simulating precision was improved by using the technology of FFT. At the same time, the efficiency of simulating calculation was improved. It was convenient for the nonlinear buffeting analysis in the time-domain under different wind speeds.
Buffeting wind load includes static wind force, buffeting force and full coupled auto-excited load. The three-component coefficients were used to calculate static wind force. The buffeting force was calculated by the quasi-steady aerodynamic formula deduced by Scanlan and the approximate formula deduced by Liepmann was used to compute the aerodynamic admittance. Based on the blunt body aerodynamic formula deduced by Scanlan, the full coupled auto-excited load in the time domain was analysis. The equivalent nodal full coupled auto-excited load method was given to translate full coupled auto-excited load to function of nodal displacement vector and velocity vector. To implement the analysis in the time domain of full coupled auto-excited load, the finite element procedure was used by importing the aerodynamic stiffness matrix and aerodynamic damping matrix.
The method of nonlinear buffeting analysis considering the structural geometric nonlinearity, the static 3-component coefficients, effective flutter derivatives, aerodynamic admittance function and angle of wind attack was established. The secondary development of ANSYS was done by the APDL parametric finite element analysis method to implement the nonlinear buffeting analysis in the time domain of the long span cable bridge.
The linear time-domain results of Hang Zhou bay bridge under the double jib condition were compared with that from the response spectrum method in the frequency domain. The compared results showed the finite element analysis result was reliable. The nonlinear influencing factor analysis results showed the maximum of vertical buckling buffeting response and root-mean-square was greater than the linear result. The maximum of buffeting response was presented increment tendency by the change of angle of wind attack.
The buffeting response analysis of the south and North Channel cable bridges was done under different construct condition. The wind resistance measures were given by the analysis result. The North Channel cable bridge was analyzed after taking measures, the results showed the wind resistance measures increased the stiffness of structure and controlled the buffeting of the bridge.
引文
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[2]Davenport A G.The application of statistical concepts to the wind loading of structures[J].Proc ICE,1961,19:449-472.
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[11]Augusti G.,et al.On the time-domain analysis of three-dimensional beam structures[J].Journal of Wind Engineering and Industrial Aerodynamics,1986,23.
[12]Borri C.,Zahlten W.Fully simulated nonlinear analysis of large structures subjected to turbulent artificial wind[J].Mech.Struct.& Mach.,1991,19(2):213-250.
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[31]Deodatis, G. Simulation of Ergodic Multivariate Stochastic Processes[J]. Journal of Engineering Mechanics, 1996, 122(8).
[32] 何光渝. Visual C++常用数值算法集[M]. 北京:科学出版社, 2002.
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[35] Spanos, P-T. D., Schultz, K. P. Numerical synthesis of trivariate velocity realizations of turbulence[J]. International Journal of Nonlinear Mechanics, 1986, 21(4): 269-277.
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[2]Davenport A G.The application of statistical concepts to the wind loading of structures[J].Proc ICE,1961,19:449-472.
[3]Davenport A G.The response of slender line-like structures to a gusty wind[J].Proc ICE,1962,23.
[4]Davenport A G.The action of wind on suspension bridges[C].Proc.Int'l.Symposium on Suspension Bridges,Lisbon,Portugal,1966.
[5]Davenport A G.The dependence of wind load upon meteorological parameters[J].Proceedings of the international Research Seminar on Wind Effects on Buildings and Structures,University of Toronto Press,Toronto,1968,19-82.
[6]Davenport A G.,et al.A study of wind action on a suspension bridge during erection and on completion[J].Rep.BLWT-3-69,Boundary Layer Tunnel Lab,Univ.of Western Ontario,London,Canada,1969,5.
[7]Jain A,Jones N P,Scanlan R H.Coupled flutter and buffeting analysis of long-span bridges[J].J Struct Engrg ASCE,1996,122(7):716-725.
[8]Lin,Y.K.Motion of suspension bridges in turbulent wind[J].J.of the Engrg.Mech.Div.,ASCE,1979,105(6).
[9]陈伟.大跨度桥梁抖振反映谱研究[D].同济大学博士学位论文,1993.
[10]Xiang H.F.Buffeting response analysis and control of long-span bridges[J].Development of wind Engineering:State-of-the-art,Davenport.
[11]Augusti G.,et al.On the time-domain analysis of three-dimensional beam structures[J].Journal of Wind Engineering and Industrial Aerodynamics,1986,23.
[12]Borri C.,Zahlten W.Fully simulated nonlinear analysis of large structures subjected to turbulent artificial wind[J].Mech.Struct.& Mach.,1991,19(2):213-250.
[13]Santos et al.Gust response of a long-span bridge by the time-domain approach[C].Third Asia-Pacitic Symposium on Wind Engineering,Dec,13-15,Hong Kong,1993.
[14]Kovacs,I.,et al.Analytical aerodynamic investigation of cable-stayed helgeland bridge[J].Journal of Structural Engineering,1992,118(1).
[15]Boonyapinyo V.,Miyata T.,Yamada H.Analysis of cable-supported bridges under wind load,part Ⅰ ultimate strength.
[16]Boonyapinyo V.,Miyata T.,Yamada H.Analysis of cable-supported bridges under wind load,part Ⅱ combined flutter and buffeting response in time domain.
[17]周述华.大跨度悬索桥空间非线性抖振响应仿真分析[D].成都:西南交通大学,1993.
[18]刘春华.多个互相关随机过程的计算机模拟及其应用[J].同济大学学报,1994,22(增).
[19]刘春华.大跨度桥梁抖振响应的非线性时程分析[D].上海:同济大学,1995.
[20]刘春华,项海帆,顾明.大跨度桥梁抖振响应的空间非线性时程分析法[J].同济大学学报,1996,24(4).
[21]Scanlan R H,Jones R H.Motion of suspended bridge spans under gusty wind[J].J Struct Engrg Div ASCE,1977,103(9):1867-1883.
[22]埃米尔.希缪,罗伯特.H.斯坎伦.风对结构的作用[M].刘尚培,项海帆,谢霁明.上海:同济大学出版社,1992.
[23]项海帆,林志兴.公路桥梁抗风设计指南[S].北京:人民交通出版社,1996.
[24]Li Mingshui,He Dexin.Numerical simulation of natural wind field[J].空气动力学学报,1999,17(1):44-51.
[25]Rice,S.O.Mathematical analysis of random noise[C].Selected papers on noise and stochastic processes,N.Wax,ed.,Dover Publish Inc.,New York,N.Y.,1954,133-294.
[26]Shinozuka,M.,and Jan,C.M.Digital simulation of random processes and its applications[J].Journal of Sound and Vibraton,1972,25(1):111-128.
[27]Yang,J.N.Simulation of random envelope processes[J].Journal of Sound and Vibration,1972,25(1):73-85.
[28]Shinozuka,M.Digital simulation of random processes in engineering mechanics with the aid of FFT technique[J].Stochastic problems in mechanics,S.T.Ariaratnam and H.H.E.Leipholz,eds.,University of Waterloo Press,Walterloo,Cananda,1974:277-286.
[29]Yamazaki,F,and Shinozuha,M.Digital generation of non-Gaussian stochastic fields[J].Journal of Engineering Mechanics,ASCE,1988,114(7):1189-1197.
[30]Shinozuka, M., Kamata, M., and Yan, C.B. Simulation of earthquake ground motion as multi-variate stochastic process[J]. Tech. Rep. No. 1989.5. Princeton-Kajima Joint Res.,Dept. of Civ. Engrg. and Operations Res. Princeton University, Princeton, N. J., 1989.
[31]Deodatis, G. Simulation of Ergodic Multivariate Stochastic Processes[J]. Journal of Engineering Mechanics, 1996, 122(8).
[32] 何光渝. Visual C++常用数值算法集[M]. 北京:科学出版社, 2002.
[33] Spanos, P-T. D., Hansen, J. E. Linear prediction theory digital simulation of sea waves[J].Journal of Energy Resources Technology, 1981, 103: 243-249.
[34] Samii, K., Vandiver, J. K. A numerically efficient technique for simulation of random wave forces on offshore structures[J]. Proceedings of the sixteenth annual offshore technology conference in Houston, TX, 1984, OTC 4811: 301-305.
[35] Spanos, P-T. D., Schultz, K. P. Numerical synthesis of trivariate velocity realizations of turbulence[J]. International Journal of Nonlinear Mechanics, 1986, 21(4): 269-277.
[36]Mignolet, M. P., Spanos, P.-D. T. Recursive simulation of stationary multivariate random processes- part I[J]. Journal of Applied Mechanics, ASME, 1987, 54.
[37]A.G. Davenport. The spectrum of horizontal gustness near the ground in high winds[J].Quarterly Journal of Royal Meterological Society, 1961, 81.
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