大跨度桥梁各态历经脉动风场的数值模拟分析
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摘要
基于本征正交分解(proper orthogonal decomposition,POD)的谱表示法,结合大跨度桥梁脉动风场的特点,推导出一种以互谱密度矩阵为POD对象的脉动风场模拟简化公式.采用以能量评判为准则的误差精确公式,对特征值合理截断阶数进行估计.引入双索引频率,实现了模拟样本的各态历经性.采用快速傅里叶变换(fast Fourier transform,FFT)对算法加速,给出了简化模拟公式在FFT算法下的具体表达式,便于程序编制.利用该法模拟了一座大跨度铁路连续刚构桥的主梁脉动风场,所得样本自功率谱和互功率谱均与目标谱吻合良好,验证了该方法的有效性和正确性.对算法的合成速度进行了分析,指出控制算法速度的关键在于矩阵的正交分解.
On the basis of the spectral representation method with proper orthogonal decomposition(POD),considering the features of fluctuating wind field of long-span bridges,a reduction simulated formula of fluctuating wind field,which considered the cross-spectral density matrix as the POD object,was deduced.The equation of end error calculation based on the energy criterion was adopted to estimate the rational truncation item number of eigenvalues.And by introducing the double-indexing of the frequencies,the simulation of ergodic time domain series was achieved.Also,the Fast Fourier Transform was adopted to improve calculation efficiency,and the improved formula based on the Fast Fourier Transform was deduced in order to program expediently.In addition,the algorithm was applied to simulate the beam stochastic wind field of a long-span railway continuous rigid frame bridge.The auto-power spectral density and cross-power spectral density of the simulated time domain samples show good agreement with target spectrum,which can verify the effectiveness and correctness of the algorithm.Finally,the algorithm resultant velocity of wind field was analyzed.Results indicate that the key point of influencing the algorithm calculation efficiency is the POD velocity of matrix.
On the basis of the spectral representation method with proper orthogonal decomposition(POD),considering the features of fluctuating wind field of long-span bridges,a reduction simulated formula of fluctuating wind field,which considered the cross-spectral density matrix as the POD object,was deduced.The equation of end error calculation based on the energy criterion was adopted to estimate the rational truncation item number of eigenvalues.And by introducing the double-indexing of the frequencies,the simulation of ergodic time domain series was achieved.Also,the Fast Fourier Transform was adopted to improve calculation efficiency,and the improved formula based on the Fast Fourier Transform was deduced in order to program expediently.In addition,the algorithm was applied to simulate the beam stochastic wind field of a long-span railway continuous rigid frame bridge.The auto-power spectral density and cross-power spectral density of the simulated time domain samples show good agreement with target spectrum,which can verify the effectiveness and correctness of the algorithm.Finally,the algorithm resultant velocity of wind field was analyzed.Results indicate that the key point of influencing the algorithm calculation efficiency is the POD velocity of matrix.
引文
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[11]HU Liang,LI Li,FAN Jian,et al.Simulation of ergodicwind field using proper orthogonal decomposition-basedspectral representation method[J].Journal of VibrationEngineering,2008,21(2):185-190.(in Chinese)胡亮,李黎,樊剑,等.用特征正交分解对各态历经风场的模拟研究[J].振动工程学报,2008,21(2):185-190.
[12]LI Li,HU Liang,FAN Jian,et al.Wind field simulationfor bridges with wind passage effects by using spectral rep-resentation method based on proper orthogonal decomposi-tion(POD)[J].Journal of Vibration and Shock,2007,26(5):14-18.(in Chinese)李黎,胡亮,樊剑,等.具有桥塔风效应的桥梁风场数值模拟[J].振动与冲击,2007,26(5):14-18.
[13]HU Liang,GU Ming,LI Li.Errors produced with properorthogonal decomposition-based spectral representationmethod in wind velocity field simulation[J].Journal ofVibration and Shock,2011,30(4):12-20.(in Chi-nese)胡亮,顾明,李黎.基于本征正交分解的谱表示法模拟风场的误差[J].振动与冲击,2011,30(4):12-20.
[14]Di Paola M.Digital simulation of wind field velocity[J].Journal of Wind Engineering and Industrial Aerodynamics,1998,74-76(1):91-109.
[15]ZOU Xiao-jiang.Wind Induced Vibration Analysis in TimeDomain and Aerostatic Stability Study for Cable-stayedBridge[D].Guangzhou:South China University andTechnology,2003:26-27.(in Chinese)邹小江.斜拉桥风振响应时域分析及静风稳定性研究[D].广州:华南理工大学,2003:26-27.
[16]JTG/T D60-O1-2004.Wind-resistant Design Code forHighway Bridges[S].(in Chinese)JTG/T D60-O1-2004.公路桥梁抗风设计规范[S].
[17]Simu E,Scanlan R H.Wind Effects on Structures[M].New York:John Wiley&Sons,1986.
[2]CAO Ying-hong,XIANG Hai-fan,ZHOU Ying.Randomsimulation of wind turbulence field for a long-span bridge[J].China Civil Engineering Journal,1998,31(3):72-79.(in Chinese)曹映泓,项海帆,周颖.大跨度桥梁随机风场的模拟[J].土木工程学报,1998,31(3):72-79.
[3]Shinozuka M,Deodatis G.Simulation of stochastic proces-ses by spectral representation[J].Applied Mechanics Re-views,1991,44(4):191-203.
[4]Deodatis G.Simulation of ergodic multivariate stochasticprocesses[J].Journal of Engineering Mechanics,1996,122(8):778.
[5]DING Shun-quan,CHEN Ai-rong,XIANG Hai-fan.Simu-lation of spatial fluctuating wind field on long span bridges[J].Chinese Quarterly of Mechanics,2006,27(2):184-189.(in Chinese)丁顺泉,陈艾荣,项海帆.大跨度桥梁空间脉动风场的计算机模拟[J].力学季刊,2006,27(2):184-189.
[6]LUO Jun-jie,HAN Da-jian.A fast simulation method ofstochastic wind fileld for long-span structures[J].Engi-neering Mechanics,2008,25(3):96-101.(in Chinese)罗俊杰,韩大建.大跨度结构随机脉动风场的快速模拟方法[J].工程力学,2008,25(3):96-101.
[7]LUO Jun-jie,HAN Da-jian.Simulation method for 3-Dstochastic wind field around long-span structures[J].Journal of Vibration and Shock,2008,27(3):87-91.(in Chinese)罗俊杰,韩大建.大跨度结构三维随机脉动风场的模拟方法[J].振动与冲击,2008,27(3):87-91.
[8]Chen X,Kareem A.Proper orthogonal decomposition-based modeling,analysis,and simulation of dynamic windload effects on structures[J].Journal of Engineering Me-chanics,2005,131(4):325-339.
[9]Hu Liang,Li Li,Fan Jian,et al.Coherency matrix-basedproper orthogonal decomposition with application to windfield simulation[J].Earthquake Engineering and Engi-neering Vibration,2006,5(2):267-272.
[10]HU Liang,LI Li,FAN Jian.Digital simulation of bridgewind fields based on spectral representation method withproper orthogonal[J].Journal of Wuhan University ofTechnology Transportation Science and Engineering,2008,32(1):16-19.(in Chinese)胡亮,李黎,樊剑.基于特征正交分解的桥梁风场模拟[J].武汉理工大学学报交通科学与工程版,2008,32(1):16-19.
[11]HU Liang,LI Li,FAN Jian,et al.Simulation of ergodicwind field using proper orthogonal decomposition-basedspectral representation method[J].Journal of VibrationEngineering,2008,21(2):185-190.(in Chinese)胡亮,李黎,樊剑,等.用特征正交分解对各态历经风场的模拟研究[J].振动工程学报,2008,21(2):185-190.
[12]LI Li,HU Liang,FAN Jian,et al.Wind field simulationfor bridges with wind passage effects by using spectral rep-resentation method based on proper orthogonal decomposi-tion(POD)[J].Journal of Vibration and Shock,2007,26(5):14-18.(in Chinese)李黎,胡亮,樊剑,等.具有桥塔风效应的桥梁风场数值模拟[J].振动与冲击,2007,26(5):14-18.
[13]HU Liang,GU Ming,LI Li.Errors produced with properorthogonal decomposition-based spectral representationmethod in wind velocity field simulation[J].Journal ofVibration and Shock,2011,30(4):12-20.(in Chi-nese)胡亮,顾明,李黎.基于本征正交分解的谱表示法模拟风场的误差[J].振动与冲击,2011,30(4):12-20.
[14]Di Paola M.Digital simulation of wind field velocity[J].Journal of Wind Engineering and Industrial Aerodynamics,1998,74-76(1):91-109.
[15]ZOU Xiao-jiang.Wind Induced Vibration Analysis in TimeDomain and Aerostatic Stability Study for Cable-stayedBridge[D].Guangzhou:South China University andTechnology,2003:26-27.(in Chinese)邹小江.斜拉桥风振响应时域分析及静风稳定性研究[D].广州:华南理工大学,2003:26-27.
[16]JTG/T D60-O1-2004.Wind-resistant Design Code forHighway Bridges[S].(in Chinese)JTG/T D60-O1-2004.公路桥梁抗风设计规范[S].
[17]Simu E,Scanlan R H.Wind Effects on Structures[M].New York:John Wiley&Sons,1986.
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