结构随机动力激励的物理模型:以脉动风速为例
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摘要
以脉动风速为背景,展示了基于物理建立结构动力激励模型的基本思想与具体路线。根据经典湍流理论,阐述了均匀剪切湍流中的惯性子区和剪切子区所服从的物理规律,并根据物理随机系统的基本思想,建立了形式十分简单的标准化随机Fourier波数谱模型。应用概率密度演化方法,得到了剪切子区与惯性子区分界位置lc的概率分布,统计给出了基本随机变量地面粗糙度z0和标准高度10min平均风速(h)的概率分布。研究表明:基于物理的随机Fourier波数谱理论预测结果与实测Fourier波数谱的均值曲线符合良好,可望为结构抗风设计与可靠度评价提供较为合理的动力输入模型。
Taking fluctuating wind speed as example,this paper displays the basic method of modeling the structural dynamic excitation based on physical process.According to classic turbulence theory,the physical laws of inertial sub-range and shear sub-range in homogeneous shear turbulence are described.Along with the basic idea of physical stochastic system,a normalized stochastic Fourier wave-number model with simple format is established.The probability distribution of the boundary position of the shear sub-range and inertial sub-range is obtained by the Probability Density Evolution Method(PDEM) and the probability distribution of the basic variables including ground roughness z 0 and 10-min mean wind speed (h) are also obtained.The research shows that the mean spectrum of the theoretical prediction based on the physical process corresponds with the measured Fourier mean wave-number spectrum well.The model proposed here is expected to provide a reasonable excitation model for wind-resistant design and reliability analysis of structures.
Taking fluctuating wind speed as example,this paper displays the basic method of modeling the structural dynamic excitation based on physical process.According to classic turbulence theory,the physical laws of inertial sub-range and shear sub-range in homogeneous shear turbulence are described.Along with the basic idea of physical stochastic system,a normalized stochastic Fourier wave-number model with simple format is established.The probability distribution of the boundary position of the shear sub-range and inertial sub-range is obtained by the Probability Density Evolution Method(PDEM) and the probability distribution of the basic variables including ground roughness z 0 and 10-min mean wind speed (h) are also obtained.The research shows that the mean spectrum of the theoretical prediction based on the physical process corresponds with the measured Fourier mean wave-number spectrum well.The model proposed here is expected to provide a reasonable excitation model for wind-resistant design and reliability analysis of structures.
引文
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[2]Davenport A G.The spectrum of horizontal gustiness near the ground in high winds[J].Quarterly Journal of the Royal Meteorological Society,1961,372(87):194―211.
[3]Neumann G.On wind generated ocean waves with special reference to the problem of wave forecasting[R].New York:College of Engineering,Department of Meteorology,New York University,1952:136.
[4]李杰.工程结构随机动力激励的物理模型[C]//李杰,陈建兵.随机振动理论与应用进展.上海:同济大学出版社,2009.Li Jie.Physical stochastic models for the dynamic excitations of engineering structures[C]//Li Jie,Chen Jiangbing.Theory and application advances in stochastic vibration.Shanghai:Tongji University Press,2009.(in Chinese)
[5]李杰.随机动力系统的物理逼近[J].中国科技论文在线,2006,1(2):95―104.Li Jie.A physical approach to stochastic dynamical systems[J].Science Paper Online,2006,1(2):95―104.(in Chinese)
[6]李杰,艾晓秋.基于物理的随机地震动模型研究[J].地震工程与工程振动,2006,26(5):21―26.Li Jie,Ai Xiaoqiu.Study on random model of earthquake ground motion based on physical process[J].Earthquake Engineering and Engineering Vibration,2006,26(5):21―26.(in Chinese)
[7]李杰,张琳琳.实测风场的随机Fourier谱研究[J].振动工程学报,2007,20(1):66―72.Li Jie,Zhang Linlin.Random Fourier spectrum of the measured wind field[J].Journal of Vibration Engineering,2007,20(1):66―72.(in Chinese)
[8]徐亚洲,李杰.风浪相互作用的Stokes模型[J].水科学进展,2009,20(2):281―286.Xu Yazhou,Li Jie.Stokes model for wind-wave interaction[J].Advances in Water Science,2009,20(2):281―286.(in Chinese)
[9]李杰,张琳琳.脉动风速功率谱与随机Fourier幅值谱的关系研究[J].防灾减灾工程学报,2004,24(4):363―369.Li Jie,Zhang Linlin.A study on the relationship between turbulence power spectrum and stochastic Fourier amplitude spectrum[J].Journal of Disaster Prevention and Mitigation Engineering,2004,24(4):363―369.(in Chinese)
[10]李杰.随机结构系统——分析与建模[M].北京:科学出版社,1996.Li Jie.Stochastic structure system——analysis and modeling[M].Beijing:Science Press,1996.(in Chinese)
[11]Hinze J Q.Turbulence[M].New York:McGraw-Hill,1975.
[12]胡非.湍流、间歇性与大气边界层[M].北京:科学出版社,1995.Hu Fei.Turbulence,intermittency and atmospheric boundary layer[M].Beijing:Science Press,1995.(in Chinese)
[13]Katul G,Chu C R.A theoretical and experimental investigation of energy-content scales in the dynamic sublayer of boundary-layer flows[J].Boundary-Layer Meteorology,1998,86:279―312.
[14]阎启,谢强,李杰.风场长期观测与数据分析[J].建筑科学与工程学报,2009,26(1):37―42.Yan Qi,Xie Qiang,Li Jie.Long-turm observation and data analysis of wind field[J].Journal of Architecture and Civil Engineering,2009,26(1):37―42.(in Chinese)
[15]GB50009-2001,建筑结构荷载规范[S].北京:中国标准出版社,2001.GB50009-2001,Load code for the design of building structures[S].Beijing:China Standard Press,2001.(in Chinese)
[16]Li Jie,Chen Jianbing.Stochastic dynamics of structures[M].Singapore:John Wiley&Sons(Asia)Pte Ltd.,2009.
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