《结构防灾技术》课程教学课件（讲稿）第三篇 结构抗风 Wind-resistant structure 第十章 脉动风的概率特性 Probabilistic Characteristic of fluctuating wind

第章脉动风的概率特性Chapter 1o Probabilistic Characteristic offluctuating wind10.1脉动风的概率分布10.1 Probabilistic distribution of fluctuating wind脉动风反映了大气边界层中自然风的瑞流特性Fluctuatingwindreflectsthefluctuatingcharacteristicsofnatural windturbulence in the atmospheric boundary layer风速的脉动特性对工程结构的作用十分重要Thefluctuationcharacteristic of wind is very important to engineeringstructures刚性结构要受到脉动风速所产生的阵风荷载Rigidstructures are subject to gust loading generated byfluctuating wind柔性结构在脉动风速作用下会发生动力响应Flexiblestructuresproducedynamicresponseunderfluctuatingwind

第十章 脉动风的概率特性 Chapter 10 Probabilistic Characteristic of fluctuating wind 10.1 脉动风的概率分布 10.1 Probabilistic distribution of fluctuating wind  脉动风反映了大气边界层中自然风的湍流特性 Fluctuating wind reflects the fluctuating characteristics of natural wind turbulence in the atmospheric boundary layer  风速的脉动特性对工程结构的作用十分重要 The fluctuation characteristic of wind is very important to engineering structures  刚性结构要受到脉动风速所产生的阵风荷载 Rigid structures are subject to gust loading generated by fluctuating wind  柔性结构在脉动风速作用下会发生动力响应 Flexible structures produce dynamic response under fluctuating wind

Chapter 10 Probabilistic Characteristic offluctuating wind10.1Probabilistic distribution of fluctuating wind柔性结构的空气动力特征的参数可以分为能量特征参数和空间特征参数Theaerodynamiccharacteristicparametersofflexiblestructures can be described by energy characteristicparameters and spatial characteristic parameters能量参数：流度、脉动风功率谱Energy parameters : turbulence intensity,wind power spectrum■空间参数：流积分尺寸、空间相关性。Space parameters : turbulence integral dimension, spatialcorrelation

Chapter 10 Probabilistic Characteristic of fluctuating wind 10.1 Probabilistic distribution of fluctuating wind  柔性结构的空气动力特征的参数可以分为能量特征参数和空间 特征参数 The aerodynamic characteristic parameters of flexible structures can be described by energy characteristic parameters and spatial characteristic parameters.  能量参数：湍流度、脉动风功率谱 Energy parameters : turbulence intensity, wind power spectrum  空间参数：湍流积分尺寸、空间相关性。 Space parameters : turbulence integral dimension, spatial correlation

10.1 Probabilistic distribution of fluctuatingwind对风速记录的分析表明，如果忽略初始阶段的严重非平稳区域，脉动风十分接近于平稳随机过程，它的概率密度很接近于正态分布Wind speed record analysis shows that if the seriousnon-stationary parts is ignored in the initial phase , thefluctuating wind is very close to stationary randomprocess, the probability distribution is very close tonormal distribution, =[ ()-] a-{u(0)al]纵向longiudinal横向voa宁lateral平时工竖直向Tw'alvertical

10.1 Probabilistic distribution of fluctuating wind  对风速记录的分析表明，如果忽略初始阶段的严重非平稳区域 ，脉动风十分接近于平稳随机过程，它的概率密度很接近于正 态分布  Wind speed record analysis shows that if the serious non-stationary parts is ignored in the initial phase，the fluctuating wind is very close to stationary random process, the probability distribution is very close to normal distribution

10.1脉动风的概率分布10.1 Probabilisticdistributionof fluctuatingwind瑞流度（Turbulenceintensity）描述脉动风强度的重要参数，是衡量脉动风能量大小的标志TheFactorthat descriptsthe strengthoffluctuatingwind.It isacriteria for measuring the energy of fluctuating windu==w=为脉动风速的根方差；为平均风速oisthestandarddeviationoffluctuatingwindanduisthemeanwindspeedAU 1996Tested无量纲的瑞流度随高度增加而减小6The turbulence intensitywithout dimension decreases50withincreasingaltitude40其具体分布规律与地貌有关Thespecificdistributionruleisrelatedtothelandforms36靠近地面一般可达20%以上。20The intensity can exceed 20 percent close to the groundA10AAA01015202530lu/%

10.1 脉动风的概率分布 10.1 Probabilistic distribution of fluctuating wind

10.1脉动风的概率分布10.1 Probabilistic distribution of fluctuatingwind一些国家的规范（如日本、澳大利亚）中给出了不同地貌条件下纵向脉动风流度随高度的变化Thecodes inothercountries such as JapanandAustraliagivesthe longitudinalfluctuating wind turbulence under differentgeomorphologicalconditions varying with height我国《建筑物荷载规范》并没有明确规定，但隐含采用下式ChineseLoad Code for the design of building has no specificregulations but implicitly recommends adopting the followingformulaIu= 0. 1(z/ Hc)-α-0.05《公路桥梁抗风设计指南》给出了建议值Wind-resistentDesign SpecificationforHighway Bridgesgivesthe recommendvaluesI, = 0.88lu Iw = 0.50u

10.1 脉动风的概率分布 10.1 Probabilistic distribution of fluctuating wind

Chapter 10 Probabilistic Characteristicoffluctuating wind10.1月脉动风的概率分布10.1Probabilistic distribution of fluctuating wind35040011350中国公路桥梁中国公路桥梁1300抗风设计规范抗风设计规范1中国建筑结构对数律，B=1.8300荷载规范中国建筑结构250日本建筑规范荷载规苑日本建筑规范250200三E200NN1501501001005050市10106868101214161820222426283022101214161820B类地貌I（%)C类地貌I（%

Chapter 10 Probabilistic Characteristic of fluctuating wind 10.1 脉动风的概率分布 10.1 Probabilistic distribution of fluctuating wind

10.1脉动风的概率分布10.1 Probabilisticdistribution of fluctuatingwind流积分长度（Turbulenceintegrallength）通过某一点气流中的速度脉动可以认为是由平均风所运输的一些理想涡旋叠加而引起的，若定义涡旋的波长就是涡旋大小的量度，紊流积分尺度则是气流中流涡旋平均尺寸的量度。The velocity fluctuation passing through a point canbe recognized as the Superposition of the ideal vortextransported by mean wind. If the wavelength isdefined as the measurement of vertex size,Turbulence integral length is the measurement ofaverage size of the turbulent vortex in the airflow

 湍流积分长度（Turbulence integral length） 通过某一点气流中的速度脉动可以认为是由平均风所运输 的一些理想涡旋叠加而引起的，若定义涡旋的波长就是涡旋 大小的量度，紊流积分尺度则是气流中湍流涡旋平均尺寸的 量度。 The velocity fluctuation passing through a point can be recognized as the Superposition of the ideal vortex transported by mean wind. If the wavelength is defined as the measurement of vertex size, Turbulence integral length is the measurement of average size of the turbulent vortex in the airflow. 10.1 脉动风的概率分布 10.1 Probabilistic distribution of fluctuating wind

10.1脉动风的概率分布10.1 Probabilistic distribution of fluctuatingwind流积分长度从数学上可定义为Themathematicaldefinitionofturbulence integral can be defined as follow:1ww(x)dx(y)dy2(z)dzCL(z)dz(x)dxL(y)dyLm(z)dz(x)dx(y)dy2函数C分别表示两个脉动风速的互协方差函数FunctionCrespectivelyrepresentscovariance functionsoftwo pieces of fluctuating wind.如果互协方差函数是相隔距离的快速递减函数，则流积分长度很小，紊流影响也很小。反之如果互协方差函数随相隔距离的增大递减很慢，则瑞流积分长度很大，紊流的影响也大。Ifthe covariance function is a fast decreasingfunction of the distance,thenthe interval of turbulenceintegral is small, correspondinglythe effect ofturbulenceissmall.Conversely,Ifthe covariancefunction decreases slowlywith distance, the interval of turbulence integral is large, the effect ofturbulenceisalsolarge

函数C分别表示两个脉动风速的互协方差函数 Function C respectively represents covariance functions of two pieces of fluctuating wind. 如果互协方差函数是相隔距离的快速递减函数，则湍流积分长度很小，紊流影响也很 小。反之如果互协方差函数随相隔距离的增大递减很慢，则湍流积分长度很大，紊流 的影响也大。 If the covariance function is a fast decreasing function of the distance, then the interval of turbulence integral is small, correspondingly the effect of turbulence is small. Conversely, If the covariance function decreases slowly with distance, the interval of turbulence integral is large, the effect of turbulence is also large. 湍流积分长度从数学上可定义为 The mathematical definition of turbulence integral can be defined as follow: 10.1 脉动风的概率分布 10.1 Probabilistic distribution of fluctuating wind

10.2脉动风的功率谱10.2 Powerspectraoffluctuatingwind脉动风功率谱（PowerSpectra）表现了脉动风能量在整个频率范围内的分布特征It describes the energy distribution of fluctuating wind over fullfrequencyrange.脉动风功率谱需由强风观测记录得出，一般有两种方法：Power spectra is obtained by observing strong winds. Generallythere are two methods:把强风记录通过超低频率滤波器，直接测出风速的功率谱曲线；Directly measure the power spectrum of wind speed by lettingstrong wind records go through ultra-low frequency filter.把强风记录经过相关性分析，获得风速的相关曲线，建立相关函数的数学表达式，然后通过傅里叶变换得到功率谱。Obtain the correlation curve by analyzing strong wind recordsand establish expressions of correlation function. And finallythe power spectrum is obtained through Fourier transformation

脉动风功率谱（Power Spectra） 表现了脉动风能量在整个频率范围内的分布特征 It describes the energy distribution of fluctuating wind over full frequency range. 脉动风功率谱需由强风观测记录得出，一般有两种方法： Power spectra is obtained by observing strong winds. Generally there are two methods: 把强风记录通过超低频率滤波器，直接测出风速的功率谱曲线； Directly measure the power spectrum of wind speed by letting strong wind records go through ultra-low frequency filter. 把强风记录经过相关性分析，获得风速的相关曲线，建立相关函数的 数学表达式，然后通过傅里叶变换得到功率谱。 Obtain the correlation curve by analyzing strong wind records and establish expressions of correlation function. And finally, the power spectrum is obtained through Fourier transformation 10.2 脉动风的功率谱 10.2 Power spectra of fluctuating wind

(s)'saampadsThour4days1day1L0mirIminSpecralAaMarologlca10.1100.9110010000.001Frequencyf(cycle/hour)（1）在中心频率为0.01（1/小时）出现第一个峰值，对应于天气系统整个运转的变化周期4天通常称为宏观气象峰值；The first peak corresponding to the whole period of the weathersystem appears at where the center frequency is 0.01(1/h), which isusually called macro meteorological peak（2）第二个峰值出现在12小时周期处，相当于夜间的温度变化The second peak occurs at the period of 12 hours, which is equivalentto the change in temperature between dayand night（3）第三个峰值出现在1分钟周期处，反映了大气流的脉动，即与边界层流作用有关的从十分钟到小于3秒周期的高频作用，通常称为微观气象峰值The third peak occurs at the period of 1 minute, reflecting thefluctuation of atmospheric turbulence, which is the high frequencyaction of a period of 3 seconds to 10 minutes and is usually calledmicro meteorological peak

（1）在中心频率为0.01（1/小时）出现第一个峰值，对应于天气系统整个运 转的变化周期4天通常称为宏观气象峰值； The first peak corresponding to the whole period of the weather system appears at where the center frequency is 0.01(1/h), which is usually called macro meteorological peak （2）第二个峰值出现在12小时周期处，相当于昼夜间的温度变化 The second peak occurs at the period of 12 hours, which is equivalent to the change in temperature between day and night. （3）第三个峰值出现在1分钟周期处，反映了大气湍流的脉动，即不边界层 湍流作用有关的从十分钟到小于3秒周期的高频作用，通常称为微观气象峰值 The third peak occurs at the period of 1 minute, reflecting the fluctuation of atmospheric turbulence, which is the high frequency action of a period of 3 seconds to 10 minutes and is usually called micro meteorological peak