基于非Gauss风载的高耸结构风振可靠性分析
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摘要
基于风载非Gauss模型推导了Davenport谱下结构脉动风载的五阶统计矩表达。通过响应概率特征函数和Fourier变换,求得Gram-Charlier级数形式的振形位移和速度响应联合概率统计分布。利用Rice公式和Poisson假设,研究了不同风载模型对高耸结构风振可靠性分析结果的影响。算例分析表明:高耸结构风振可靠性分析需要采用风载非Gauss模型;模态位移和速度响应的联合概率统计分布在截断于五阶Hermite多项式时具有较好精度;可以引入模态位移与速度独立性假设以简化高耸结构风振可靠性分析,计算结果是偏于安全的。
With special reference to the non-Gaussian model of wind-load,the statistical moments of fluctuating wind forces until the 5th order are deduced for Davenport spectrum.The probabilistic characteristic function and Fourier transformation are employed to evaluate the joint statistical distribution of modal responses,which has the form of Gram-Charlier series.Based on Rice formula and Poisson assumption,the effects of both wind-load models on the reliability analysis of high-rise slender structures are discussed.An example demonstrates that the reliability analysis of high-rise slender structures requires the non-Gaussian model of wind load.The 5th order Hermite series is recommended for describing the joint statistical distribution with the purpose of higher accuracy.It is acceptable to assume the statistical independence between the modal displacement and its derivative for simplified analysis,with the failure probability slightly overestimated.
With special reference to the non-Gaussian model of wind-load,the statistical moments of fluctuating wind forces until the 5th order are deduced for Davenport spectrum.The probabilistic characteristic function and Fourier transformation are employed to evaluate the joint statistical distribution of modal responses,which has the form of Gram-Charlier series.Based on Rice formula and Poisson assumption,the effects of both wind-load models on the reliability analysis of high-rise slender structures are discussed.An example demonstrates that the reliability analysis of high-rise slender structures requires the non-Gaussian model of wind load.The 5th order Hermite series is recommended for describing the joint statistical distribution with the purpose of higher accuracy.It is acceptable to assume the statistical independence between the modal displacement and its derivative for simplified analysis,with the failure probability slightly overestimated.
引文
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[2]Ma Xing,Wang Zhonggang,Deng Hongzhou.Theoretical and experimental research on dynamic behavior of guyed masts under wind load[J].Acta Mechanica Solida Sinica,2004,17(2):166～171.
[3]王仲刚,程华,邓洪洲.高耸结构非Gauss风载响应分析[J].重庆大学学报(自然科学版),2004,27(1):66～68.Wang Zhonggang,Chen Hua,Deng Hongzhou.Dynamic responses of the high-rise slender structure under non-Gaussian model of wind load[J].Journal of Chongqing University(Natural Science Edition),2004,27(1):66～68.(in Chinese)
[4]Vaicaitis R,Simiu E.Nonlinear pressure terms and along-wind response[J].J.Structure Div.,ASCE,1977,103(ST4):903～906.
[5]张炳根,赵玉芝.科学和工程中的随机微分方程[M].北京:海洋出版社,1980.Zhang Binggen,Zhao Yuzhi.Random Differential Equations in Science and Engineering[M].Beijing:The Ocean Press,1980.(in Chinese)
[6]张书文,孙孚,管长龙.三阶非线性海浪波面斜率的联合概率统计分布[J].海洋学报,1999,21(4):14～20.Zhang Shuwen,Sun Fu,Guan Changlong.Joint statistical distribution of surface slopes for the third-order nonlinear random sea waves[J].Acta Oceanologica Sinica,1999,21(4):14～20.(in Chinese)
[7]王肇民.上海电视塔用TMD进行结构风振控制的风洞试验研究[J].特种结构,1994,11(3):14～17.Wang Zhaomin.A wind-tunnel experimental investigation on the wind-induced vibration reduction of the Shanghai TV tower with TMD[J].Journal of Special Structures,1994,11(3):14～17.(in Chinese)
[8]王仲刚,邓洪洲.桅杆风振试验研究[J].工程力学,2003,20(5):42～47.(in Chinese)Wang Zhonggang,Deng Hongzhou.Experimental study of the dynamic behavior of guyed masts in wind tunnel[J].Engineering Mechanics,2003,20(5):42～47.
[9]朱位秋.随机振动[M].北京:科学出版社,1992.Zhu Weiqiu.Random Vibration[M].Beijing:The Science Press,1992.(in Chinese)
[10]刘春华.多个互相关随机过程的计算模拟及应用[J].同济大学学报,1994,28(增):61～68.Liu Chunhua.Numerical simulation of interrelated random processes and its application[J].Journal of Tongji University,1994,28(A):61～68.(in Chinese)
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