水平荷载作用下建筑结构响应的理论分析
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摘要
应用随机优化方法,推导建筑结构在风和地震共同作用下的动力响应。可用于进一步进行应用研究的参考。风荷载先建立频域和时域分析的数学模型,并确定平均风速下确定性的矢量和波动风速下随机矢量,再应用结构运动方程,通过对功率谱矩阵的分析,建立一系列结构响应的随机微分方程。地震作用应用结构动力方程和功率谱密度函数,通过分析频域随机过程的特性,建立地震作用下结构的振动微分方程。得出在风和地震这两个主要的随机荷载作用下,多自由度结构体系结构响应可通过叠加随机荷载的方式求得总的响应方程。
The stochastic optimization method is applied to deduce the dynamic response of building structures under the wind and earthquake excitation.For the wind load, the mathematical models in the frequency and time domain are set up first,and the vectors under the average and fluctuated wind velocity are determined,then a set of stochastic differential equations are set up based on the power spectrum matrix.For the earthquake action,the dynamic differential equations of structures are set up through analyzing the random processes in the frequency domain and using the structural equation and power spectrum density functions.In view of the above,the total dynamic response equation for the structure with multifreedom degrees could be obtained by a random load-superposition method.
The stochastic optimization method is applied to deduce the dynamic response of building structures under the wind and earthquake excitation.For the wind load, the mathematical models in the frequency and time domain are set up first,and the vectors under the average and fluctuated wind velocity are determined,then a set of stochastic differential equations are set up based on the power spectrum matrix.For the earthquake action,the dynamic differential equations of structures are set up through analyzing the random processes in the frequency domain and using the structural equation and power spectrum density functions.In view of the above,the total dynamic response equation for the structure with multifreedom degrees could be obtained by a random load-superposition method.
引文
[1]W.S.Zhang.Generalized pseudo-excitation method and its appli-cation for vibration control of wind seismic resistant buildings.ADissertation for the Degree of Philosophy[D].Hong Kong Poly-technic University,2000.
[2]W.Q.Zhu,M.Luo1,Z.G.Ying.Nonlinear stochastic optimalcontrol of tall buildings under wind loading[J].Engineering Struc-tures,2004,26:1561-1572.
[3]S.S.Lawa,J.Q.Bub,X.Q.Zhua.Time-varying wind load i-dentification from structural responses[J].Engineering Struc-tures,2005,27:1586-1598.
[4]Benfratello S,Muscolino G.Filter approach to the stochastic anal-ysis of MDOF wind-excited structures[J].Probability EngineeringMechanics,1999,14:311-321.
[5]GB50009-2001中华人民共和国标准.建筑结构荷载规范[S].北京:建筑工业出版社,2001.
[2]W.Q.Zhu,M.Luo1,Z.G.Ying.Nonlinear stochastic optimalcontrol of tall buildings under wind loading[J].Engineering Struc-tures,2004,26:1561-1572.
[3]S.S.Lawa,J.Q.Bub,X.Q.Zhua.Time-varying wind load i-dentification from structural responses[J].Engineering Struc-tures,2005,27:1586-1598.
[4]Benfratello S,Muscolino G.Filter approach to the stochastic anal-ysis of MDOF wind-excited structures[J].Probability EngineeringMechanics,1999,14:311-321.
[5]GB50009-2001中华人民共和国标准.建筑结构荷载规范[S].北京:建筑工业出版社,2001.
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