多层框架在水平与竖向随机地震同时作用的稳定性与响应分析
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摘要
论文的目的:分析高层框架结构在水平和竖向随机地震同时作用下稳定性和地震响应,为结构设计人员提供更好的设计依据。
研究内容:
1.用简明的运动模型建立单层框架结构体系在水平和竖向随机地震同时作用下的振动方程,运用随机平均法得到伊藤随机微分方程。然后对结构分别进行了基于矩法和标准随机平均法的结构稳定性分析和响应分析,获得了结构稳定性条件,得到结构位移和速度一二阶矩响应方差解析解。
2.分析了两层结构在双向地震作用下的稳定性和随机地震响应,得到结构稳定条件和响应特征。在此基础上,将单层框架结构体系在水平和竖向随机地震同时作用下扩展至多层框架结构,建立n层框架体系在水平和竖向随机地震同时作用下的运动方程,然后通过随机平均法处理得到伊藤随机微分方程,分析结构稳定性和地震响应,获得n层框架结构稳定的不等式和结构位移与速度方差响应解析解。最后,分别取n等于1,2,3时,将得到结果与前面分析单层框架和两层框架结果进行比较,得到结论是一致的。这就验证了多层框架结构稳定性和随机地震响应分析得到一般通式是正确的。
3.在对单层和多层框架结构在竖向和水平双向随机地震同时作用下的稳定性和响应分析基础上,运用随机平均法对带粘滞和粘弹性阻尼器单自层框架减震结构在竖向和水平双向随机地震同时作用下的运动方程进行分析,得到伊藤随机微分方程,从而分析带粘滞粘弹性阻尼器单自由度框架减震结构的稳定性和地震响应,得到稳定条件和位移与速度方差响应解析解。
成果和结论:通过对多层结构同时在双向地震作用下的稳定性分析和响应分析得到多层框架结构在双向地震作用下的结构稳定性和随机响应特征一般解析通式,同时可知,竖向地震对结构的随机地震响应有明显的影响,值得重视。
This paper studies stability analysis and stochastic earthquake response of the multi-frame structure subjected to both horizontal and vertical random earthquakes. It provides better design bas- is for structure designers.
Main contents are follows:
1. On the foundation of the simplified motion model of frame structures subjected to horizontal-vertical random earthquake excitations, the paper establishes the vibration equation of single-story frame. Then get the Ito? stochastic differential equations by using stochastic averaging method and analysis the structural stability and Earthquake Response based on the moment method and standard random average method and get the stability condition and random response half-theory.
2. Analysis the two layers structure stability and random response which subjected to in two-way earthquake .And get the structure stability conditions and response characteristics. On this basis, extend to the multilayer frame structure ansysis. Then get the Ito? stochastic differential equation by the random average method processing, analysis structure stability and seismic response. obtain n layer frame structure stability condition and random response expression. Finally, take n equal to 1, 2, 3 for example to compare the results. This will verify the multilayer frame structure stability and random response analysis being correct .
3. Based on the analysis of the structure stability and stochastic earthquake response of the multi-frame structure in both horizontal and vertical random earthquakes. Then get the Viscous and Viscoelastic dampers with single frame structure’s Ito? stochastic differential equations by using stochastic averaging method and analysis the structural stability and Earthquake Response. Results and conclusion: by ansysis n frame structure stability and random response using
The stochastic averaging method to get the general expression. Meanwhile, the vertical earthquake seismic response of the stochastic has obvious effect .
研究内容:
1.用简明的运动模型建立单层框架结构体系在水平和竖向随机地震同时作用下的振动方程,运用随机平均法得到伊藤随机微分方程。然后对结构分别进行了基于矩法和标准随机平均法的结构稳定性分析和响应分析,获得了结构稳定性条件,得到结构位移和速度一二阶矩响应方差解析解。
2.分析了两层结构在双向地震作用下的稳定性和随机地震响应,得到结构稳定条件和响应特征。在此基础上,将单层框架结构体系在水平和竖向随机地震同时作用下扩展至多层框架结构,建立n层框架体系在水平和竖向随机地震同时作用下的运动方程,然后通过随机平均法处理得到伊藤随机微分方程,分析结构稳定性和地震响应,获得n层框架结构稳定的不等式和结构位移与速度方差响应解析解。最后,分别取n等于1,2,3时,将得到结果与前面分析单层框架和两层框架结果进行比较,得到结论是一致的。这就验证了多层框架结构稳定性和随机地震响应分析得到一般通式是正确的。
3.在对单层和多层框架结构在竖向和水平双向随机地震同时作用下的稳定性和响应分析基础上,运用随机平均法对带粘滞和粘弹性阻尼器单自层框架减震结构在竖向和水平双向随机地震同时作用下的运动方程进行分析,得到伊藤随机微分方程,从而分析带粘滞粘弹性阻尼器单自由度框架减震结构的稳定性和地震响应,得到稳定条件和位移与速度方差响应解析解。
成果和结论:通过对多层结构同时在双向地震作用下的稳定性分析和响应分析得到多层框架结构在双向地震作用下的结构稳定性和随机响应特征一般解析通式,同时可知,竖向地震对结构的随机地震响应有明显的影响,值得重视。
This paper studies stability analysis and stochastic earthquake response of the multi-frame structure subjected to both horizontal and vertical random earthquakes. It provides better design bas- is for structure designers.
Main contents are follows:
1. On the foundation of the simplified motion model of frame structures subjected to horizontal-vertical random earthquake excitations, the paper establishes the vibration equation of single-story frame. Then get the Ito? stochastic differential equations by using stochastic averaging method and analysis the structural stability and Earthquake Response based on the moment method and standard random average method and get the stability condition and random response half-theory.
2. Analysis the two layers structure stability and random response which subjected to in two-way earthquake .And get the structure stability conditions and response characteristics. On this basis, extend to the multilayer frame structure ansysis. Then get the Ito? stochastic differential equation by the random average method processing, analysis structure stability and seismic response. obtain n layer frame structure stability condition and random response expression. Finally, take n equal to 1, 2, 3 for example to compare the results. This will verify the multilayer frame structure stability and random response analysis being correct .
3. Based on the analysis of the structure stability and stochastic earthquake response of the multi-frame structure in both horizontal and vertical random earthquakes. Then get the Viscous and Viscoelastic dampers with single frame structure’s Ito? stochastic differential equations by using stochastic averaging method and analysis the structural stability and Earthquake Response. Results and conclusion: by ansysis n frame structure stability and random response using
The stochastic averaging method to get the general expression. Meanwhile, the vertical earthquake seismic response of the stochastic has obvious effect .
引文
[1]胡聿贤.地震工程学[M].北京:地震工程学,2006:2,129-131.
[2]李爱群.工程结构减振控制[M].北京:机械工业出版社,2007:1-8,306-315.
[3]包世华,张铜生.清华大学出版社[M].京:高层建筑结构设计和计算(上册),2005:50-53.
[4]谢礼立,马玉宏.现代抗震理论的发展过程[J].国际地震动态,2003,10:1-8.
[5]于海英,王栋,杨永强等.汶川8.0级地震强震动加速度记录的初步分析[J].地震工程与工程振动,2009.29(1):1～13[6]陈念英.竖向地震力与自贡震害工程抗震.第1期,1986.
[6]陈念英.竖向地震力与自贡震害工程抗震.第1期,1986.
[7]陈念英.从日本阪神地震再谈竖向地震作用的重要性[J].成都大学学报(自然科学版),1996,(3).
[8]洪时明译“纵摇”超过“横摇”—被蒙敝了的设计思想, 1995年1月26日.日本《朝日新闻》.
[9]“5·12”汶川地震房屋震害研究专家组.“5·1 2”汶川地震房屋建筑震害分析与对策研究报告[J].四川地震,2009
[10]钱培风.竖向地震力和抗震砌块建筑[M].北京:中国大地出版社,1997.
[11]钱培风.高层建筑的抗震问题[J].世界地震工程,1992,(3).
[12]邓雪松,聂一恒,周云.竖向地震的研究与应用进展[A].周福霖,张雁.防震减灾工程研究与进展[M].北京:科学出版社,2005
[13]辛娅云.竖向地震作用的重要性[J].工程抗震与加固改造,2005.27(增):48～50
[14]高小旺,龚思礼等.建筑抗震设计规范理解与应用.北京:中国建筑工业出版社,2002.
[15]李桂青.抗震结构计算理论和方法[M].北京:地震出版社,1985.
[16]朱镜清.结构抗震分析原理[M].北京:地震出版社,2002.
[17]任耀辉,甘梅,王泽军.烟囱竖向地震作用的计算方法综述[J].特种结构,2009,(26).4.
[18]钱培风.烟囱在地震作用下破坏情形的若干解释.第一次全国抗震会议论文.1957
[19]钱培风,苏文藻,张悉德,杨亚弟.烟囱在地震作用下的纵波应力[J].力学学报,1978(2):125～134.
[20]钱培风.论竖向地震力[J].建筑结构,1979(3):l~7
[21]李应斌,张国军,吴涛.第12届世界地震工程会议论文综述(1)[J].工程抗震,2O02.3
[22]Yousef Bzorgnia,Kenpelh W Campbell,Mansour Niazi.Observed spectral characteristics of vertical ground motion recorded during worldwide earthquakes from 1975 to 1995.1WCEE:paper No.2671
[23]Adfredo Reyes-Salazar,Achintya Haldar.Consideration of vertical acceleration an flexibility of connections on seismic response of steel frames.12WCEE:paper NO.1171
[24]Mukat Lsharama.Attenuation relationship for estimation of peak ground vertical acceleration using data from strong motion arrays in Inia.12WCEE:paper No.1964
[25]Shinji Yamazaki,Susumu Minami,Hiroaki Mimura .Effects of vertical ground motions on earthquake response of steel frames. 12WCEE:paper No.0663
[26]Miller K S,Ross B.An Introduction to the Fractional Calculus and Fractional Differential Equations[M].New York:John Wiley and Sons,1993.
[27]Oldham K B,Spanier J.The Fractional Calculus[M].New York:Academic,1974.
[28]Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999.
[29]方同.工程随机振动[M].北京:国防工业出版社,1995:47-51,119-136,287-361.
[30]朱位秋.随机振动[M].北京:科学出版社,1998:278-309.
[31]蔡国强,朱位秋.推导随机平均方程的一种新方法[J].应用力学学报,1987,4(4):49-59.
[32]朱位秋.拟Hamilton系统的随机平均[J].中国科学(A辑),1995,25(10):1092-1100.
[33]朱位秋.随机平均法及其应用[J].力学进展,1987,17(3):342-253.
[34] Stratonovich,R.L.Topics in the Theory of Random Noise [J].Gordon and Breach,Vol.1, 1963;Vol. 2, 1967.
[35]Khasminskii, R. Z.,A limit theorem for the solutions of differential equations with random right-hand sides, theory probab. Appl.,11(1966),390-405.
[36]Papanicolaou, G. C., and Kohler, W., Asymptotic theory of mixing stochastic ordinary differential equations, Commum. Pure Appl. Math., 27(1974),641-668.
[37]KHAS’MINSKII,R.Z.,Stability of Systems of Differential Equations with Random Parametric Excitation,Izdat.Nauka,Moscow (1969).
[38]Stratonovich,R.L.Topics in the Theory of Random Noise [J].Vol.I and II,Gordon and Breach, New York,1963.
[39]Lin,Y.K.Probabilistic Theory of Structural Dynamics,R.E.Krieger,Huntington,New York,Reprint,1976.
[40]Dennemeyer,R.Introduction to Partial Differential Equations and Boundary Value Problems.McGraw-Hill,New York,1968.
[41]WONG,E.and ZAKAI,M.On the Relation Between Ordinary and Stochastic Differential Equations,Rep. 64-26,University of California at Berkely(1964).
[42]欧进萍.模糊随机振动[D].哈尔滨:哈尔滨建筑工程学院,1987.
[2]李爱群.工程结构减振控制[M].北京:机械工业出版社,2007:1-8,306-315.
[3]包世华,张铜生.清华大学出版社[M].京:高层建筑结构设计和计算(上册),2005:50-53.
[4]谢礼立,马玉宏.现代抗震理论的发展过程[J].国际地震动态,2003,10:1-8.
[5]于海英,王栋,杨永强等.汶川8.0级地震强震动加速度记录的初步分析[J].地震工程与工程振动,2009.29(1):1～13[6]陈念英.竖向地震力与自贡震害工程抗震.第1期,1986.
[6]陈念英.竖向地震力与自贡震害工程抗震.第1期,1986.
[7]陈念英.从日本阪神地震再谈竖向地震作用的重要性[J].成都大学学报(自然科学版),1996,(3).
[8]洪时明译“纵摇”超过“横摇”—被蒙敝了的设计思想, 1995年1月26日.日本《朝日新闻》.
[9]“5·12”汶川地震房屋震害研究专家组.“5·1 2”汶川地震房屋建筑震害分析与对策研究报告[J].四川地震,2009
[10]钱培风.竖向地震力和抗震砌块建筑[M].北京:中国大地出版社,1997.
[11]钱培风.高层建筑的抗震问题[J].世界地震工程,1992,(3).
[12]邓雪松,聂一恒,周云.竖向地震的研究与应用进展[A].周福霖,张雁.防震减灾工程研究与进展[M].北京:科学出版社,2005
[13]辛娅云.竖向地震作用的重要性[J].工程抗震与加固改造,2005.27(增):48～50
[14]高小旺,龚思礼等.建筑抗震设计规范理解与应用.北京:中国建筑工业出版社,2002.
[15]李桂青.抗震结构计算理论和方法[M].北京:地震出版社,1985.
[16]朱镜清.结构抗震分析原理[M].北京:地震出版社,2002.
[17]任耀辉,甘梅,王泽军.烟囱竖向地震作用的计算方法综述[J].特种结构,2009,(26).4.
[18]钱培风.烟囱在地震作用下破坏情形的若干解释.第一次全国抗震会议论文.1957
[19]钱培风,苏文藻,张悉德,杨亚弟.烟囱在地震作用下的纵波应力[J].力学学报,1978(2):125～134.
[20]钱培风.论竖向地震力[J].建筑结构,1979(3):l~7
[21]李应斌,张国军,吴涛.第12届世界地震工程会议论文综述(1)[J].工程抗震,2O02.3
[22]Yousef Bzorgnia,Kenpelh W Campbell,Mansour Niazi.Observed spectral characteristics of vertical ground motion recorded during worldwide earthquakes from 1975 to 1995.1WCEE:paper No.2671
[23]Adfredo Reyes-Salazar,Achintya Haldar.Consideration of vertical acceleration an flexibility of connections on seismic response of steel frames.12WCEE:paper NO.1171
[24]Mukat Lsharama.Attenuation relationship for estimation of peak ground vertical acceleration using data from strong motion arrays in Inia.12WCEE:paper No.1964
[25]Shinji Yamazaki,Susumu Minami,Hiroaki Mimura .Effects of vertical ground motions on earthquake response of steel frames. 12WCEE:paper No.0663
[26]Miller K S,Ross B.An Introduction to the Fractional Calculus and Fractional Differential Equations[M].New York:John Wiley and Sons,1993.
[27]Oldham K B,Spanier J.The Fractional Calculus[M].New York:Academic,1974.
[28]Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999.
[29]方同.工程随机振动[M].北京:国防工业出版社,1995:47-51,119-136,287-361.
[30]朱位秋.随机振动[M].北京:科学出版社,1998:278-309.
[31]蔡国强,朱位秋.推导随机平均方程的一种新方法[J].应用力学学报,1987,4(4):49-59.
[32]朱位秋.拟Hamilton系统的随机平均[J].中国科学(A辑),1995,25(10):1092-1100.
[33]朱位秋.随机平均法及其应用[J].力学进展,1987,17(3):342-253.
[34] Stratonovich,R.L.Topics in the Theory of Random Noise [J].Gordon and Breach,Vol.1, 1963;Vol. 2, 1967.
[35]Khasminskii, R. Z.,A limit theorem for the solutions of differential equations with random right-hand sides, theory probab. Appl.,11(1966),390-405.
[36]Papanicolaou, G. C., and Kohler, W., Asymptotic theory of mixing stochastic ordinary differential equations, Commum. Pure Appl. Math., 27(1974),641-668.
[37]KHAS’MINSKII,R.Z.,Stability of Systems of Differential Equations with Random Parametric Excitation,Izdat.Nauka,Moscow (1969).
[38]Stratonovich,R.L.Topics in the Theory of Random Noise [J].Vol.I and II,Gordon and Breach, New York,1963.
[39]Lin,Y.K.Probabilistic Theory of Structural Dynamics,R.E.Krieger,Huntington,New York,Reprint,1976.
[40]Dennemeyer,R.Introduction to Partial Differential Equations and Boundary Value Problems.McGraw-Hill,New York,1968.
[41]WONG,E.and ZAKAI,M.On the Relation Between Ordinary and Stochastic Differential Equations,Rep. 64-26,University of California at Berkely(1964).
[42]欧进萍.模糊随机振动[D].哈尔滨:哈尔滨建筑工程学院,1987.
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