基于Adomian分解和回归分析的高耸钢烟囱动力特性研究(Ⅱ):模态振型
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摘要
模态振型是精确分析结构风振响应的关键之一,主要围绕高耸钢烟囱模态振型展开研究工作:首先,采用Adomian分解法(Adomian decomposition method,ADM),并引入边界条件和连续条件对模态振型进行求解;随后,以论文(Ⅰ)统计得到的高耸钢烟囱参数分布规律,进行随机抽样,得到拟合样本;最后,借助回归分析的方法,分别用欧洲规范(Eurocode)表达式、多项式、指数函数求和、正弦函数求和、傅里叶级数等表达式对高耸钢烟囱的无量纲模态振型进行拟合,得到高耸钢烟囱前四阶模态振型表达式,并对各类表达式的拟合精度、复杂程度和适用情况进行讨论。研究表明:多项式和傅里叶级数形式的振型表达式更适用于进一步的风振统一理论研究。本研究工作能够为高耸钢烟囱的设计和相应规范的修订提供一定的参考。
Modal shape is one of the key factors for analyzing wind induced responses,and hence in this work the modal shape of high-rise steel chimneys is studied.Firstly,after the boundary conditions and continuity conditions being introduced,the modal shape is solved via Adomian Decomposition Method(ADM).Secondly,the sample data of modal shape are obtained using random sampling method based on the statistical distributions of the parameters of high steel chimneys,as investigated in previous studies of the authors.Lastly,the expressions of dimensionless modal shape,which contain the Eurocode function,polynomial,summation of exponential function,summation of Sine function and Fourier series,are fitted by introducing regression analysis method.Then the expressions of first four modal shapes are presented,and the fitting precision,complexity and applicability of all expressions are also discussed.The results show that the expression in the form of Polynomial or Fourier series is more suitable for the further investigation of unified wind vibration theory.This work may offer some reference for the design of high-rise steel chimneys and the revision of relevant codes.
Modal shape is one of the key factors for analyzing wind induced responses,and hence in this work the modal shape of high-rise steel chimneys is studied.Firstly,after the boundary conditions and continuity conditions being introduced,the modal shape is solved via Adomian Decomposition Method(ADM).Secondly,the sample data of modal shape are obtained using random sampling method based on the statistical distributions of the parameters of high steel chimneys,as investigated in previous studies of the authors.Lastly,the expressions of dimensionless modal shape,which contain the Eurocode function,polynomial,summation of exponential function,summation of Sine function and Fourier series,are fitted by introducing regression analysis method.Then the expressions of first four modal shapes are presented,and the fitting precision,complexity and applicability of all expressions are also discussed.The results show that the expression in the form of Polynomial or Fourier series is more suitable for the further investigation of unified wind vibration theory.This work may offer some reference for the design of high-rise steel chimneys and the revision of relevant codes.
引文
[1]梁枢果,李辉民,瞿伟廉.高层建筑风荷载计算中的基本振型表达式分析[J].同济大学学报:自然科学版,2002,30(5):578-582(Liang Shuguo,Li Huimin,QuWeilian.Analysis of fundamental mode shape expressionsof tall buildings for evaluating wind loads[J].Journal ofTongji University:Natural Science Edition,2002,30(5):578-582(in Chinese))
[2]邹垚,梁枢果,彭德喜,等.考虑二阶振型的矩形高层建筑横风向风振响应简化计算[J].建筑结构学报,2011,32(4):39-45(Zou Yao,Liang Shuguo,Peng Dexi,et al.Simplified formulas for evaluation of cross-windinduced dynamic responses of rectangular high-risebuildings considering the second mode[J].Journal ofBuilding Structures,2011,32(4):39-45(in Chinese))
[3]牛春良.现行规范对“锁住区”起点高度简化处理的影响[J].建筑结构,2005,35(1):59-61(Niu Chunliang.Effect of predigest treatment on starting height of lock inrange in current code[J].Building Structure,2005,35(1):59-61(in Chinese))
[4]刘强,周瑞忠,袁文君.高耸结构地震瞬态反应计算与动力特性研究[J].土木工程学报,2010,43(5):63-69(Liu Qiang,Zhou Ruizhong,Yuan Wenjun.Computationof earthquake transient response of skyscraper structuresand study of the dynamic properties[J].China CivilEngineering Journal,2010,43(5):63-69(in Chinese))
[5]GB50009—2001建筑结构荷载规范[S].北京:中国建筑工业出版社,2006(GB50009—2001Load code for thedesign of building structures[S].Beijing:ChinaArchitecture&Building Press,2006(in Chinese))
[6]GB50051—2002烟囱设计规范[S].北京:中国计划出版社,2003(GB50051—2002Code for design of chimneys[S].Beijing:China Planning Press,2003(in Chinese))
[7]GB50135—2006高耸结构设计规范[S].北京:中国计划出版社,2006(GB50135—2006Code for design ofhigh-rising structures[S].Beijing:China Planing Press,2006((in Chinese))
[8]Model code for steel chimneys[S].Zurich:CICIND,2002
[9]ASME STS-1-2006 Steel stacks[S].New York:TheAmerican Society of Mechanical Engineers,2006
[10]BS EN 1993-3-2 Eurocode 3:design of steel structures—Part 3-2:towers,masts and chimneys-chimneys[S].Brussels:European Committee for Standardization,2006
[11]DIN V 4133-2007 Free-standing steel stacks[S].Berlin:Deutsches Institut für Normung,2007
[12]Tranvik P,Alpsten A.Dynamic behavior under wind loadingof a 90m steel chimney[R].Vaxjo:Alstom Power SwedenAB,2002
[13]陈鑫,李爱群,程文瀼,等.基于Adomian分解和回归分析的高耸烟囱动特性研究(Ⅰ):模态频率[J].土木工程学报,2013,46(4):26-35(Chen Xin,Li Aiqun,ChengWenrang,et al.Study on dynamic characteristics of high-rise steel chimneys based on Adomian decompositionmethod and regression analysis(Ⅰ):Modal frequency[J].China Civil Engineering Journal,2013,46(4):26-35(in Chiinese)
[14]BS EN 1991-1-4 Eurocode 1:actions on structures—Part1-4:general actions-wind actions[S].Brussels:EuropeanCommittee for Standardization,2005
[2]邹垚,梁枢果,彭德喜,等.考虑二阶振型的矩形高层建筑横风向风振响应简化计算[J].建筑结构学报,2011,32(4):39-45(Zou Yao,Liang Shuguo,Peng Dexi,et al.Simplified formulas for evaluation of cross-windinduced dynamic responses of rectangular high-risebuildings considering the second mode[J].Journal ofBuilding Structures,2011,32(4):39-45(in Chinese))
[3]牛春良.现行规范对“锁住区”起点高度简化处理的影响[J].建筑结构,2005,35(1):59-61(Niu Chunliang.Effect of predigest treatment on starting height of lock inrange in current code[J].Building Structure,2005,35(1):59-61(in Chinese))
[4]刘强,周瑞忠,袁文君.高耸结构地震瞬态反应计算与动力特性研究[J].土木工程学报,2010,43(5):63-69(Liu Qiang,Zhou Ruizhong,Yuan Wenjun.Computationof earthquake transient response of skyscraper structuresand study of the dynamic properties[J].China CivilEngineering Journal,2010,43(5):63-69(in Chinese))
[5]GB50009—2001建筑结构荷载规范[S].北京:中国建筑工业出版社,2006(GB50009—2001Load code for thedesign of building structures[S].Beijing:ChinaArchitecture&Building Press,2006(in Chinese))
[6]GB50051—2002烟囱设计规范[S].北京:中国计划出版社,2003(GB50051—2002Code for design of chimneys[S].Beijing:China Planning Press,2003(in Chinese))
[7]GB50135—2006高耸结构设计规范[S].北京:中国计划出版社,2006(GB50135—2006Code for design ofhigh-rising structures[S].Beijing:China Planing Press,2006((in Chinese))
[8]Model code for steel chimneys[S].Zurich:CICIND,2002
[9]ASME STS-1-2006 Steel stacks[S].New York:TheAmerican Society of Mechanical Engineers,2006
[10]BS EN 1993-3-2 Eurocode 3:design of steel structures—Part 3-2:towers,masts and chimneys-chimneys[S].Brussels:European Committee for Standardization,2006
[11]DIN V 4133-2007 Free-standing steel stacks[S].Berlin:Deutsches Institut für Normung,2007
[12]Tranvik P,Alpsten A.Dynamic behavior under wind loadingof a 90m steel chimney[R].Vaxjo:Alstom Power SwedenAB,2002
[13]陈鑫,李爱群,程文瀼,等.基于Adomian分解和回归分析的高耸烟囱动特性研究(Ⅰ):模态频率[J].土木工程学报,2013,46(4):26-35(Chen Xin,Li Aiqun,ChengWenrang,et al.Study on dynamic characteristics of high-rise steel chimneys based on Adomian decompositionmethod and regression analysis(Ⅰ):Modal frequency[J].China Civil Engineering Journal,2013,46(4):26-35(in Chiinese)
[14]BS EN 1991-1-4 Eurocode 1:actions on structures—Part1-4:general actions-wind actions[S].Brussels:EuropeanCommittee for Standardization,2005
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