基于Ritz-POD的大跨屋盖结构风振响应分析和风效应静力等效方法
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摘要
大跨屋盖风振响应中的多振型参与特性,及由此导致的多目标等效静风荷载问题,一直是大跨屋盖结构风工程研究和工程应用十分关注的问题。对作者及合作者近年来在该方面的研究工作所取得的进展进行了总结,并加以发展。利用POD分解得到本征模态表达的脉动风荷载空间分布形式,确定与荷载分布形式对应的Ritz向量,即主导模态;推导脉动风响应中背景响应和共振响应的数学表达式,给出背景响应与共振响应间的相关性分析方法;根据结构风振响应特性,以风荷载主要本征模态和结构主导振型惯性力构造多目标等效静风荷载的基本向量,利用最小二乘法得到基本向量的最优组合系数,从而得到针对多个等效目标的等效静风荷载。并通过对跨度40 m的K6型单层球面网壳结构的计算验证本文方法的有效性和准确性。
The contribution of higher vibration modes is important to the wind-induced response of long span roofs.A lack of knowledge of this contribution makes it difficult to estimate the wind induced response and equivalent static wind loads accurately.The authors and their research team have been studying this topic for a number of years.Some main research outcomes are presented in this paper.The Ritz-Proper Orthogonal Decomposition(POD) method is applied to choose the dominant modes of the wind-induced response of long span roofs;the eigenvectors of the fluctuating wind load obtained from the POD method are regarded as the spatial distribution of the load to generate the Ritz vectors;the background and resonant response are redefined on the basis of modal acceleration method,and a method to calculate the correlation coefficient between the background response and the resonant response is proposed;the target responses are expressed as the linear combination of the basis vectors,which are the dominant eigen-modes of wind loads and structural vibration modes representing the background and the resonant responses respectively.The combination factors of these basis vectors are determined with the least-squares approximation method.The wind-induced response and equivalent static wind loads of a single layer reticular shell is analyzed as a case study,in which the accuracy and efficiency of the propose methods are verified.
The contribution of higher vibration modes is important to the wind-induced response of long span roofs.A lack of knowledge of this contribution makes it difficult to estimate the wind induced response and equivalent static wind loads accurately.The authors and their research team have been studying this topic for a number of years.Some main research outcomes are presented in this paper.The Ritz-Proper Orthogonal Decomposition(POD) method is applied to choose the dominant modes of the wind-induced response of long span roofs;the eigenvectors of the fluctuating wind load obtained from the POD method are regarded as the spatial distribution of the load to generate the Ritz vectors;the background and resonant response are redefined on the basis of modal acceleration method,and a method to calculate the correlation coefficient between the background response and the resonant response is proposed;the target responses are expressed as the linear combination of the basis vectors,which are the dominant eigen-modes of wind loads and structural vibration modes representing the background and the resonant responses respectively.The combination factors of these basis vectors are determined with the least-squares approximation method.The wind-induced response and equivalent static wind loads of a single layer reticular shell is analyzed as a case study,in which the accuracy and efficiency of the propose methods are verified.
引文
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[12]Yang Qing-Shan,Liu Rui-Xia.On aerodynamic stabilityof membrane structures[J].International Journal ofSpace Structures,2005,20(3):181-188.
[13]Yang Qingshan,Wu Yue,Zhu Weiliang.Experimentalstudy on interaction between membrane structures andwind environment[J].Earthquake Engineering andEngineering Vibration,2010,9(4):523-532.
[14]武岳,孙晓颖,沈世钊.单向悬挂屋盖结构的风致气弹耦合效应数值模拟[J].计算力学学报,2007,24(5):571-578.(Wu Yue,Sun Xiao-ying,Shen Shi-zhao.Numerical simulation on the aero-elastic effects ofuni-directional suspension structures[J].ChineseJournal of Computational Mechanics,2007,24(5):571-578.(in Chinese))
[15]Chen Bo,Wu Yue,Shen Shizhao.A new method forwind-induced response analysis of long span roofs[J].International Journal of Space Structures,2006,21(2):93-101.
[16]陈波,武岳,沈世钊.Ritz-POD法的原理及应用[J].计算力学学报,2007,24(4):499-504.(ChenBo,Wu Yue,Shen Shi-zhao.Principle and applicationof Ritz-POD method[J].Chinese Journal ofComputational Mechanics,2007,24(4):499-504.(inChinese))
[17]陈波,武岳,沈世钊.背景响应、共振响应定义及其相关性分析方法[J].振动工程学报,2008,21(2):140-145.(Chen Bo,Wu Yue,Shen Shi-zhao.Definitions and correlation analyses for backgroundresponse and resonant response[J].Journal ofVibration Engineering,2008,21(2):140-145.(inChinese))
[18]陈波,杨庆山,武岳,等.大跨空间结构的多目标等效静风荷载分析方法[J].土木工程学报,2010,43(3):62-67.(Chen Bo,Yang Qing-shan,Wu Yue,et al.Multi-objective equivalent static wind loads forlarge-span structures[J].China Civil EngineeringJournal,2010,43(3):62-67.(in Chinese))
[19]Yang Qingshan,Tian Yuji.Wind-induced responses ofBeijing National Stadium[J].Wind and Structures,2011,14(3):239-252.
[20]田玉基,杨庆山.北京奥林匹克公园网球中心赛场悬挑钢屋盖结构风振响应分析[J].建筑结构学报,2009,30(3):126-133.(TIAN Yuji,YANG Qingshan.Wind-induced responses of cantilevered steel roof ofOlympic Park Tennis Center Stadium[J].Journal ofBuilding Structures,2009,30(3):126-133.(inChinese))
[21]Nakayama Masanao,Sasaki Yasuhito,Masuda Keiji,et al.An efficient method for selection of vibrationmodes contributory to wind response on dome-like roofs[J].Journal of Wind Engineering and IndustrialAerodynamics,1998,73:31-43.
[22]方勇,倪振华,谢壮宁.模态加速度法在屋盖结构风致响应分析中的应用[J].应用力学学报,2004,21(2):122-125.(Fang Yong,Ni Zhenhua,XieZhuangning.Use of mode-acceleration solution inresponse analysis of roof structures[J].Chinese Journalof Applied Mechanics,2004,21(2):122-125.(inChinese))
[23]黄明开,倪振华,谢壮宁.大跨圆拱屋盖结构的风振响应分析[J].振动工程学报,2004,17(3):275-279.(Huang Ming-kai,Ni Zhen-hua,Xie Zhuang-ning.Analysis of wind-induced response for large-spandome roofs[J].Journal of Vibration Engineering,2004,17(3):275-279.(in Chinese))
[24]Tamura Y,Suganuma S,Kikuchi H,et al.Properorthogonal decomposition of random wind pressure field[J].Journal of Fluids and Structures,1999,13(7):1069-1095.
[25]Gu Jianmin,Ma Zheng-Dong,Hulbert Gregory M.Anew load-dependent Ritz vector method for structuraldynamics analysis:quasi-staitic Ritz vectors[J].FiniteElements in Analysis and Design,2000,36(3):261-278.
[26]Chen Xinzhong,Kareem Ahsan.Equivalent static windloads for buffeting response of bridges[J].Journal ofStructural Engineering,2001,127(12):1467-1475.
[27]陈波.大跨屋盖结构等效静风荷载精细化理论研究[D].哈尔滨:哈尔滨工业大学,2006:18-124.(Chen Bo.Refined theory of the equivalent static windloads on large span roofs[D].Harbin:Harbin Instituteof Technology,2006:18-124.(in Chinese))
[28]Katsumura A,Tamura Y,Nakamura O.Universal windload distribution simultaneously reproducing largest loadeffects in all subject members on long span cantileveredroof[J].Journal of Wind Engineering and IndustrialAerodynamics,2007(95):1145-1165.
[29]Hu Xiaohong.Wind loading effects and equivalentstatic wind loading on low-rise buildings[D].Texas:Texas Tech University,2006:130-145.
[30]靳全勤,张华隆.线性代数[M].上海:上海交通大学出版社,2008:63-98.(Jin Quanqin,ZhangHualong.Linear algebra[M].Shanghai:ShanghaiJiaotong University Press,2008:63-98.(in Chinese))
[2]王国砚,黄本才,林颖儒,等.基于CQC方法的大跨屋盖结构随机风振响应计算[J].空间结构,2003,9(4):22-26.(Wang Guo-yan,Huang Ben-cai,LinYing-ru,et al.Solution of wind induced randomvibration of large span roof structures based on CQCmethod[J].Spatial Structures,2003,9(4):22-26.(in Chinese))
[3]Clough Ray W,Penzien Joseph.Dynamics of structures[M].2nd ed.Newyork:Mcgraw-Hill InternationalEditions,Civil Engineering Series,1993.
[4]Davenport A G.Gust loading factors[J].Journal ofStructural Division,1967,93(3):11-34.
[5]Davenport A G.How can we simplify and generalizewind loads[J].Journal of Wind Engineering andIndustrial Aerodynamics,1995,(54/55):657-669.
[6]Simiu Emil.Equivalent static wind loads for tallbuilding design[J].Journal of the Structural Division,1976,102(4):719-737.
[7]Piccardo G,Solari G.A refined model for calculating3-D equivalent static wind forces on structures[J].Journal of Wind Engineering and IndustrialAerodynamics,1996,65(1/2/3):21-30.
[8]Kasperski M,Niemann,H-J.The LRC(load-responsecorrelation)method:a general method of estimatingunfavorable wind load distributions for linear andnonlinear structural behavior[J].Journal of WindEngineering and Industrial Aerodynamics,1992,43(1/2/3):1753-1763.
[9]Zhou Y,Kareem A,Gu M.Equivalent static buffetingwind loads on structures[J].Journal of StructuralEngineering,2000,126(8):989-992.
[10]Holmes J D.Effective static load distributions in windengineering[J].Journal of Wind Engineering andIndustrial Aerodynamics,2002(90):91-109.
[11]杨庆山,沈世钊.悬索结构随机风振反应分析[J].建筑结构学报,1998,19(4):29-39.(YANG Qingshan,SHEN Shizhao.Wind-induced random responseanalysis of cable roof structures[J].Journal of BuildingStructures,1998,19(4):29-39.(in Chinese))
[12]Yang Qing-Shan,Liu Rui-Xia.On aerodynamic stabilityof membrane structures[J].International Journal ofSpace Structures,2005,20(3):181-188.
[13]Yang Qingshan,Wu Yue,Zhu Weiliang.Experimentalstudy on interaction between membrane structures andwind environment[J].Earthquake Engineering andEngineering Vibration,2010,9(4):523-532.
[14]武岳,孙晓颖,沈世钊.单向悬挂屋盖结构的风致气弹耦合效应数值模拟[J].计算力学学报,2007,24(5):571-578.(Wu Yue,Sun Xiao-ying,Shen Shi-zhao.Numerical simulation on the aero-elastic effects ofuni-directional suspension structures[J].ChineseJournal of Computational Mechanics,2007,24(5):571-578.(in Chinese))
[15]Chen Bo,Wu Yue,Shen Shizhao.A new method forwind-induced response analysis of long span roofs[J].International Journal of Space Structures,2006,21(2):93-101.
[16]陈波,武岳,沈世钊.Ritz-POD法的原理及应用[J].计算力学学报,2007,24(4):499-504.(ChenBo,Wu Yue,Shen Shi-zhao.Principle and applicationof Ritz-POD method[J].Chinese Journal ofComputational Mechanics,2007,24(4):499-504.(inChinese))
[17]陈波,武岳,沈世钊.背景响应、共振响应定义及其相关性分析方法[J].振动工程学报,2008,21(2):140-145.(Chen Bo,Wu Yue,Shen Shi-zhao.Definitions and correlation analyses for backgroundresponse and resonant response[J].Journal ofVibration Engineering,2008,21(2):140-145.(inChinese))
[18]陈波,杨庆山,武岳,等.大跨空间结构的多目标等效静风荷载分析方法[J].土木工程学报,2010,43(3):62-67.(Chen Bo,Yang Qing-shan,Wu Yue,et al.Multi-objective equivalent static wind loads forlarge-span structures[J].China Civil EngineeringJournal,2010,43(3):62-67.(in Chinese))
[19]Yang Qingshan,Tian Yuji.Wind-induced responses ofBeijing National Stadium[J].Wind and Structures,2011,14(3):239-252.
[20]田玉基,杨庆山.北京奥林匹克公园网球中心赛场悬挑钢屋盖结构风振响应分析[J].建筑结构学报,2009,30(3):126-133.(TIAN Yuji,YANG Qingshan.Wind-induced responses of cantilevered steel roof ofOlympic Park Tennis Center Stadium[J].Journal ofBuilding Structures,2009,30(3):126-133.(inChinese))
[21]Nakayama Masanao,Sasaki Yasuhito,Masuda Keiji,et al.An efficient method for selection of vibrationmodes contributory to wind response on dome-like roofs[J].Journal of Wind Engineering and IndustrialAerodynamics,1998,73:31-43.
[22]方勇,倪振华,谢壮宁.模态加速度法在屋盖结构风致响应分析中的应用[J].应用力学学报,2004,21(2):122-125.(Fang Yong,Ni Zhenhua,XieZhuangning.Use of mode-acceleration solution inresponse analysis of roof structures[J].Chinese Journalof Applied Mechanics,2004,21(2):122-125.(inChinese))
[23]黄明开,倪振华,谢壮宁.大跨圆拱屋盖结构的风振响应分析[J].振动工程学报,2004,17(3):275-279.(Huang Ming-kai,Ni Zhen-hua,Xie Zhuang-ning.Analysis of wind-induced response for large-spandome roofs[J].Journal of Vibration Engineering,2004,17(3):275-279.(in Chinese))
[24]Tamura Y,Suganuma S,Kikuchi H,et al.Properorthogonal decomposition of random wind pressure field[J].Journal of Fluids and Structures,1999,13(7):1069-1095.
[25]Gu Jianmin,Ma Zheng-Dong,Hulbert Gregory M.Anew load-dependent Ritz vector method for structuraldynamics analysis:quasi-staitic Ritz vectors[J].FiniteElements in Analysis and Design,2000,36(3):261-278.
[26]Chen Xinzhong,Kareem Ahsan.Equivalent static windloads for buffeting response of bridges[J].Journal ofStructural Engineering,2001,127(12):1467-1475.
[27]陈波.大跨屋盖结构等效静风荷载精细化理论研究[D].哈尔滨:哈尔滨工业大学,2006:18-124.(Chen Bo.Refined theory of the equivalent static windloads on large span roofs[D].Harbin:Harbin Instituteof Technology,2006:18-124.(in Chinese))
[28]Katsumura A,Tamura Y,Nakamura O.Universal windload distribution simultaneously reproducing largest loadeffects in all subject members on long span cantileveredroof[J].Journal of Wind Engineering and IndustrialAerodynamics,2007(95):1145-1165.
[29]Hu Xiaohong.Wind loading effects and equivalentstatic wind loading on low-rise buildings[D].Texas:Texas Tech University,2006:130-145.
[30]靳全勤,张华隆.线性代数[M].上海:上海交通大学出版社,2008:63-98.(Jin Quanqin,ZhangHualong.Linear algebra[M].Shanghai:ShanghaiJiaotong University Press,2008:63-98.(in Chinese))
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