基于Ritz-POD法的格构式塔架结构风致振动分析
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摘要
根据自立式塔架结构脉动风荷载的空间分布形式,实现了本征特征分解(proper orthogonal decomposition,POD)和基于荷载-里兹模态分析相结合的Ritz-POD算法求解Ritz振型,并结合谐波激励法(harmonic excitation method,HEM)和荷载-响应相关法(load response correlation method,LRC)实现了塔架结构风振响应和等效静力风荷载(equivalent static wind load,ESWL)的高效分析。计算结果表明:采用40阶基于荷载-里兹振型和100阶传统自由振动振型计算的节点风振响应和等效静力风荷载结果及变化规律一致且二者吻合度高,说明较少阶Ritz振型的计算精度是能够保障的。并且较少阶Ritz振型减少了谐波激励法与荷载-响应相关法的运算工作量,提高了风致振动分析的效率。另外,本文利用大型通用有限元软件SAP2000基于MATLAB系统的应用程序接口(API)开发环境,实现了塔架结构风致动力响应和等效静力风荷载的高效分析平台,可为其他大型复杂工程的风致振动分析提供参考。
The wind-induced response and equivalent static wind load(ESWL) for a lattice tower was conducted by adopting the combined POD-Ritz method,harmonic excitation method(HEM) and load response correlation method(LRC).The load-dependent-Ritz vibration modes for the lattice tower were obtained by utilizing the proper orthogonal decomposition(POD) method on the simulated fluctuating wind loading in the proposed POD-Ritz method.By selecting 40 load-dependent-Ritz vibration modes and 100 traditional free vibration modes,the wind-induced responses and equivalent static wind loads for the lattice tower were conducted respectively.The comparison between these two sets of numerical analyzed results showed that the difference in wind-induced response obtained by using two different types of vibration modes is very small.The numerical analysis accuracy in evaluation of windinduced vibration response for the lattice tower could be obtained with less load-dependent-Ritz vibration modes and high efficiency in reducing run time and less computation memory.Furthermore an integrated analysis system for the wind-induced response and equivalent static wind loading of the lattice tower was proposed by adopting the SAP2000 API for the MATLAB environment and the previous analysis procedure.This integrated analysis system could be used as a good reference for wind-induced response analysis for other large complex structures.
The wind-induced response and equivalent static wind load(ESWL) for a lattice tower was conducted by adopting the combined POD-Ritz method,harmonic excitation method(HEM) and load response correlation method(LRC).The load-dependent-Ritz vibration modes for the lattice tower were obtained by utilizing the proper orthogonal decomposition(POD) method on the simulated fluctuating wind loading in the proposed POD-Ritz method.By selecting 40 load-dependent-Ritz vibration modes and 100 traditional free vibration modes,the wind-induced responses and equivalent static wind loads for the lattice tower were conducted respectively.The comparison between these two sets of numerical analyzed results showed that the difference in wind-induced response obtained by using two different types of vibration modes is very small.The numerical analysis accuracy in evaluation of windinduced vibration response for the lattice tower could be obtained with less load-dependent-Ritz vibration modes and high efficiency in reducing run time and less computation memory.Furthermore an integrated analysis system for the wind-induced response and equivalent static wind loading of the lattice tower was proposed by adopting the SAP2000 API for the MATLAB environment and the previous analysis procedure.This integrated analysis system could be used as a good reference for wind-induced response analysis for other large complex structures.
引文
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8 SAP2000 application programming interface documentation.Copyright Computers and Structures,Inc,2015
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10梁栋,段文博,朱亚洲,等.双悬臂状态高墩连续刚构桥的风振及控制研究.科学技术与工程,2017;17(6):276-282Liang Dong,Duan Wenbo,Zhu Yazhou,et al.Study on the windinduced vibration and control of continuous rigid frame bridge with high-pier under double cantilever state.Science Technology and Engineering,2017;17(6):276-282
11吴本刚,傅继阳,吴玖荣.实测风场风速风向耦合的三维非平稳特征研究.建筑结构学报,2016;37(2):106-113Wu Bengang,Fu Jiyang,Wu Jiurong.Three dimensional non-stationary analysis on field measured wind data with coupling wind speed and wind direction.Journal of Building Structures,2016;37(2):106-113
12 DL/T 5154-2002架空送电线路杆塔结构设计技术规定.北京:中国电力出版社,2002DL/T 5154-2002 Technical regulation of design for steel tubular tower structures of overhead transmission line.Beijing:China Electric Power Press,2002
13 American National Standards Institute.Minimum design load for building and other structure(ASCE7-10).New York:American Society of Civil Engineers,2010
14 European Committee for Standardization.Actions on structures general actions Part 1-4:wind actions(BS EN1991-1-4:2005 Eurocode).Brussels:Standards Policy and Strategy Committee,2005
2 Carril C F,Isyumov N,Brasil R M L R F.Experimental study of the wind forces on rectangular latticed communication towers with antennas.Journal of Wind Engineering&Industrial Aerodynamics,2003;91(8):1007-1022
3邹良浩,梁枢果,邹垚,等.格构式塔架风载体型系数的风洞试验研究.特种结构,2008;25(5):61-63,88Zou Lianghao,Liang Shuguo,Zou Yao,et al.Wind tunnel tests for wind load shape coefficients of latticed tower.Special Structures,2008;25(5):61-63,88
4楼文娟,王东,沈国辉,等.角钢输电塔杆件风压及体型系数的风洞试验研究.华中科技大学学报(自然科学版),2013;41(4):114-118Lou Wenjuan,Wang Dong,Shen Guohui,et al.Wind tunnel tests for wind load distribution and shape coefficient of angle-made-transmission towers.J.Huazhong Univ of Sci&Tech(Natural Science E-dition),2013;41(4):114-118
5林家浩,张亚辉.随机振动的虚拟激励法.北京:科学出版社,2004Lin Jiaohao,Zhang Yahui.Pseudo-excitation method of random vibration.Beijing:Science Press,2004
6谢壮宁.风致复杂结构随机振动分析的一种快速算法---谐波激励法.应用力学学报,2007;24(2):263-266Xie Zhuangning.Wind induced random vibration analysis of complex structure,a fast algorithm of harmonic excitation method.Journal of Applied Mechanics,2007;24(2):263-266
7陈波.大跨屋盖结构等效静风荷载精细化理论研究.哈尔滨:哈尔滨工业大学,2006Chen Bo.Refined theory of the equivalent static wind loads on large span roofs.Harbin:Harbin Institute of Technology,2006
8 SAP2000 application programming interface documentation.Copyright Computers and Structures,Inc,2015
9徐明骁,葛耀君,马婷婷,等.大跨度斜拉索参数振动研究.科学技术与工程,2011;11(19):4509-4515Xu Mingxiao,Ge Yaojun,Ma Tingting,et al.Research on parametric oscillation of super long cables.Science Technology and Engineering,2011;11(19):4509-4515
10梁栋,段文博,朱亚洲,等.双悬臂状态高墩连续刚构桥的风振及控制研究.科学技术与工程,2017;17(6):276-282Liang Dong,Duan Wenbo,Zhu Yazhou,et al.Study on the windinduced vibration and control of continuous rigid frame bridge with high-pier under double cantilever state.Science Technology and Engineering,2017;17(6):276-282
11吴本刚,傅继阳,吴玖荣.实测风场风速风向耦合的三维非平稳特征研究.建筑结构学报,2016;37(2):106-113Wu Bengang,Fu Jiyang,Wu Jiurong.Three dimensional non-stationary analysis on field measured wind data with coupling wind speed and wind direction.Journal of Building Structures,2016;37(2):106-113
12 DL/T 5154-2002架空送电线路杆塔结构设计技术规定.北京:中国电力出版社,2002DL/T 5154-2002 Technical regulation of design for steel tubular tower structures of overhead transmission line.Beijing:China Electric Power Press,2002
13 American National Standards Institute.Minimum design load for building and other structure(ASCE7-10).New York:American Society of Civil Engineers,2010
14 European Committee for Standardization.Actions on structures general actions Part 1-4:wind actions(BS EN1991-1-4:2005 Eurocode).Brussels:Standards Policy and Strategy Committee,2005