单点和多点荷载输入的虚拟激励法实用求解模式
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摘要
在实际工程中采用虚拟激励法(pseudo excitation method,PEM)往往需要编写复杂计算程序,为方便工程应用,建立了一种对应单点和多点荷载输入的虚拟激励法实用求解模式。考虑地震作用、风荷载等多种随机荷载,提取单点和多点荷载输入下计算结构虚拟响应的实用求解模式,并利用常规有限元分析软件的谐振稳态分析完成PEM核心计算,最后通过线性组合重新构建结构虚拟响应和功率谱密度函数的求解公式,从而在常规有限元分析软件中实现了PEM算法。由于采用建议方法可将PEM算法的核心计算交由有限元分析软件完成,在保持PEM高效准确计算优势的前提下显著提高了工作效率,避免了编写复杂计算程序,方便实际工程应用。通过两个典型数值算例验证了建议方法的正确性与有效性,并且指出其对于多种荷载工况的计算效率具有一定优势。
Application of pseudo-excitation method(PEM) in practical engineering usually needs to complete complex calculation program.The practical solution mode for calculating structural pseudo response under single and multiple point load input was established.Considering several types of random loads such as earthquake,wind and so on,and extracting practical solution mode,the core calculation of PEM algorithm can be easily performed by harmonic steady analysis in general finite element analysis software.And then the pseudo response and power spectrum density function of structure are given by simple linear combination rule.As the core calculation of PEM algorithm is solved by software,the method proposed in this paper possesses both of computational efficiency and precision of the pseudo-excitation method.And stochastic analysis of practical engineering by PEM algorithm is greatly facilitated and programming is avoided.Finally,two numerical examples are given to verify the simplicity and validity of proposed method in this paper,and calculation efficiency of the method corresponding to multiple cases is also pointed out.
Application of pseudo-excitation method(PEM) in practical engineering usually needs to complete complex calculation program.The practical solution mode for calculating structural pseudo response under single and multiple point load input was established.Considering several types of random loads such as earthquake,wind and so on,and extracting practical solution mode,the core calculation of PEM algorithm can be easily performed by harmonic steady analysis in general finite element analysis software.And then the pseudo response and power spectrum density function of structure are given by simple linear combination rule.As the core calculation of PEM algorithm is solved by software,the method proposed in this paper possesses both of computational efficiency and precision of the pseudo-excitation method.And stochastic analysis of practical engineering by PEM algorithm is greatly facilitated and programming is avoided.Finally,two numerical examples are given to verify the simplicity and validity of proposed method in this paper,and calculation efficiency of the method corresponding to multiple cases is also pointed out.
引文
[1]Kiureghion A D,Neuenhofer A.Response spectrummethod for multi-support seismic excitations[J].Earthquake Engineering and Structural Dynamics,1992,21(8):713-740.
[2]Emesto H Z,Vonmarcke E H.Seismic random-vibration analysis of multi-support structural system[J].Journal of Engineering Mechanics,1994,120(5):1107-1128.
[3]Lin J H.A fast CQC algorithm of PSD matrices forrandom seismic responses[J].Computers andStructures,1992,44(3):683-687.
[4]Lin J H,Zhang Y H,Li Q S,et a1.Seismic spatialeffects for long-span bridges using the pseudo excitationmethod[J].Engineering Structures,2004,26(9):1207-1216.
[5]卜国雄,谭平,张颖,周福霖.大型超高层建筑的随机风振响应分析[J].哈尔滨工业大学学报,2010,42(2):175-179.(Bu Guoxiong,Tan Ping,ZhangYing,Zhou Fulin.Random wind-induced responseanalysis of a large-scale and high-rise building[J].Journal of harbin Institute of Technology,2010,42(2):175-179.(in Chinese))
[6]张志超,张亚辉,赵岩.车-桥系统非平稳随机振动的PEM-PIM算法[J].计算力学学报,2009,26(1):26-32.(Zhang Zhichao,Zhang Yahui,ZhaoYan.Combined PEM-PIM scheme for the non-stationaryvibration analysis of vehicle-bridge systems[J].Chinese Journal of Computational Mechanics,2009,26(1):26-32.(in Chinese))
[7]张志超,张亚辉,林家浩.三维车桥耦合系统的非平稳随机振动分析[J].应用力学学报,2010,27(1):151-158.(Zhang Zhichao,Zhang Yahui,LinJiahao.Seepage calculation model for face slab jointand crack of concrete face rockfill dam[J].ChineseJournal of Applied Mechanics,2010,27(1):151-158.(in Chinese))
[8]Zhang W S,Xu Y L.Modal analysis and seismicresponse of steel frames with connection dampers[J].Engineering Structures,2001,3(4):385-396.
[9]汪洋,石永久,王元清.实用多点输入虚拟激励法在通用有限元软件中的实现[J].地震工程与工程振动,2010,30(1):46-52.(Wang Yang,Shi YongJiu,Wang Yuanqing.Implementation of the practicalpseudo excitation method for multi-support seismicresponse analysis in general FEM software[J].Journalof Earthquake Engineering and Engineering Vibration,2010,30(1):46-52.(in Chinese))
[10]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185-190.(LiYonghua,Li Siming.Pseudo excitation based onsolving absolute displacement[J].Journal of Vibrationand Shock,2009,28(10):185-190.(in Chinese))
[11]陈建兵,彭勇波,李杰.关于虚拟激励法的一个注记[J].计算力学学报,2011,28(2):163-167.(Chen Jianbing,Peng Yongbo,Li Jie.A note on thepseudo-excitation method[J].Chinese Journal ofComputational Mechanics,2011,28(2):163-167.(in Chinese))
[12]Edward L W.Static and dynamic analysis of structures[M].Berkeley,CA:Computer and Structures,Inc,2004.
[13]Liu G H,Guo W,Li H N.An effective and practicalmethod for solving an unnegligible problem inherent inthe current calculation model for multi-support seismicanalysis of structures[J].Science China:TechnologicalSciences,2010,53(7):1774-1784.
[14]刘树屯,关忆卢.首都机场306m跨飞机库屋盖钢结构设计施工中的一些问题[J].钢结构,1996,11(4):4-8.(Liu Shutun,Guan Yilu.Several problemsof design and construction of 306 m-span hangar roof incapital airport[J].Steel Construction,1996,11(4):4-8.(in Chinese))
[15]Clough R W,Penzien J.Dynamics of structures[M].3rd ed.Berkeley,CA:Computers&Structures,Incorporated,2004.
[16]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程震动,1991,11(3):45-53.(Ou Jinping,Niu Ditao,Du Xiuli.Random earthquake ground motion model and itsparameter determination used in aseismic design[J].Earthquake Engineering and Engineering Vibration,1991,11(3):45-53.(in Chinese))
[2]Emesto H Z,Vonmarcke E H.Seismic random-vibration analysis of multi-support structural system[J].Journal of Engineering Mechanics,1994,120(5):1107-1128.
[3]Lin J H.A fast CQC algorithm of PSD matrices forrandom seismic responses[J].Computers andStructures,1992,44(3):683-687.
[4]Lin J H,Zhang Y H,Li Q S,et a1.Seismic spatialeffects for long-span bridges using the pseudo excitationmethod[J].Engineering Structures,2004,26(9):1207-1216.
[5]卜国雄,谭平,张颖,周福霖.大型超高层建筑的随机风振响应分析[J].哈尔滨工业大学学报,2010,42(2):175-179.(Bu Guoxiong,Tan Ping,ZhangYing,Zhou Fulin.Random wind-induced responseanalysis of a large-scale and high-rise building[J].Journal of harbin Institute of Technology,2010,42(2):175-179.(in Chinese))
[6]张志超,张亚辉,赵岩.车-桥系统非平稳随机振动的PEM-PIM算法[J].计算力学学报,2009,26(1):26-32.(Zhang Zhichao,Zhang Yahui,ZhaoYan.Combined PEM-PIM scheme for the non-stationaryvibration analysis of vehicle-bridge systems[J].Chinese Journal of Computational Mechanics,2009,26(1):26-32.(in Chinese))
[7]张志超,张亚辉,林家浩.三维车桥耦合系统的非平稳随机振动分析[J].应用力学学报,2010,27(1):151-158.(Zhang Zhichao,Zhang Yahui,LinJiahao.Seepage calculation model for face slab jointand crack of concrete face rockfill dam[J].ChineseJournal of Applied Mechanics,2010,27(1):151-158.(in Chinese))
[8]Zhang W S,Xu Y L.Modal analysis and seismicresponse of steel frames with connection dampers[J].Engineering Structures,2001,3(4):385-396.
[9]汪洋,石永久,王元清.实用多点输入虚拟激励法在通用有限元软件中的实现[J].地震工程与工程振动,2010,30(1):46-52.(Wang Yang,Shi YongJiu,Wang Yuanqing.Implementation of the practicalpseudo excitation method for multi-support seismicresponse analysis in general FEM software[J].Journalof Earthquake Engineering and Engineering Vibration,2010,30(1):46-52.(in Chinese))
[10]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185-190.(LiYonghua,Li Siming.Pseudo excitation based onsolving absolute displacement[J].Journal of Vibrationand Shock,2009,28(10):185-190.(in Chinese))
[11]陈建兵,彭勇波,李杰.关于虚拟激励法的一个注记[J].计算力学学报,2011,28(2):163-167.(Chen Jianbing,Peng Yongbo,Li Jie.A note on thepseudo-excitation method[J].Chinese Journal ofComputational Mechanics,2011,28(2):163-167.(in Chinese))
[12]Edward L W.Static and dynamic analysis of structures[M].Berkeley,CA:Computer and Structures,Inc,2004.
[13]Liu G H,Guo W,Li H N.An effective and practicalmethod for solving an unnegligible problem inherent inthe current calculation model for multi-support seismicanalysis of structures[J].Science China:TechnologicalSciences,2010,53(7):1774-1784.
[14]刘树屯,关忆卢.首都机场306m跨飞机库屋盖钢结构设计施工中的一些问题[J].钢结构,1996,11(4):4-8.(Liu Shutun,Guan Yilu.Several problemsof design and construction of 306 m-span hangar roof incapital airport[J].Steel Construction,1996,11(4):4-8.(in Chinese))
[15]Clough R W,Penzien J.Dynamics of structures[M].3rd ed.Berkeley,CA:Computers&Structures,Incorporated,2004.
[16]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程震动,1991,11(3):45-53.(Ou Jinping,Niu Ditao,Du Xiuli.Random earthquake ground motion model and itsparameter determination used in aseismic design[J].Earthquake Engineering and Engineering Vibration,1991,11(3):45-53.(in Chinese))
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