波谱单元法在空间桁架地震响应分析中的应用
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摘要
针对传统波谱单元法(SEM)只能用于求解节点集中荷载作用下结构动力响应问题的不足,提出了一种通过计算地震等效波谱节点荷载求解桁架结构地震响应的方法。基于虚功原理,利用波谱形函数积分得到地震等效波谱节点荷载的显式表达式,通过修改波谱单元法中单元刚度矩阵的波数,考虑了阻尼对结构动力特征的影响,采用数值拉普拉斯(Laplace)变换替换快速傅里叶(FFT)变换,回避了传统波谱单元法中FFT的周期性问题。利用地震荷载等效后的波谱节点荷载对三维空间桁架结构进行地震响应分析,结果表明,采用本文的方法能方便的计算桁架结构的地震等效波谱节点荷载,精确求解结构的地震响应,与传统有限元法(FEM)相比,大大减少计算单元数量,提高计算精度,且便于编程计算。
An extended spectral element method(SEM) was established to get dynamic responses of a space truss subjected to seismic load.The seismic load was equivalent to concentrated node forces by integrating the shape function in SEM based on the principle of virtual work.Both internal viscoelastic damping and external viscous damping of the truss bar were considered by just simply modifying the wave number.Laplace transformation instead of fast Fourier transformation(FFT) was utilized in SEM to avoid the periodicity of FFT.To evaluate the accuracy of Laplace-based SEM,the dynamic responses of a space truss under seismic load was analyzed as a numerical example.The numerical results obtained using FEM were compared with those using SEM.It was found that SEM provides good dynamic results under seismic load;the equivalent seismic node forces are convenient to get by programming calculation;SEM is proved to be an efficient method to analyze dynamic responses of structures accurately while the number of element greatly decreases.
An extended spectral element method(SEM) was established to get dynamic responses of a space truss subjected to seismic load.The seismic load was equivalent to concentrated node forces by integrating the shape function in SEM based on the principle of virtual work.Both internal viscoelastic damping and external viscous damping of the truss bar were considered by just simply modifying the wave number.Laplace transformation instead of fast Fourier transformation(FFT) was utilized in SEM to avoid the periodicity of FFT.To evaluate the accuracy of Laplace-based SEM,the dynamic responses of a space truss under seismic load was analyzed as a numerical example.The numerical results obtained using FEM were compared with those using SEM.It was found that SEM provides good dynamic results under seismic load;the equivalent seismic node forces are convenient to get by programming calculation;SEM is proved to be an efficient method to analyze dynamic responses of structures accurately while the number of element greatly decreases.
引文
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[2]Dolyle J F,Farris TN.Aspectrally formulated finite elementfor flexural wave propagation in beams[J].The internationaljournal of Analytical and Experimental Modal Analysis,1990,5(2):99-107.
[3]Lee U,Kim J H,Leung AY T.The spectral element Methodin Structural dynamics[J].The Shock and Vibration Digest,2000,32(6):451-465.
[4]Dolyle J F,Farris TN.Aspectrally formulated finite elementfor wave propagation in 3-D frame structures[J].Theinternational journal of Analytical and Experimental ModalAnalysis,1990,5(4):223-237.
[5]Dolyle J F.A spectrally formulated finite element forlongitudinal wave propagation[J].The international journalof Analytical and Experimental Modal Analysis.1988,3(1):1-5.
[6]Cho J Y,Go H S,Lee U.Dynamic response of the spectralelement model by using the FFT[J].2007,345-346:845-848.
[7]Igawa H,Komatsu K,Yamaguchi I et al.Wave propagationanalysis of frame structures using the spectral element method[J].Journal of sound and vibration,2004,277:1071-1081.
[8]Lee U,Lee J K.Spectral element analysis of the structureunder dynamic distributed loads[J].Journal of MechanicalScience and Technology,1998,12(4):565-571.
[9]Lee U,Cho J Y.FFT-based spectral element analysis for thelinear continuum dynamic systems subjected to arbitrary initialconditions by using the pseudo-force method[J].International Journal for Numerical Methods in Engineering,2007,74(1):159-174.
[10]R.克拉夫,J.彭津.结构动力学[M].王光远等译.北京:高等教育出版社,2006.
[11]刘树棠.杆系结构有限元分析与matlab应用[M].北京:中国水利水电出版社,2007.
[12]王元汉,李丽娟,李银平.有限元法基础与程序设计[M].广州:华南理工大学出版社,2001.
[13]Soh C K,Tseng KKH,Bhalla S,et al.Performance of smartpiezoceramic patches in health monitoring of a RC bridge[J].Smart Materials and Structures,2000,9(4),533-542.
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