结构地震反应的频域精细传递矩阵法
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摘要
传统的传递矩阵法需要对控制微分方程进行求解,获得相应的传递矩阵。公式繁琐、复杂。文中提出将传递矩阵法与精细积分法中的指数矩阵运算技巧结合起来,在频域内对结构进行动力分析。与传统的传递矩阵法相比,无需对微分方程进行求解,只需按照迭代公式进行计算,就可以得到所需要的传递矩阵。这种方法公式简单,理论上可实现任意精度,而且计算效率较高,能够快速、高精度的进行结构的地震反应分析。算例显示了精细传递矩阵法的有效性。
The traditional transfer matrix method needs to solve differential equations,and gets the transfer matrix.Formula is cumbersome and complex.The transfer matrix method and the computing skills of exponent for precise integration method is combined,and the structure is dynamically analyzed in frequency domain.Comparing with traditional transfer matrix methods,this method needs not to solve the differential equations,but just uses the iterative formula to get the necessary transfer matrix.The formula of this method is simple and able to achieve any precision in theory with higher efficiency.It is able to do the seismic response analysis of structure with high-precision and high-speed.Examples show effectiveness of the precise transfer matrix method.
The traditional transfer matrix method needs to solve differential equations,and gets the transfer matrix.Formula is cumbersome and complex.The transfer matrix method and the computing skills of exponent for precise integration method is combined,and the structure is dynamically analyzed in frequency domain.Comparing with traditional transfer matrix methods,this method needs not to solve the differential equations,but just uses the iterative formula to get the necessary transfer matrix.The formula of this method is simple and able to achieve any precision in theory with higher efficiency.It is able to do the seismic response analysis of structure with high-precision and high-speed.Examples show effectiveness of the precise transfer matrix method.
引文
[1]吉伯海,高建明,张杰.传递矩阵法在钢斜拉桥结构计算中的应用[J].东南大学学报,2004,34(6):838-841.Ji Bohai,Gao Jianming,Zhang Jie.Structural calculation of steel cable-stayed bridges with transfer matrix method[J].Journal of Southeast Universi-ty(Natural Science Edition),2004,34(6):838-841.
[2]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,5(1)18-23.Li Qingning.The transfer matrix method of bar elements with variable cross-section[J].Journal of Xi'an University of Architecture&Technology(Natural Science Edition),2001,5(1):18-23.
[3]董刚,朱镜清.结构地震反应分析的频域传递矩阵法[J].计算结构力学及其应用,1994,11(4),429-435.Dong Gang,Zhu Jingqing.Transfer matrix method for the earthquake response of the structure in frequency domain[J].Chinese Journal of Compu-tational Mechanics1994,11(4):429-435.
[4]Zhong Wanxie,On precise time-intergration method forstructural dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131-136.
[5]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191-195.Wang Mengfu,Zhou Xiyuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191-195.
[6]朱镜清.结构抗震分析原理[M].北京:地震出版社,2004.Zhu Jingqing.Principle of Structure Seismic analysis[M].Beijing:Earthquake Publishing House,2004.
[7]张荣山.工程振动与控制[M].北京:中国建筑工业出版社,2003Zhang Rongshan.Engineering Vibration and Control[M].Beijing:China Building Industry Press,2003.
[8]郭泽英,李青宁.动力反应分析的显式积分方法及其稳定性[J].地震工程与工程振动,2008,28(2):15-19.Guo Zeying,Li Qingning,ZhangShoujun.An explicit integral method and the stability of dynamic response analysis[J].Journal of Earthquake Engi-neering and Engineering Vibration,2008,28(2):15-19.
[9]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增):554-566.Wang Yifan.Solving structural dynamic equation using combination of the precise integraton method and direct precise integraton method[J].Indus-trial Architecture2006,36(addition):554-566.
[2]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,5(1)18-23.Li Qingning.The transfer matrix method of bar elements with variable cross-section[J].Journal of Xi'an University of Architecture&Technology(Natural Science Edition),2001,5(1):18-23.
[3]董刚,朱镜清.结构地震反应分析的频域传递矩阵法[J].计算结构力学及其应用,1994,11(4),429-435.Dong Gang,Zhu Jingqing.Transfer matrix method for the earthquake response of the structure in frequency domain[J].Chinese Journal of Compu-tational Mechanics1994,11(4):429-435.
[4]Zhong Wanxie,On precise time-intergration method forstructural dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131-136.
[5]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191-195.Wang Mengfu,Zhou Xiyuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191-195.
[6]朱镜清.结构抗震分析原理[M].北京:地震出版社,2004.Zhu Jingqing.Principle of Structure Seismic analysis[M].Beijing:Earthquake Publishing House,2004.
[7]张荣山.工程振动与控制[M].北京:中国建筑工业出版社,2003Zhang Rongshan.Engineering Vibration and Control[M].Beijing:China Building Industry Press,2003.
[8]郭泽英,李青宁.动力反应分析的显式积分方法及其稳定性[J].地震工程与工程振动,2008,28(2):15-19.Guo Zeying,Li Qingning,ZhangShoujun.An explicit integral method and the stability of dynamic response analysis[J].Journal of Earthquake Engi-neering and Engineering Vibration,2008,28(2):15-19.
[9]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增):554-566.Wang Yifan.Solving structural dynamic equation using combination of the precise integraton method and direct precise integraton method[J].Indus-trial Architecture2006,36(addition):554-566.
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