非平稳多维多点虚拟激励法的快速模拟方法
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摘要
为研究实际地震动非平稳性与空间效应的快速模拟方法,运用绝对位移直接求解非平稳多维多点虚拟激励法,不必将绝对位移分解为拟静力位移项及动力相对位移项,避免求解静力影响矩阵的繁琐;将非平稳激励响应转换为一系列确定性外力作用下运动方程瞬态解,以有限元软件ANSYS瞬态分析模块为平台,在结构有限元模型各支撑处激励方向设置大质量块后,直接将地震虚拟激励荷载施加于大质量块,实现绝对位移求解动力方程,提高随机振动响应计算效率,高效地在通用有限元软件中实现多维多点非平稳虚拟激励法,避免自编程序的繁琐,简化实现方法,使多维多点非平稳虚拟激励法在理论及工程应用中获得进一步拓展。
To investigate a fast simulation technique for non-stationarity and spatial effects of actual ground motion,the equations of motion of a system were solved divectly using absolute displacements not to decompose absolute displacements into quasi-static displacements and dynamic relative ones,and to avoid solving a static influence matrix.The responses to non-stationary excitations were converted into transient solutions of the equations of motion of a system under a series of deterministic external force actions.The transient analysis module of the FE software ANSYS was taken as a platform,large masses subjected to earthquake pseudo excitation loads were put on supports of a FE model of a system,and then its dynamic equations were solved with absolute displacements.The studying results showed that using the proposed fast simulation technique,the computing efficiency of random vibration responses can be improved,the nonstationary multi-dimensional and multi-support pseudo excitation method can be realized effectively using the generalpurpose FE soft ware ANSYS not to self-write a code.
To investigate a fast simulation technique for non-stationarity and spatial effects of actual ground motion,the equations of motion of a system were solved divectly using absolute displacements not to decompose absolute displacements into quasi-static displacements and dynamic relative ones,and to avoid solving a static influence matrix.The responses to non-stationary excitations were converted into transient solutions of the equations of motion of a system under a series of deterministic external force actions.The transient analysis module of the FE software ANSYS was taken as a platform,large masses subjected to earthquake pseudo excitation loads were put on supports of a FE model of a system,and then its dynamic equations were solved with absolute displacements.The studying results showed that using the proposed fast simulation technique,the computing efficiency of random vibration responses can be improved,the nonstationary multi-dimensional and multi-support pseudo excitation method can be realized effectively using the generalpurpose FE soft ware ANSYS not to self-write a code.
引文
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[4]Zhang Z C,Lin J H,Zhang Y H.Non-stationary random vibration analysis for train-bridge systems subjected to horizontal earthquakes[J].Engineering Structures,2010,32(11):3571-3582.
[5]江洋,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.JIANG Yang,SHI Yong-jiu,WANG Yuan-qing.Practical multi-input pseudo-excitation method in general-purpose finite element software implementation[J].Earthquake Engineering and Engineering Vibration,2010,30(1):46-52.
[6]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.LI Yong-hua,LI Si-ming.Pseudo excitation method based on solving absolute displacement[J].Journal of Vibration and Shock,2009,28(10):185-190.
[7]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2006.
[8]Caughey T K,Stumpf H J.Transient response of a dynamic system under random vibration[J].Journal of Applied Mechanics,1961,28(1):563-566.
[9]丁阳,林伟,李忠献.大跨度空间结构多维多点非平稳随机地震反应分析[J].工程力学,2007,24(3):97-103.DING Yang,LIN Wei,LI Zhong-xian.Non-stationary random seismic analysis of long-span spatial structures under multi-support and multi-dimensional earthquake excitations[J].Engineering Mechanics,2007,24(3):97-103.
[10]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.QU Tie-jun,WANG Jun-jie,WANG Qian-xin.Practical PSD ground motion model with spatial effect[J].Journal of Earthquake,1996,18(1):55-62.
[11]Lin J H,Zhao Y,Zhang Y H.Accurate and highly efficient algorithms for structural stationary/non-stationary random responses[J].Computer Methods in Applied Mechanics and Engineering,2001,191(1-2):103-111.
[2]Xia C Y,Zhong T Y.Numerical analysis of the nanjing dashengguan yangtze river bridge subjected to non-uniform seismic excitations[J].Journal of Mechanical Science and Technology,2011,25(5):1297-1306.
[3]Lin J H,Zhang Y H,Li Q S.Seismic spatial effects for longspan bridges,using the pseudo excitation method[J].Engineering Structures,2004,26(9):1207-1216.
[4]Zhang Z C,Lin J H,Zhang Y H.Non-stationary random vibration analysis for train-bridge systems subjected to horizontal earthquakes[J].Engineering Structures,2010,32(11):3571-3582.
[5]江洋,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.JIANG Yang,SHI Yong-jiu,WANG Yuan-qing.Practical multi-input pseudo-excitation method in general-purpose finite element software implementation[J].Earthquake Engineering and Engineering Vibration,2010,30(1):46-52.
[6]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.LI Yong-hua,LI Si-ming.Pseudo excitation method based on solving absolute displacement[J].Journal of Vibration and Shock,2009,28(10):185-190.
[7]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2006.
[8]Caughey T K,Stumpf H J.Transient response of a dynamic system under random vibration[J].Journal of Applied Mechanics,1961,28(1):563-566.
[9]丁阳,林伟,李忠献.大跨度空间结构多维多点非平稳随机地震反应分析[J].工程力学,2007,24(3):97-103.DING Yang,LIN Wei,LI Zhong-xian.Non-stationary random seismic analysis of long-span spatial structures under multi-support and multi-dimensional earthquake excitations[J].Engineering Mechanics,2007,24(3):97-103.
[10]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.QU Tie-jun,WANG Jun-jie,WANG Qian-xin.Practical PSD ground motion model with spatial effect[J].Journal of Earthquake,1996,18(1):55-62.
[11]Lin J H,Zhao Y,Zhang Y H.Accurate and highly efficient algorithms for structural stationary/non-stationary random responses[J].Computer Methods in Applied Mechanics and Engineering,2001,191(1-2):103-111.
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