耗能减震结构的复模态矩阵摄动法
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摘要
针对耗能减震结构的分析和优化设计过程中要遇到非比例阻尼和参数改变的情况,如果要较精确地求解系统的广义特征值问题,需经过两重迭代计算,这种迭代振动分析是非常麻烦的。为了保证非比例阻尼结构分析的精度和结构参数改变时迭代分析的效率,推导适用于非经典阻尼情况的复模态矩阵摄动法,提高了结构重分析的效率,通过算例分析,表明了该方法在一定范围内具有较高的精度。
Changing parameters and non-proportional damping is usually encountered in the optimum analysis and design of structures with energy dissipaters. Double iterative computations are necessary to compute the generalized Eigen value accurately, which is very complicated. A complex modal matrix perturbation method for symmetrical systems is deduced for optimum analysis of non-proportionally damped structures. The method is proved to be efficient by the numerical example.
Changing parameters and non-proportional damping is usually encountered in the optimum analysis and design of structures with energy dissipaters. Double iterative computations are necessary to compute the generalized Eigen value accurately, which is very complicated. A complex modal matrix perturbation method for symmetrical systems is deduced for optimum analysis of non-proportionally damped structures. The method is proved to be efficient by the numerical example.
引文
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[2]范文亮.被动耗能减震结构的分析与设计方法研究[D].重庆:重庆大学,2003.Fan Wenliang.Study on analysis and design methods of passive energy dissipation systems[D].Chongqing:Chongqing University,2003.(in Chinese)
[3]周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程学报,2003,36(5):30~36.Zhou Xiyuan,Dong Di,Su Youpo.New method for linear systems with non-classic damping under ground motion[J].China Civil Engineering Journal,2003,36(5):30~36.(in Chinese)
[4]桂国庆,何玉敖.非比例阻尼结构复模态问题求解的矩阵摄动法[J].同济大学学报,1996,24(6):613~618.Gui Guoqing,He Yuao.Matrix perturbation method for solving the complex modal problem of non-proportionally damped structures[J].Journal of Tongji University,1996,24(6):613~618.(in Chinese)
[5]Giovanni Falsone,Giuseppe Muscolino.New real-value modal combination rules for non-classically dampedstructures[J].EESD,2004,33:1187~1209.
[6]李杰,李国强.地震工程学导论[M].北京:地震工程出版社,1992.Li Jie,Li Guoqiang.Introduction to earthquake engineering[M].Beijing:Earthquake Engineering Press,1992.(in Chinese)
[7]方同,薛璞.振动理论及应用[M].西安:西北工业大学出版社,1998.Fang Tong,Xue Pu.Vibration theory and its application[M].Xi’an:Northwestern Polytechnic University Press,1998.(in Chinese)
[8]曹树谦,张文德,萧龙翔.振动结构模态分析——理论,实验及应用[M].天津:天津大学出版社,2001.Cao Shuqian,Zhang Wende,Xiao Longxiang.Modal analysis for structure vibration——theory,experiment and application[M].Tianjin:Tianjin University Press,2001.(in Chinese)
[9]陈塑寰.结构振动分析的矩阵摄动理论[M].重庆:重庆出版社,1991.Chen Suhuan.Matrix perturbation theory for structure vibration analysis[M].Chongqing:Chongqing Press,1991.(in Chinese)
[10]陈塑寰.结构动态设计的矩阵摄动理论[M].北京:科学出版社,1999.Chen Suhuan.Matrix perturbation theory for structures’dynamic design[M].Beijing:Science Press,1999.(in Chinese)
[11]Clough R W,Penzien J.Dynamics of structures[M].NewYork:McGraw-Hill Inc.1993.
[12]王勖成.有限单元法[M].北京:清华大学出版社,2003.Wang Xucheng.Finite elements method[M].Beijing:Tsinghua University Press,2003.(in Chinese)
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