基于状态空间理论的工程结构地震时程响应分析
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摘要
基于状态空间理论分析与计算工程结构地震时程响应问题,根据结构动力学方程,引入结构系统的状态变量,建立结构地震时程响应分析的状态方程,并给出非齐次状态方程的解.为了求解矩阵指数函数,着重介绍了凯莱-哈密尔顿(Kaley-Hamilton)法、状态空间迭代法和精细积分法.对结构动力时程响应问题按这三种解法分别建立了计算格式,并编制相应计算程序.最后,给出若干数值算例,其计算结果表明,状态空间法分析计算结构动力时程响应,其精度好,效率高,是一种非常有效的方法.
The engineering structure time history response in earthquakes was analyzed by means of state space theory.The state equations of the engineering structure time history responses were established with the inhomogeneous solutions given on the basis of the structure dynamic equations and the state variables.The Kely-Hamilton method,the state space method and the fine integral method were applied with the corresponding computing format and programs to solve the matrix exponential function.Several numerical examples demonstrate that the state space method has better accuracy and higher efficiency for analyzing structures dynamic time history responses.
The engineering structure time history response in earthquakes was analyzed by means of state space theory.The state equations of the engineering structure time history responses were established with the inhomogeneous solutions given on the basis of the structure dynamic equations and the state variables.The Kely-Hamilton method,the state space method and the fine integral method were applied with the corresponding computing format and programs to solve the matrix exponential function.Several numerical examples demonstrate that the state space method has better accuracy and higher efficiency for analyzing structures dynamic time history responses.
引文
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[2]常春馨.现代控制理论基础[M].北京:机械工业出版社,1988.
[3]Zhong Wan-xie.Precise computation for transientanalysis[J].Computational Structural Mechanics andApplications,1995,12(1):1-6.钟万勰.暂态历程的精细计算方法[J].计算结构力学及其应用,1995,12(1):1-6.
[4]钟万勰,吴志刚,谭述君.状态空间控制理论与计算[M].北京:科学出版社,2007.
[5]沈鹏程.多变量样条有限元法[M].北京:科学出版社,1997.
[6]Mizusawa T,Kondo Y.Application of the splineelement method to analyze vibration of skew Mindlinplates with varying thickness in one direction[J].Journal of Sound and Vibration,2001,241(29):485-501.
[7]Attallah K M Z,Ye J Q,Sheng H Y.Three-dimensional finite strip analysis of laminated panels[J].Computers and Structures,2007,85(23-24):1 769-1 781.
[8]Ch ng H N,Pan J.Cubic spline elements for modellingmicrostructural evolution of materials controlled bysolid-state diffusion and grain-boundary migration[J].Journal of Computational Physics,2004,196(2):724-750.
[9]Ch ng H N,Pan J.Modelling microstructuralevolution of porous polycrystalline materials and anumerical study of anisotropic sintering[J].Journal ofComputational Physics,2005,204(2):430-461.
[10]Shen Xiao-pu,Xiao Zhuo.State space iteration methodfor analysis of dynamic time history response of tallbuilding structures[J].Journal of Building Structures,1998,19(5):8-16.沈小璞,肖卓.高层建筑结构动力时程响应分析的状态空间迭代法[J].建筑结构学报,1998,19(5):8-16.
[11]Shen Xiao-pu,Yu Jing-ping,Chen Rong-yi.Splineelement state space approach for analysis of structuraldynamic response[J].Journal of Hefei University ofTechnology(Natural Science),1998,21(3):78-84.沈小璞,余景平,陈荣毅.样条元状态空间法分析结构动力响应问题[J].合肥工业大学学报,1998,21(3):78-84.
[12]Shen Xiao-pu,Yu Jing-ping,Chen Rong-yi,et al.Dynamic response analysis spherical shells by splinestate variable method[J].Chinese Journal ofComputational Mechanics,2001,18(2):205-209.沈小璞,余景平,陈荣毅,等.样条状态变量法分析扁球壳的动力响应[J].计算力学学报,2001,18(2):205-209.
[13]Shen Xiao-pu,Yu Jing-ping,Lei Qing-guan,et al.Method of multivariable responses for elastic dynamics[J].Journal of Vibration Engineering,2001,14(3):368-372.沈小璞,余景平,雷庆关,等.弹性动力学的多变量响应问题的解法[J].振动工程学报,2001,14(3):368-372.
[14]Shen Xiao-pu,Wang Jin-hui,Zhang Hong-ya,et al.Analysis and study of the very thin-walled light-gaugesteel structural multiple story dwelling system[J].Earthquake Resistant Engineering and Retrofitting,2006,28(3):15-20.沈小璞,王金辉,张红亚,等.超薄壁型轻钢结构多层住宅结构体系的地震动时程响应分析[J].工程抗震与加固改造,2006,28(3):15-20.
[15]巴斯K J.工程分析中的有限元法[M].傅子智,译.北京:机械工业出版社,1991.
[16]宋雅桐.结构分析程序设计[M].南京:东南大学出版社,1990.
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