复阻尼结构动力方程的高斯精细时程积分法
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摘要
复阻尼振动系统的瞬态响应通常只能在频域内求解。该文根据复阻尼理论应遵循对偶复化的原则,结合精细积分指数矩阵和高斯积分的运算方法,通过理论推导,给出了复阻尼结构动力方程的高斯精细时程积分法。分别采用Newmark-法和高斯精细时程积分法计算了复阻尼多自由度系统地震时程响应,并与频域法(视为精确解)的计算结果进行比较。结果表明:高斯精细时程积分法可用于复阻尼系统动力时程分析;且比Newmark-法有更高的精度和效率。
The vibration analysis of complex damping systems is fulfilled mainly in frequency domain.Based on the dual principle of complex damping theory,a new time-history analysis method is proposed for complex damping systems,which combines the Gauss quadrature with the calculation technique of an exponential function matrix in the precise time-integration method.The responses of complex damping MDOF systems are calculated by Newmark-β method and Gauss precise time-integration method respectively,and compared with the frequency-domain solution.It is shown that Gauss precise time-integration method,having higher precision and efficiency than Newmark-β method,can be used to solve the complex damping vibration equation.
The vibration analysis of complex damping systems is fulfilled mainly in frequency domain.Based on the dual principle of complex damping theory,a new time-history analysis method is proposed for complex damping systems,which combines the Gauss quadrature with the calculation technique of an exponential function matrix in the precise time-integration method.The responses of complex damping MDOF systems are calculated by Newmark-β method and Gauss precise time-integration method respectively,and compared with the frequency-domain solution.It is shown that Gauss precise time-integration method,having higher precision and efficiency than Newmark-β method,can be used to solve the complex damping vibration equation.
引文
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[14]钟万勰.结构动力方程的精细时程积分法[J].大连理工学报,1994,34(2):131―135.Zhong Wanxie.On precise time-integration method forstructural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131―135.(in Chinese)
[15]张森文,曹开彬.计算结构动力响应的状态方程直接积分法[J].计算力学学报,2000,17(1):94―97.Zhang Senwen,Cao Kaibin.Direct integration of stateequation method for dynamic response of structure[J].Chinese Journal of Computational Mechanics,2000,17(1):94―97.(in Chinese)
[16]Zhu X Q,Law S S.Precise time-step integration for thedynamic response of a continuous beam under movingloads[J].Journal of Sound and Vibration,2001,240(5):962―970.
[17]储德文,王元丰.精细直接积分法的积分方法选择[J].工程力学,2002,19(6):115―119.Chu Dewen,Wang Yuanfeng.Integration formulaselection for precise direct integration method[J].Engineering Mechanics,2002,19(6):115―119.(inChinese)
[18]汪梦甫,周锡元.结构动力方程的高斯精细时程积分法[J].工程力学,2004,21(4):13―16.Wang Mengfu,Zhou Xiyuan.Gauss precise time-integration of structural dynamic analysis[J].Engineering Mechanics,2004,21(4):13―16.(inChinese)
[19]Wang Mengfu,Au F T K.Assessment and improvementof precise time step integration method[J].Computersand Structures,2006,84:779―786.
[2]Nashif A D,et al.Vibration damping[M].New York:John Wiley&Sons,1985.
[3]Singiresu S R.Mechanical vibrations[M].New York:Addison-Wesley Publishing Company,1990.
[4]胡海岩.结构阻尼模型及系统时域动响应[J].振动工程学报,1992,5(1):8―15.Hu Haiyan.Structural damping model and systemdynamic response at time domain[J].Journal ofVibration Engineering,1992,5(1):8―15.(in Chinese)
[5]Henwood D J.Approximating the hysteretic dampingmatrix by a viscous matrix for modelling in the timedomain[J].Journal of Sound and Vibration,2002,254(3):575―593.
[6]Lin R M,Zhu J.On the relationship between viscous andhysteretic damping models and the importance of correctinterpretation for system identification[J].Journal ofSound and Vibration,2009,325:14―33.
[7]朱镜清.关于复阻尼理论的两个基本问题[J].固体力学学报,1992,13(2):113―118.Zhu Jingqing.On the two basic problems of complexdmping theory[J].Acta Mechanica Solida Sinica,1992,13(2):113―118.(in Chinese)
[8]何钟怡.复本构理论中的对偶原则[J].固体力学学报,1994,15(2):177―180.He Zhongyi.The dual principe in theory of complexconstitutive equations[J].Acta Mechanica Solida Sinica,1994,15(2):177―180.(in Chinese)
[9]朱镜清.结构抗震分析原理[M].北京:地震出版社,2002.Zhu Jingqing.Seismic Analysis of Structures[M].Beijing:Earthquake Press,2002.(in Chinese)
[10]朱敏,朱镜清.复阻尼地震反应谱的计算方法及其它[J].地震工程与工程振动,2000,20(2):19―23.Zhu Min,Zhu Jingqing.Calculation of complex dampingspectra from earthquake records[J].EarthquakeEngineering and Engineering Vibration,2000,20(2):19―23.(in Chinese)
[11]朱镜清,朱敏.复阻尼多自由度系统动力分析的模态叠加法[J].地震工程与工程振动,2004,24(1):55―58.Zhu Jingqing,Zhu Min.Two mode-superpositionmethods for dynamic analysis of MDOF systems withcomplex damping characteristics[J].EarthquakeEngineering and Engineering Vibration,2004,24(1):55―58.(in Chinese)
[12]李鹏,王元丰.黏性阻尼与复阻尼对钢筋混凝土结构框架地震响应影响的分析[J].地震工程与工程振动,2007,27(3):54―57.Li Peng,Wang Yuanfeng.Analysis of seismic responsesof RC frames with viscous damping or complex damping[J].Earthquake Engineering and Engineering Vibration,2007,27(3):54―57.(in Chinese)
[13]克拉夫R W,彭津J.结构动力学[M].第2版.王光远,译.北京:高等教育出版社,2006.Clough R W,Penzien J.Dynamics of structures[M].2nded.Translated by Wang Guangyuan.Beijing:HigherEducation Press,2006.(in Chinese)
[14]钟万勰.结构动力方程的精细时程积分法[J].大连理工学报,1994,34(2):131―135.Zhong Wanxie.On precise time-integration method forstructural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131―135.(in Chinese)
[15]张森文,曹开彬.计算结构动力响应的状态方程直接积分法[J].计算力学学报,2000,17(1):94―97.Zhang Senwen,Cao Kaibin.Direct integration of stateequation method for dynamic response of structure[J].Chinese Journal of Computational Mechanics,2000,17(1):94―97.(in Chinese)
[16]Zhu X Q,Law S S.Precise time-step integration for thedynamic response of a continuous beam under movingloads[J].Journal of Sound and Vibration,2001,240(5):962―970.
[17]储德文,王元丰.精细直接积分法的积分方法选择[J].工程力学,2002,19(6):115―119.Chu Dewen,Wang Yuanfeng.Integration formulaselection for precise direct integration method[J].Engineering Mechanics,2002,19(6):115―119.(inChinese)
[18]汪梦甫,周锡元.结构动力方程的高斯精细时程积分法[J].工程力学,2004,21(4):13―16.Wang Mengfu,Zhou Xiyuan.Gauss precise time-integration of structural dynamic analysis[J].Engineering Mechanics,2004,21(4):13―16.(inChinese)
[19]Wang Mengfu,Au F T K.Assessment and improvementof precise time step integration method[J].Computersand Structures,2006,84:779―786.
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