直接确定Rayleigh阻尼系数的一种优化方法
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摘要
为避免构造Rayleigh阻尼矩阵过程中选择两阶参考振动模态的任意性,提出了一种直接确定Rayleigh阻尼系数的优化求解方法。在该方法中,利用输入时程的位移反应谱和模态分析结果,以结构某一动力反应的峰值误差构造目标函数,使目标函数取最小值即可得到Rayleigh阻尼系数的优化解。随后,以一栋5层剪切型建筑的谐振反应为例,系统研究了结构动力特性、激励空间分布和频谱特性对Rayleigh阻尼系数的影响。同时,验证所提方法的精度与有效性。
In order to avoid an arbitrary selection of two reference vibration modes which are used to evaluate the two coefficients of Rayleigh damping,an optimization method for direct determination of the two Rayleigh damping coefficients is proposed.In the method,by formulating and minimizing an objective function which is an error term of the peak response at certain degree of a structure,the two coefficients can be systematically evaluated following the deformation response spectrum of excitation and modal analysis.Then,based on the harmonic response analysis of a five-storey shear building,the effects of both spatial distribution and frequency content of excitations and the effects of structural dynamic characteristics on selection of natural frequencies in Rayleigh damping are investigated in detail,and the accuracy and effectiveness of the proposed method are demonstrated.
In order to avoid an arbitrary selection of two reference vibration modes which are used to evaluate the two coefficients of Rayleigh damping,an optimization method for direct determination of the two Rayleigh damping coefficients is proposed.In the method,by formulating and minimizing an objective function which is an error term of the peak response at certain degree of a structure,the two coefficients can be systematically evaluated following the deformation response spectrum of excitation and modal analysis.Then,based on the harmonic response analysis of a five-storey shear building,the effects of both spatial distribution and frequency content of excitations and the effects of structural dynamic characteristics on selection of natural frequencies in Rayleigh damping are investigated in detail,and the accuracy and effectiveness of the proposed method are demonstrated.
引文
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[4]淡丹辉,孙利民.结构损伤有限元建模中的阻尼问题研究[J].工程力学,2006,23(9):48-54.Dan Danhui,Sun Limin.Damp research on the damage based structure FEM modeling[J].Engineering Mechanics,2006,23(9):48-54.(in Chinese)
[5]Caughey T K.Classical normal modes in damped linear dynamic systems[J].Journal of Applied Mechanics,1960,27(2):269-271.
[6]Wilson E L.Evaluation of orthogonal damping matrices[J].International Journal for Numerical Methods in Engineering,1972,4(1):5-10.
[7]Xu J A.Synthesis formulation of explicit damping matrix for non-classically damped systems[J].Nuclear Engineering and Design,2004,227(2):125-132.
[8]Lee S H,Min K W,Hwang J S,Kim J.Evaluation of equivalent damping ratio of a structure with added dampers[J].Engineering Structures,2004,26(3):335-346.
[9]Bilbao A,Aviles R,Agirrebeitia J,Ajuria D.Proportional damping approximation for structures with added viscoelastic dampers[J].Finite Elements in Analysis and Design,2006,42(6):492-502.
[10]Occhiuzzi A.Additional viscous dampers for civil structures:Analysis of design methods based on effective evaluation of modal damping ratios[J].Engineering Structures,2009,31(5):1093-1101.
[11]杜永峰,李慧,苏磐石,赵国藩.非比例阻尼隔震结构地震响应的实振型分解法[J].工程力学,2003,20(4):24-32.Du Yongfeng,Li Hui,Billie F Spencer,Jr,Zhao Guofan,et al.Real mode superposition method for analysis of seismic response of non-proportionally damped isolated structures[J].Engineering Mechanics,2003,20(4):24-32.(in Chinese)
[12]Chopra A K.Dynamics of structures:Theory and applications to earthquake engineering[M].New Jersey:Englewood Cliffs,Prentice-Hall,1995:416-421.
[2]Kareem A,Gurley K.Damping in structures:Its evaluation and treatment of uncertainty[J].Journal of Wind Engineering and Industrial Aerodynamics,1996,59(2/3):131-157.
[3]Jeary A P.Damping in structures[J].Journal of Wind Engineering and Industrial Aerodynamics,1997,72(1):345-355.
[4]淡丹辉,孙利民.结构损伤有限元建模中的阻尼问题研究[J].工程力学,2006,23(9):48-54.Dan Danhui,Sun Limin.Damp research on the damage based structure FEM modeling[J].Engineering Mechanics,2006,23(9):48-54.(in Chinese)
[5]Caughey T K.Classical normal modes in damped linear dynamic systems[J].Journal of Applied Mechanics,1960,27(2):269-271.
[6]Wilson E L.Evaluation of orthogonal damping matrices[J].International Journal for Numerical Methods in Engineering,1972,4(1):5-10.
[7]Xu J A.Synthesis formulation of explicit damping matrix for non-classically damped systems[J].Nuclear Engineering and Design,2004,227(2):125-132.
[8]Lee S H,Min K W,Hwang J S,Kim J.Evaluation of equivalent damping ratio of a structure with added dampers[J].Engineering Structures,2004,26(3):335-346.
[9]Bilbao A,Aviles R,Agirrebeitia J,Ajuria D.Proportional damping approximation for structures with added viscoelastic dampers[J].Finite Elements in Analysis and Design,2006,42(6):492-502.
[10]Occhiuzzi A.Additional viscous dampers for civil structures:Analysis of design methods based on effective evaluation of modal damping ratios[J].Engineering Structures,2009,31(5):1093-1101.
[11]杜永峰,李慧,苏磐石,赵国藩.非比例阻尼隔震结构地震响应的实振型分解法[J].工程力学,2003,20(4):24-32.Du Yongfeng,Li Hui,Billie F Spencer,Jr,Zhao Guofan,et al.Real mode superposition method for analysis of seismic response of non-proportionally damped isolated structures[J].Engineering Mechanics,2003,20(4):24-32.(in Chinese)
[12]Chopra A K.Dynamics of structures:Theory and applications to earthquake engineering[M].New Jersey:Englewood Cliffs,Prentice-Hall,1995:416-421.
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