根据非完整模态信息进行结构动力模型识别*
A Model ldentification Method of Vibrating Structures from lncomplete Modal lnformation
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摘要: 对于复杂结构的振动问题,我们很难给出比较准确的数学模型。本文建立了一种利用非完整模态试验数据来确定结构线性动力模型的识别办法。该方法的主要特点是不需要知道系统的全部模态信息,便可同时地唯一地识别出系统的质量矩阵、阻尼矩阵、刚度矩阵及其他相关参数。我们假定系统的质量矩阵、阻尼矩阵和刚度矩阵具有实对称性和正定性,并且系统的部分特征值和相应的特征向量已由实验给出,在此基础上利用最小二乘法及迭代修正技术进行系统矩阵及其他相关参数的识别。为了验证方法的可靠性,文中给出了若干构造性算例。Abstract: The accurate mathematical models for complicated structures are very difficult to construct.The work presented here provides an identification method for estimating the mass.damping,and stiffness matrices of linear dynamical systems from incomplete experimental data.The mass,stiffness and damping matrices are assumed to be real,symmetric,and positive definite The partial set of experimental complex eigenvalues and corresponding eigenvectors are given.In the proposed method the least squares algorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters.Seeveral illustative examples,are presented to demonstrate the reliability of the proposed method.It is emphasized that the mass,damping and stiffness matrices can be identified simultaneously.
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[1] S.R.Ibrahim,Dynamic modeling of structures from measured complex modes,AIAA Journal,21(1983),888-811. [2] C.P.Fritzen,Identification of mass damping,and stiffness matrices of mechanical system,ASME Journal or Vibration,Acoustics,Stress,and Reliabiliy in Design,108(1986),9-16. [3] M.J.Roemer and D.J.Mook,Mass,stiffness,and damping matrix identification:an integrated approach,ASME Journal of Vibration,Acoustics,114(1992),358-363. [4] R.J.Guyan,Reduction of stiffness and mass matrices,AIAA Journal.14(1965),1627-1628. [5] D.J.Ewins,Modal Testing:Theory and Practice,Research Studies Press Ltd,England(1986). [6] C.Minas and D.J.Inman,Identification of a nonproportional damping matrix from incomplete modal information,ASME Journal of Vibration,Acoustics,113((991),219-224. -
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