AAM  >> Vol. 4 No. 3 (August 2015)

    梁的广义特征值反问题及离散模型修正
    Generalized Inverse Eigenvalue Problem and Model Updating for Discrete Beam

  • 全文下载: PDF(440KB) HTML   XML   PP.230-237   DOI: 10.12677/AAM.2015.43029  
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作者:  

孙振威,马茹茹,贾志刚:江苏师范大学数学与统计学院,江苏 徐州

关键词:
广义特征值反问题最小二乘矩阵范数模型修正最优解Generalized Inverse Eigenvalue Problem Least Squares Matrix Norm Model Updating Optimal Solution

摘要:

本文研究当梁的总质量未知时给定两个特征对的广义特征值反问题与梁的最佳模型修正问题,给出了广义特征值反问题的通解表达式。针对梁的模型修正问题,利用最小二乘方法选取最优参数,使得新梁的物理参数与原梁物理参数的误差达到最小。

In this paper, we study the generalized inverse eigenvalue problem and the optimal model updating problem according to two given eigenpairs, while the total mass of beam is unknown. We present the general solution of the inverse generalized eigenvalue problem. Aiming at the beam model updating problem, we use the least squares method to compute the optimal quality parameter to minimize the distance between the physical parameters of the new beam system and those of the original one.

文章引用:
孙振威, 马茹茹, 贾志刚. 梁的广义特征值反问题及离散模型修正[J]. 应用数学进展, 2015, 4(3): 230-237. http://dx.doi.org/10.12677/AAM.2015.43029

参考文献

[1] Gladwell, G.M.L. (1986) Inverse Problems in Vibration. Martinus Nijhoff Publishers, Dordrecht, 59-119.
http://dx.doi.org/10.1007/978-94-015-1178-0
[2] Gladwell, G.M.L. (1984) Inverse Problems for the Vibrating Beam. Proceedings of the Royal Society of London A, 393, 277-295.
http://dx.doi.org/10.1098/rspa.1984.0058
[3] Gladwell, G.M.L. (1986) The Inverse Problems for the Eu-ler-Bernoulli Beam. Proceedings of the Royal Society of London A, 407, 199-218.
http://dx.doi.org/10.1098/rspa.1986.0093
[4] Ram, Y.M. (1994) Inverse Mode Problems for the Discrete Model of a Vibrating Beam. Journal of Sound and Vibration, 169, 239-252.
http://dx.doi.org/10.1006/jsvi.1994.1016
[5] 田霞, 戴华 (2005) 梁的离散模型的模态反问题. 振动与冲击, 6, 29-31.
[6] 戴华 (1994) Jacobi矩阵特征值反问题. 计算物理, 4, 451-456.
[7] 徐树方, 高立, 张平文 (2013) 数值线性代数. 第二版, 北京大学出版社, 北京, 90-96.