用加速度和位移反馈修正无阻尼振动系统的一种迭代法

摘要/Abstract

摘要： 该文给出了一种同时修正质量和刚度矩阵的迭代方法.通过该方法可以得到满足特征方程的加速度和位移反馈增益矩阵，据此可以得到Frobenius范数下的最优修正质量矩阵和刚度矩阵.该方法不仅可以保证修正后的矩阵是对称的，同时还可以保证修正是不溢出的.最后两个数值算例表明该方法是有效的.

关键词: 模型修正, 迭代算法, 部分指定谱信息, 不溢出, 无阻尼振动系统, 最优逼近

Abstract: In this paper, an iterative method for simultaneously updating mass and stiffness matrices is presented. By the method, the required control gain matrices of acceleration and displacement feedback are determined, and thus the optimal approximation mass and stiffness matrices which satisfies the required eigenvalue equation are found under the Frobenius norm sense and the large number of unmeasured and unknown eigeninformation of the original model is preserved. Two numerical examples show that the proposed method is reliable and attractive.

Key words: Model updating, Iterative algorithm, Partially prescribed spectral information, No spill-over, Undamped structural system, Optimal approximation

中图分类号:

O241

张骞, 袁永新. 用加速度和位移反馈修正无阻尼振动系统的一种迭代法[J]. 数学物理学报, 2018, 38(2): 358-371.

Zhang Qian, Yuan Yongxin. An Iterative Updating Method for Undamped Vibration Systems Using Acceleration and Displacement Feedback[J]. Acta mathematica scientia,Series A, 2018, 38(2): 358-371.

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