数学季刊 ›› 2021, Vol. 36 ›› Issue (4): 419-429.doi: 10.13371/j.cnki.chin.q.j.m.2021.04.009

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利用特征结构配置方法修正质量和刚度矩阵

  

  1. 1. School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;
    2. Library of Hubei Normal University, Huangshi 435002, China
  • 收稿日期:2021-08-25 出版日期:2021-12-30 发布日期:2021-12-30
  • 通讯作者: YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.
  • 作者简介: LIU Li-na (1992-), female, native of Fuyang, Anhui, postgraduate student of Hubei Normal University, engages in basic mathematics; YUAN Yu-ying (1993-), female, native of Zhenjiang, Jiangsu, librarian of Library of Hubei Normal University, engages in reference service for readers; YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.

Updating Mass and Stiffness Matrices Using Eigenstructure Assignment Methods

  1. 1. School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;
    2. Library of Hubei Normal University, Huangshi 435002, China
  • Received:2021-08-25 Online:2021-12-30 Published:2021-12-30
  • Contact: YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.
  • About author: LIU Li-na (1992-), female, native of Fuyang, Anhui, postgraduate student of Hubei Normal University, engages in basic mathematics; YUAN Yu-ying (1993-), female, native of Zhenjiang, Jiangsu, librarian of Library of Hubei Normal University, engages in reference service for readers; YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.

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摘要： A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback. By the method, the required displacement and acceleration output feedback gain matrices are determined, and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found. The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions. The numerical example shows that the proposed method is reliable and attractive.

关键词: Model updating, Undamped vibration system, Eigenstructure assignment, Acceleration and displacement feedback, Optimal approximation

Abstract: A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback. By the method, the required displacement and acceleration output feedback gain matrices are determined, and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found. The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions. The numerical example shows that the proposed method is reliable and attractive.

Key words: Model updating, Undamped vibration system, Eigenstructure assignment; Acceleration and displacement feedback, Optimal approximation

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