Bisymmetric Damping and Stiffness Matrices Calibration With Test Data of Vibration Systems

ZHOU Shuo; HAN Ming-hua; MENG Huan-huan

doi:10.3879/j.issn.1000-0887.2014.06.012

Volume 35 Issue 6

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ZHOU Shuo, HAN Ming-hua, MENG Huan-huan. Bisymmetric Damping and Stiffness Matrices Calibration With Test Data of Vibration Systems[J]. Applied Mathematics and Mechanics, 2014, 35(6): 697-711. doi: 10.3879/j.issn.1000-0887.2014.06.012

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Bisymmetric Damping and Stiffness Matrices Calibration With Test Data of Vibration Systems

doi: 10.3879/j.issn.1000-0887.2014.06.012

College of Science, Northeast Dianli University, Jilin, Jilin 132012, P.R.China

Funds: The National Natural Science Foundation of China(11072085）

Received Date: 2013-10-09
Rev Recd Date: 2014-04-30
Publish Date: 2014-06-11

Abstract

Abstract

The problem of bisymmetric damping and stiffness matrices calibration with test data of vibration systems was discussed. Based on the eigen equation as well as bisymmetry of the damping and stiffness matrices, existence and uniqueness of the solution to the problem was studied by means of the theory and method for the inverse algebraic quadratic eigenvalue problem. A new method for the calibration of damping and stiffness matrices was presented. According to the properties of bisymmetric matrices, the bisymmetric solution to the matrix equation was studied. The general expression of the bisymmetric solution was obtained. Moreover, the related optimal approximation problem of any related matrix was addressed and the solution given. The damping and stiffness matrices calibrated with the method not only satisfy the quadratic eigen equation, but also are the unique bisymmetric matrix solution. A numerical example proves efficiency of the present method.
- structural model,
- inverse problem,
- calibration,
- damping matrix,
- stiffness matrix,
- bisymmetric matrix

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References(11)

References

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