Centrosymmetric Solutions of Constrained Matrix Equation and Its Application to Inverse Problem of Vibration Theory

ZHOU Shuo; WANG Lin; HAN Ming-hua

doi:10.3879/j.issn.1000-0887.2013.03.010

Volume 34 Issue 3

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ZHOU Shuo, WANG Lin, HAN Ming-hua. Centrosymmetric Solutions of Constrained Matrix Equation and Its Application to Inverse Problem of Vibration Theory[J]. Applied Mathematics and Mechanics, 2013, 34(3): 306-317. doi: 10.3879/j.issn.1000-0887.2013.03.010

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Centrosymmetric Solutions of Constrained Matrix Equation and Its Application to Inverse Problem of Vibration Theory

doi: 10.3879/j.issn.1000-0887.2013.03.010

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

Received Date: 2013-01-18
Rev Recd Date: 2013-02-07
Publish Date: 2013-03-15

Abstract

Abstract

The centrosymmetric solutions of constrained matrix equation under a central principal submatrix constraint were studied.By using matrix to quantify, Kronecker product and singular value decomposition (SVD) method, the necessary and sufficient conditions for solvability and the general expression of solutions were obtained. Then, the expression of solution to the related optimal approximation problem was considered. Moreover, the applications in the inverse problem of vibration theory were given, by using the reduction principal mass matrix (or principal stiffness matrix), reduction modal matrix and central principal submatrix of the mass matrix (or stiffness matrix), the mass matrix (or stiffness matrix) of the system was obtained.Finally, the proposed method was demonstrated by two examples.
- vibration theory,
- matrix inverse problem,
- matrix equation,
- central principal submatrix constraint,
- centrosymmetric matrices,
- optimal approximation

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References(13)

References

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