Abstract
This paper is concerned with the problem of the optimal approximation for a given matrix pencil (Ma, Da, Ga, Ka, Na ) under the spectral constraint and the symmetric constraint. Such a problem arises in finite element model updating for damped gyroscopic systems. By using constrained optimization theory and matrix derivatives, an explicit formulation for the solution of the problem is established. The efficiency and accuracy of the proposed method is numerically verified by a simple five-degree-of-freedom system.
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