Model updating of the complex modeshapes and the damping matrix

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Abstract
The problem of updating the damping matrix from incomplete modal experimental data is considered. It is assumed that the mass and stiffness matrices are accurate, or have been updated before. Hence the suggested model updating procedure is restricted to the damping matrix while the normal system and its modal parameters do not change. The first step is modification of the complex eigenvectors so that they satisfy the governing orthogonality conditions for damped systems. Using an approximation of these conditions a closed form solution is obtained. With the modified eigenvectors, the damping matrix is updated using the reference basis approach. Two solutions are given. One for the case of accurate eigendata, and a second, less sensitive to errors, for corrected, yet inaccurate, eigenvectors. The proposed method is demonstrated by means of two examples.