Correlation between analytical and experimental modal vectors is verified to check the adequacy of a Finite Element(FE)-model. In order to investigate the cause of error on FE-model, it is important to calculate cross orthogonality using analytical system matrices. However, to obtain the system matrices in an apposite form is usually an uphill task. In this paper, we propose a new theory for cross orthogonality check, using a General Definition of Projector(GDOP). Since the proposed cross orthogonality check can be computed without mass or stiffness matrix, this method is easier to use and saves remarkably efforts to perform orthogonality checks. In addition, this method can be applied even if the modal vectors are complex for non-proportional damping case, Hence, we can estimate the cross orthogonality among experimentally determined modal vectors, and there are many possible applications. This paper introduces the theory based on GDOP. Then we demonstrates the validity on numerical examples.
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