Cross Orthogonality Checks of Modal Vectors. 1st Report. Coordinate Cross Orthogonality Checks without a Mass Matrix.

Abstract

In this paper, a new theory for cross orthogonality check between analytical and experimental modal vectors based on a General Definition of Projectors is described. Since this cross orthogonality check can be computed without a mass matrix, this method is easier to use and saves remarkably efforts to perform cross orthogonality checks. In addition, this cross orthogonality check can be applied even if the modal vectors are complex. Hence, we estimate the cross orthogonality among experimentally determined modal vectors, and there are many possible applications in experimental modal analysis. Moreover, a new theory for coordinate cross orthogonality check method based on the orthogonality check is proposed. This coordinate cross orthogonality check can quantify the correlation of the modal displacements for a given degree of freedom without a mass matriX. This paper introduces the theory and demonstrates the validity on numerical models. The results show that these checks are sufficiently reliable to estimate the difference between analytical and experimental modal vectors.