Quantifying the Correlation Between Measured and Computed Mode Shapes

This paper proposes a method whereby a set of computed mode shapes for a structure and set of measured mode shapes may be compared through the mass matrix. The errors between the two are found to fall into three categories: (a) mutual orthogonality of the measured modes is not satisfied, (b) the sets of modal vectors do not span the same subspaces, and (c) the modes are not perfectly aligned with the common subspace. In all three cases, the errors emerge as a set of angles, and the number of angles associated with each class of error is the same as the number of modes in the sets being compared. The sets of angles can each be combined into a single error angle for each class and ultimately a single angle, which reflects the degree of agreement between the measured and computed mode shapes.