2.6.           Comparing Test and Analysis Modes

After a modal test is concluded, the measured modal frequencies and mode shapes are extracted from the test data. These are then compared with FEM shapes using the same orthogonality and MAC measures used to compare TAM and FEM shapes. The first step is to calculate the test-test self-orthogonality with respect to the TAM reduced mass matrix as follows:

                                     (2.6-1)

where

            = Test mode shapes for the TAM A‑set DOF

             = TAM reduced A‑set mass matrix

The cross-orthogonality between test and analysis modes is then calculated as follows:

                                    (2.6-2)

where

          = FEM mode shapes calculated with full FEM matrices at the TAM A‑set DOF

There is a subtle difference between the way these calculations are applied to test modes and the way that they are applied prior to the test. Prior to the test, the TAM and FEM modes are mass normalized with respect to their respective mass matrices, but the FEM modes are typically not renormalized to the TAM mass matrix. This is because the diagonal elements of the FEM psuedo-orthogonality matrix provide a measure of the accuracy of the mass matrix reduction. The test modes, however, must be normalized to the TAM mass matrix, so that the diagonal elements of the test self-orthogonality matrix are always 1.0. Only the off-diagonal elements are relevant. These should ideally be less than 10%, though some larger values are often inevitable in complex modal tests. To be consistent, the FEM modes are also typically renormalized so that the diagonal elements of the FEM self-orthogonality matrix are 1.0[9].