A modal method for detection and exclusion of interactions

In structural dynamics or acoustics, one may wish to detect interactions with a system that isinvestigated by modal testing. Since the weighted modal assurance criterion (WMAC) constitutesan orthogonality check, the addition of an interacting system can influence the auto-WMACmatrices of the system under investigation. This applies for a structure interacting with aninvestigated fluid, a fluid interacting with an investigated structure, and for a substructure thatis not included in the modal test. Decoupled mass matrices are assumed in the latter case, andthe effect of interaction is considered for multi-degree-of-freedom models of undamped systems.Then, it is proved that for the above applications, the diagonality of a suitably weighted autoWMAC matrix guarantees the absence of interacting systems. In case of an interaction, upperand lower limits are found for the number of coupled modes. The upper limit is given by thenumber of non-zero off-diagonal auto-WMAC matrix values. The lower limit is given by thenumber of modes associated with these values, and the associated modes are coupled. Theseresults can be used in the search for system boundaries, in the extension of models, and incondition monitoring problems. In an experiment, they are applied to the hydraulic subsystemof a coupled hydraulic-mechanical system and verified by the calculation of hydraulic andmechanical energy contributions to overall coupled hydraulic-mechanical modes.