Increasing the sensitivity of the modal assurance criteria (MAC) to small mode shape changes : The IMAC

This paper reviews the concepts behind and the need for a measure of the accuracy of mode shapes. Experimental-to-analytical Anaytical-to-Analytical, and Experimental-to-Experimental mode shape comparisons are made daily by the dynamics community. The problem is that the conventional measure of mode shape accuracy, the Modal Assurance Criteria (MAC), is used to assess the correlation or coherence between two modes or operating shapes. This measure computes the least squares deviation of the shape points from a straight-line correlation. However, the anti-nodes of the mode shape dominate this computation. Observation of small errors in modes shapes result in the conclusion that changes in mode shapes are most easily detected in the region of the node points and the spatial movement of same. Certainly the MAC will not be sensitive to small changes in nodal position since the MAC's properties are dominated by the larger anti-nodal information. This paper proposes the use of the inverse of the mode shapes to form the basis function for the MAC calculation. This new measure wW be called the IMAC (Inverse Modal Assurance Criteria). That is, the complex arithmetic inverse of the mode shape is used in the conventional MAC calculation. Examples will be given of comparative sensitivities of the MAC and IMAC to small mode shape errors.