Application of Mac in the Frequency Domain

The Modal Assurance Criterion (MAC) has been used for numerous years as a measure of correlation between test and analytical mode shapes. The fact that the MAC considers only mode shapes usually means that a separate frequency comparison must be used in conjunction with the MAC values to determine the correlated mode pairs. The mode shape correlation has generally been displayed as the MAC matrix tabulated or plotted versus experimental mode number on the x axis and analytical mode number on the y axis. The natural frequency correspondence is usually displayed with a separate plot such as the experimental natural frequency versus the analytical natural frequency. Together, the two plots are used to determine the overall correlation/correspondence of the modes. This paper presents a new way of plotting the MAC such that both the mode shape correlation as well as the natural frequency comparisons can be viewed simultaneously. Further, the new plot method is naturally extended to the correlation of frequency response functions (FRFs) using the Frequency Domain Assurance Criterion (FDAC) and a new technique called the Modal FRF Assurance Criterion (MFAC). Two case studies of real structures are presented to illustrate the advantages of the new methods.