Higher Order MAC for the Correlation of Close and Multiple Modes

In this paper, an extension of Modal Assurance Criterion (MAC) is proposed. It considers the correlation between a modal vector and a subspace spanned by several modal vectors, instead of the usual correlation between two modal vectors. Such higher-order MAC provides additional insight whenever multiple or close eigenvalues exist. In principle, any number of modal vectors can be considered to span the subspace. A closed-form expression is, derived for the correlation of a modal vector with a two-dimensional subspace, referred to as S2MAC (subspace of order. 2 Modal Assurance Criterion). This allows a better understanding in situations involving double eigenvalues or pairs of close natural frequencies, as highlighted by the discussed test cases.