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.
Higher order MAC for the correlation of close and multiple modes
D'AMBROGIO, WALTER;
2003-01-01
Abstract
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.Pubblicazioni consigliate
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