Symmetry properties of natural frequency and mode shape sensitivities in symmetric structures. (September 2020) - Bartilson, Daniel T.; Jang, Jinwoo; Smyth, Andrew W.
Highlights: Natural frequency and mode shape sensitivities are studied in symmetric structures. Symmetric parameter pairs are proven to have equal effect on natural frequencies. Symmetric parameter pairs are proven to have strictly unequal effect on mode shapes. Ramifications for sensitivity-based updating and parametrization are discussed. Abstract: When updating a finite element (FE) model to match the measured properties of its corresponding structure, the sensitivities of FE model outputs to parameter changes are of significant interest. These sensitivities form the core of sensitivity-based model updating algorithms, but they are also used for developing reduced parametrizations, such as in subset selection and clustering. In this work, the sensitivities of natural frequencies and mode shapes are studied for structures having at least one plane of reflectional symmetry and distinct natural frequencies. It is first shown that the mode shapes of these structures are either symmetric and anti-symmetric, which is used to prove that natural frequency sensitivities are equal for symmetric parameters. Conversely, mode shape sensitivities are shown to be unequal for symmetric parameters, as measured by cosine distance. These topics are explored with a small numerical example, where it is noted that mode shape sensitivities for symmetric parameters exhibit similar properties to asymmetric parameters.