A mode tracking method in modal metamodeling for structures with clustered eigenvalues

Modal metamodels can be effectively used as surrogates for expensive simulations in structural dynamics analysis with parametric variations. However, in the case of a system with clustered eigenvalues, e.g., a structure exhibiting symmetry or periodicity, mode interactions due to parametric variations are challenging to handle. Clustered eigenvalues are potentially associated with high sensitivity in eigenvectors. That is, a small perturbation to clustered eigenvalues may lead to significant changes in the corresponding eigenvectors. Neglecting the effect of mode interactions may produce large errors for modal metamodels in this case. To meet this challenge, we develop a novel automated mode tracking method (AMTM) for structures with clustered eigenvalues. Specifically, the changes in corresponding eigenvectors due to parametric variations are characterized by a transformation matrix representing a rotation in the subspace spanned by the reference eigenvectors. Modal metamodels are subsequently trained to predict both eigenvalues and eigenvectors in the presence of mode interactions. The effectiveness of the proposed method is demonstrated using a four-edge clamped symmetric plate structure. In addition, an application of the proposed approach to uncertainty propagation (UP) of modal properties is presented using an example with a multi-dimensional parametric space.