Mode traces in degenerate eigensystems and augmented assurance.
Eigenpairs, contextually indicative of the frequencies and oscillatory modes of structural systems, are considered as functions of a single parameter. Undesired permutation of modal designations is noted to arise following events of transitory eigenvalue coalescence with respect to the parameter, resulting in the definition of nonsmooth functions. The tracing of eigenpairs across such events is outlined for the permanently degenerate, general eigenproblem as the general case; the cases of transitorily degenerate and distinct eigenvalues are thus accounted for. The foundation for mode tracing is the assumption of eigenvector consistency across parameter intervals, used as a means of eigenpair reconciliation. The resulting traced modes are smooth and their variations physically pertinent, which is necessary in iterative schemes in which convergence may otherwise be jeopardized. The proposal of an augmented modal assurance routine that potentially augments the assurance of tracing and, therefore, the maximum permissible parameter perturbation, is given; a threefold increase in the insight to consistency entails. The notion of the routine is to forward and backward cast eigenvectors utilizing their derivatives in affine modeling. A numerical example of the modes of A cyclic frame as functions of a cyclic distribution of membrane forces demonstrates the concepts and utility of the proposal.
|Title:||Mode traces in degenerate eigensystems and augmented assurance|
|Keywords:||EIGENVECTOR DERIVATIVES, REPEATED EIGENVALUES, OPTIMIZATION, TRACKING, SYSTEMS|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science
UCL > School of BEAMS > Faculty of Engineering Science > Civil, Environmental and Geomatic Engineering
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