A full PGD/HBM-based algorithm for a low-dimensional NNM continuation with modal enrichment
Résumé
This work proposes a full algorithm to compute Nonlinear Normal Modes (NNMs) using a Proper Generalized Decomposition (PGD) approach combined to a continuation method. Because periodic solutions are sought, a harmonic balance method (HBM) is implemented to process the time-dependent functions. The interest of this study is first to couple this approach to a continuation method with a progressive enrichment of the PGD modes family and second to improve some of the PGD steps to get a robust algorithm. In particular , the initializations of solvers are chosen consistently with the available physical data through the use of LNMs shapes. The reduced basis is kept as small as possible since it is computed with on the fly enrichment, possibly from a unique mode. No particular assumptions on the non linearity have been made and hence a wide class of mechanical problems can be processed. The resulting method is applied on several beam models with localized nonlinearities which allows for an accurate analysis of its performance.
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