Nonlinear normal mode continuation through a Proper Generalized Decomposition approach with modal enrichment

Nonlinear normal modes (NNMs) of a mechanical structure provide a mean to understand nonlinear vibrational phenomena measured experimentally. As they are an interesting extension of the linear normal modes (LNMs), numerical methods are needed to estimate these oscillatory motions, generally including continuation aspects with respect to the circular frequency. In this paper, a continuation method combined to a model reduction based on Proper Generalized Decomposition (PGD) technique is described. This formulation mixes PGD, harmonic balance method (HBM) and basic continuation techniques in order to reach a highly reduced description of the NNMs. This PGD/HBM-based continuation algorithm includes a modal enrichment as the NNM energy grows. The method is applied to two conservative problems including a cubic spring and a unilateral contact. (C) 2018 Elsevier Ltd. All rights reserved.