[en] This work proposes a novel efficient method to track the evolution of amplitude extrema featured by frequency responses of nonlinear systems using the harmonic balance method. Means to compute the amplitude of a Fourier series are first outlined, and a set of equations characterizing a local extremum of a nonlinear frequency response amplitude curve is derived. Efficient numerical procedures are used to evaluate these equations and their derivatives (including second‐order ones) to embed them in a predictor‐corrector continuation framework. The proposed approach is illustrated on three examples of increasing complexity, namely a Helmholtz–Duffing oscillator, a two‐degree‐of‐freedom system with a modal interaction, and a doubly clamped von Kàrmàn beam with a nonlinear tuned vibration absorber.
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Funding text :
Ghislain Raze is a Postdoctoral Researcher of the Fonds de la Recherche Scientifique - FNRS which is gratefully acknowledged.
Commentary :
This is the accepted version of the following article: Raze G, Volvert M, Kerschen G. Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method. Int J Numer Methods Eng. 2023;e7376. doi: 10.1002/nme.7376, which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/nme.7376.
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