Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method

Abstract

AbstractThis 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.