Parametric optimization of fold bifurcation points

Adrien Mélot, Enora Denimal, Ludovic Renson

Abstract: The aim of this work is to optimize the parameters of a mechanical system in order to force fold bifurcation points to appear at targeted frequencies. To this end, an original harmonic balance-based optimization procedure is developed. Functions similar to those employed during bifurcation tracking analyses are used to characterize fold bifurcations in the objective function. The proposed approach is illustrated on a Duffing oscillator with cubic nonlinearity.