A two-harmonic homotopy method to experimentally uncover isolated resonances

Abstract

Secondary resonances of nonlinear systems may appear as isolated branches of solutions, challenging their characterization and making them particularly difficult to observe experimentally. This work exploits a two-harmonic homotopy method that leverages two-harmonic forcing as a proxy to connect primary and secondary resonances. An experimental implementation with simple feedback controllers is presented. This approach is then validated with an electronic Duffing oscillator and a doubly clamped beam featuring a distributed geometrical nonlinearity. It is shown to experimentally uncover isolas in both of these examples.