Summary
Nonlinear systems exhibit a wide variety of resonances of a primary or non-primary type. Among the latter, some can appear as isolated branches of solutions, making them difficult to obtain with traditional numerical and experimental approaches. In this work, we propose to leverage multiharmonic forcing to bridge different resonances associated with the same mode together. The method starts with a given harmonic forcing, and progressively increases the amplitude of a second harmonic component, all the while decreasing the amplitude of the first. It eventually reaches another harmonic forcing situation where only the second harmonic component subsists. By doing so, this multiharmonic transition method can continuously go from an easily attainable primary resonance to a (possibly isolated) non-primary resonance by transiting through a simultaneous resonance state. The method is illustrated numerically with a Duffing oscillator and a doubly-clamped Von Kármán beam.
