Identification of secondary resonances of nonlinear systems using phase-locked loop testing

One unique feature of nonlinear dynamical systems is the existence of superharmonic and subharmonic resonances in addition to primary resonances. In this study, an effective vibration testing methodology is introduced for the experimental identification of these secondary resonances. The proposed method relies on phase-locked loop control combined with adaptive filters for online Fourier decomposition. To this end, the monotonic evolution of the phase lag around secondary resonances is exploited for their identification. The method is demonstrated using two systems featuring cubic nonlinearities, namely a numerical Duffing oscillator and a physical experiment comprising a clamped–clamped thin beam. The obtained results highlight that the control scheme can accurately characterize secondary resonances as well as track their backbone curves. A particularly salient feature of the developed algorithm is that, starting from the rest position, it facilitates an automatic and smooth dynamic state transfer toward one point of a subharmonic isolated branch, hence, inducing branch switching experimentally.