Resonance control for a forced single-degree-of-freedom nonlinear system

The main characteristic of a forced single-degree-of-freedom weakly nonlinear system is determined by its primary, super- and sub-harmonic resonances. A nonlinear parametric feedback control is proposed to modify the steady-state resonance responses, thus to reduce the amplitude of the response and to eliminate the saddle-node bifurcations that take place in the resonance responses. The nonlinear gain of the feedback control is determined by analyzing the bifurcation digrams associated with the corresponding frequency-response equation, from the singularity theory approach. It is shown by illustrative examples that the proposed nonlinear feedback is effective for controlling three kinds of resonance responses.