Dynamic responses and mitigation of limit cycle oscillations in Van der Pol–Duffing oscillator with nonlinear energy sink

The paper considers dynamics of Van der Pol–Duffing (VdPD) oscillator with attached nonlinear energy sink. Due to a cubic nonlinearity of the VdPD oscillator, a frequency of oscillations near the unstable origin strongly differs from the frequency of limit cycle oscillations (LCO). The paper demonstrates that, despite the strong nonlinearity of the model system, one can efficiently describe the dynamics with a combination of averaging and multiple scales methods. Global structure of possible response regimes is revealed. It is also demonstrated that the nonlinear energy sink can efficiently control and mitigate the undesired LCOs in this system.