High-frequency tuning of internal resonance and targeted energy transfer in a Van der Pol oscillator coupled to a nonlinear energy sink

Targeted energy transfer (TET) from a Van der Pol oscillator coupled to a nonlinear energy sink (NES) is investigated under the action of a high-frequency external drive, which tunes the effective natural stiffness and promotes resonance capture, facilitating energy transfer. Using $\mathit{\text{direct}}\mathit{\text{partition}}\mathit{\text{of}}\mathit{\text{motion}}$ with $\mathit{\text{complexification}}\mathit{\text{averaging}}$, the mechanism of energy flow and instability control through $\mathit{\text{hopf}}\mathit{\text{bifurcation}}$ is characterized. A spectrally evaluated Q-factor, based on FFT at the effective slow frequency, captures the resonance peaks indicating the efficient energy transfer. Finally, the energy-dissipation metric is consistent with these Q-maps and identifies the regions where transient energy pumping is most effective.