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

TL;DR

This paper explores high-frequency tuning in a Van der Pol oscillator with a nonlinear energy sink to enhance targeted energy transfer and control instability via resonance and bifurcation analysis.

Contribution

It introduces a novel high-frequency tuning method to optimize energy transfer in a coupled oscillator system using advanced spectral and bifurcation analysis techniques.

Findings

Resonance capture is facilitated by high-frequency tuning of the system.

Q-factor spectral analysis effectively identifies resonance peaks.

Energy dissipation metrics align with Q-maps, indicating optimal energy transfer regions.

Abstract

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 \textit{direct partition of motion} with \textit{complexification averaging}, the mechanism of energy flow and instability control through \textit{hopf 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.