Collective vibrational resonance and mode selection in nonlinear resonator arrays

TL;DR

This paper demonstrates how high-frequency drives can actively tune nonlinear resonator arrays, enabling selective mode activation and control of phonon dispersion for applications in MEMS/NEMS devices.

Contribution

It introduces a systematic analytical approach to control mode selection in nonlinear resonator arrays via high-frequency external drives, validated by numerical simulations.

Findings

High-frequency drive shifts phonon dispersion relations.

Selective activation of specific normal modes is achievable.

External tuning enables active control of nonlinear responses.

Abstract

This article investigates how a uniform high frequency (HF) drive applied to each site of a weakly-coupled discrete nonlinear resonator array can modulate the onsite natural stiffness and damping and thereby facilitate the active tunability of the nonlinear response and the phonon dispersion relation externally. Starting from a canonical model of parametrically excited \textit{van der Pol-Duffing} chain of oscillators with nearest neighbor coupling, a systematic two-widely separated time scale expansion (\textit{Direct Partition of Motion}) has been employed, in the backdrop of Blekhman's perturbation scheme. This procedure eliminates the fast scale and yields the effective collective dynamics of the array with renormalized stiffness and damping, modified by the high-frequency drive. The resulting dispersion shift controls which normal modes enter the parametric resonance window, allowing highly selective activation of specific bulk modes through external HF tuning. The collective resonant response to the parametric excitation and mode-selection by the HF drive has been analyzed and validated by detailed numerical simulations. The results offer a straightforward, experimentally tractable route to active control of response and channelize energy through selective mode activation in MEMS/NEMS arrays and related resonator platforms.