Collective vibrational resonance and mode selection in nonlinear resonator arrays

Area of Science:

• Nonlinear Dynamics
• Condensed Matter Physics
• Mechanical Engineering

Background:

• Discrete nonlinear resonator arrays exhibit complex dynamics.
• Controlling these dynamics is crucial for advanced applications.
• External modulation offers a pathway for active tunability.

Purpose of the Study:

• To investigate the effect of high-frequency (HF) drives on nonlinear resonator arrays.
• To demonstrate active tunability of nonlinear response and phonon dispersion.
• To enable selective activation of specific normal modes.

Main Methods:

• Utilized a canonical model of parametrically excited van der Pol-Duffing oscillators.
• Employed a two-timescale expansion (Direct Partition of Motion) and Blekhman's perturbation scheme.
• Performed detailed numerical simulations to validate analytical findings.

Main Results:

• HF drives effectively renormalize stiffness and damping, modifying collective dynamics.
• Dispersion shifts enable selective activation of normal modes via HF tuning.
• Demonstrated control over parametric resonance and mode selection.

Conclusions:

• External HF drives provide a tractable method for active control of resonator array responses.
• Selective mode activation allows for efficient energy channeling.
• The findings are applicable to microelectromechanical system/nano electro-mechanical system arrays.