Capture into resonance of coupled Duffing oscillators

Area of Science:

• Nonlinear Dynamics
• Mechanical Vibrations
• Chaos Theory

Background:

• Autoresonance enables a single oscillator to achieve persistent resonance with growing oscillation amplitude.
• Coupled oscillators present complex dynamics not fully understood under autoresonance conditions.

Purpose of the Study:

• Investigate autoresonance capture in a pair of coupled Duffing oscillators.
• Determine conditions under which both coupled oscillators achieve resonance.
• Analyze the role of autoresonance in the forced oscillator on the coupled system's dynamics.

Main Methods:

• Utilized theoretical analysis to model coupled Duffing oscillators.
• Employed numerical simulations to explore system behavior.
• Identified quasisteady states governing amplitude growth.

Main Results:

• Autoresonance in the driven oscillator is insufficient for inducing oscillations with increasing amplitude in the coupled oscillator.
• A specific parametric domain for simultaneous resonance capture in both oscillators was identified.
• Quasisteady states accurately predict amplitude growth dynamics.

Conclusions:

• Coupled autoresonance requires specific parametric conditions beyond individual oscillator autoresonance.
• The findings provide a deeper understanding of resonance phenomena in coupled nonlinear systems.
• Theoretical predictions align well with numerical simulations, validating the model.