Multiple resonance and anti-resonance in coupled Duffing oscillators

TL;DR

This paper studies resonance and anti-resonance phenomena in coupled Duffing oscillators, deriving theoretical response equations, analyzing the effects of coupling strength, and validating findings with electronic circuit simulations.

Contribution

It provides a theoretical framework for understanding multiple resonance and anti-resonance in coupled nonlinear oscillators, including large systems.

Findings

Frequency-response curves show multiple resonance and anti-resonance peaks.

Theoretical predictions closely match numerical simulations.

Resonance behaviors are confirmed in electronic circuit experiments.

Abstract

We investigate the resonance behaviour in a system composed by n-coupled Duffing oscillators where only the first oscillator is driven by a periodic force, assuming a nearest neighbour coupling. We have derived the frequency-response equations for a system composed of two-coupled oscillators by using a theoretical approach. Interestingly, the frequency-response curve displays two resonance peaks and one anti-resonance. A theoretical prediction of the response amplitudes of two oscillators closely match with the numerically computed amplitudes. We analyse the effect of the coupling strength on the resonance and anti-resonance frequencies and the response amplitudes at these frequencies. For the n-coupled oscillators system, in general, there are n-resonant peaks and (n-1) anti-resonant peaks. For large values of n, except for the first resonance, other resonant peaks are weak due to linear damping. The resonance behaviours observed in the n-coupled Duffing oscillators are also realized in an electronic analog circuit simulation of the equations. Understanding the role of coupling and system size has the potential applications in music, structural engineering, power systems, biological networks, electrical and electronic systems.