2015/10/06 by R. Jothimurugan, K. Thamilmaran, Jothimurugan, R. +6 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #nlin.CD
paper · pdf · doi:10.48550/arxiv.1510.01564
16 pages, 11 figures, 2 tables, The manuscript is accepted in Nonlinear Dynamics
arxiv created 2015/10/06 · openalex publication_date 2015/10/06 · arxiv updated 2015/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.