UNVEILING THE PARAMETRIC DEPENDENCIES OF HYSTERESIS IN COUPLED NONLINEAR OSCILLATORS
Abstract
This research investigates the intricate dynamical responses of an array of three nonlinearly coupled Duffing oscillators subjected to harmonic excitation, focusing specifically on hysteresis phenomena and the critical influence of coupling strength and nonlinear stiffness parameters. Despite significant advancements in understanding individual Duffing oscillator behavior, existing studies have inadequately explored how variations in coupling stiffness (kc) and nonlinear stiffness (k3) collectively alter hysteresis and stability landscapes. Through comprehensive numerical simulations and multidimensional basin-of-attraction analyses, this study reveals nuanced interactions between these parameters, resulting in distinct dynamic regimes such as energy localization, stability shifts, and significant variations in hysteresis loops. We adopt an approach integrating systematic frequency sweeps and basin-of-attraction mapping to quantify how parameter adjustments shape solution stability and hysteresis behavior. Our findings illuminate previously unrecognized interactions where increased coupling strength can either stabilize or destabilize specific amplitude responses, altering the existence and stability of hysteresis branches. Notably, these effects manifest as shifts in hysteresis jump frequencies, profoundly impacting system dynamics and offering fresh insights into designing adaptive mechanical structures. This research addresses a critical gap by demonstrating that hysteresis effects are not only inherent nonlinear phenomena but can be systematically controlled through precise tuning of coupling and nonlinear parameters. This discovery opens pathways for engineering adaptable and responsive structures with targeted dynamical characteristics, significantly advancing both theoretical comprehension and practical applications in areas such as microelectromechanical resonators, vibration mitigation systems, and structural health monitoring technologies. Our approach and findings underscore the necessity of considering parameter variability in nonlinear dynamics research, moving beyond traditional fixed-parameter analyses. Future studies are encouraged to expand this exploration to larger arrays and asymmetric coupling conditions, further enhancing the understanding and utility of coupled nonlinear oscillator systems.
Publication Title
Proceedings of the ASME Design Engineering Technical Conference
Recommended Citation
Zaraza, J., & Agarwal, V. (2025). UNVEILING THE PARAMETRIC DEPENDENCIES OF HYSTERESIS IN COUPLED NONLINEAR OSCILLATORS. Proceedings of the ASME Design Engineering Technical Conference, 6 https://doi.org/10.1115/DETC2025-168709
