Self-transformation approach for forced 2DOF damped nonlinear dynamical systems

This study presents a robust analytical framework using the Harmonic Equivalent Linearization Method (HELM) to overcome limitations in existing analyses of two-degree-of-freedom nonlinear oscillatory systems. The use of HELM in system transformation enables the precise evaluation of stability boundaries, coupling effects, and the influence of critical parameters, offering analytical tractability and high accuracy through numerical simulations. This approach generates stability diagrams, revealing interactions between damping, coupling strength, and forcing parameters, allowing researchers to understand dynamic transitions and resonance phenomena in nonlinear coupled systems. This research presents a powerful, generalizable approach for analyzing complex nonlinear oscillators, addressing deficiencies in current methodologies, and enhancing engineering and applied physics applications.