Advanced dynamical analysis of coupled oscillators shows improved response prediction, indicating enhanced design in engineering applications.
Key Points
This study aims to develop a non-perturbative framework to derive periodic solutions for coupled oscillators, enhancing response prediction and stability.
Examined three distinct 2DOF coupled oscillator models with varied restoring forces.
Applied He’s Frequency Formula to transform nonlinear equations into linear forms.
Validated analytical solutions via numerical simulations using Mathematica Software.
Utilized bifurcation diagrams and Poincaré maps to analyze dynamical transitions.
The non-perturbative approach showed significant accuracy and computational efficiency compared to classical methods.
Bifurcation diagrams revealed complex response patterns in coupled models.
Analytical and numerical results demonstrated close agreement, validating the proposed framework.