APPROXIMATE DYNAMICAL ANALYSIS OF DAMPED NONLINEAR MECHANICAL SYSTEMS WITH TIME-VARYING PARAMETERS USING HYBRID ANALYTICAL METHODS
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Abstract
Nonlinear oscillators characterized by strong damping and time-varying coefficients present notable analytical challenges, primarily attributable to the limitations of classical perturbation techniques. The Krylov–Bogoliubov–Mitropolskii (KBM) method generally applies to weakly nonlinear and weakly damped systems, while the Harmonic Balance (HB) method often encounters convergence difficulties in time-dependent situations. To address these issues, this paper introduces a hybrid analytical framework that integrates the KBM and HB methods with amplitude-phase modulation. This innovative approach effectively approximates strongly damped nonlinear systems with slowly varying parameters by methodically eliminating secular factors and enhancing convergence. The efficacy of the proposed framework is validated using a fourth-order Runge-Kutta scheme on a nonlinear oscillator with varying coefficients. A comparative quantitative error analysis indicates enhanced accuracy over traditional KBM methods, particularly in scenarios involving moderate to large damping. These results suggest that the hybrid KBM-HB methodology significantly expands the applicability of perturbation-based analytical techniques to a broader class of nonlinear dynamical systems, with potential engineering applications in areas such as energy harvesting and vibration control.
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