This randomized trial investigates solutions and artifacts in nonlinear dynamics of the Duffing oscillator, implying important distinctions for future analysis.
Key Points
The aim is to explore the characteristics of nonlinear oscillations in the Duffing oscillator and to apply Urabe's existence criterion to identify solution artifacts.
Examined stationary solutions and their basins of attraction for a harmonically excited Duffing oscillator.
Applied the Harmonic Balance Method in combination with numerical continuation to analyze the frequency response.
Demonstrated Urabe's existence criterion to differentiate between artifacts and legitimate solutions.
Identified that the Harmonic Balance Method can produce artifacts in large amplitude solutions in the softening case.
Urabe's criterion successfully distinguishes artifacts from regular solutions in certain conditions.
Provided insights on the limitations of the criterion across different excitation frequency ranges.