Stability Analysis of a Parametric Duffing Oscillator
Publication: Journal of Engineering Mechanics
Volume 146, Issue 5
Abstract
The Duffing oscillator represents an important example to describe, mathematically, the nonlinear behavior of several phenomena in physics and engineering. In view of its diverse applications in science and engineering, the current work investigates the stability analysis of the parametric Duffing oscillator. This equation represents a second-order ordinary differential equation with cubic nonlinearity and periodic coefficient. A coupling of the homotopy perturbation method (HPM) and Laplace transform (), an approximate solution is derived. The HPM is adapted to find another accurate approximate solution. The latter analysis reveals the exact solution of the cubic Duffing equation. In addition, an expanded frequency parameter is achieved to find another approximate periodic solution. Therefore, this method is exercised to govern the stability criteria of the problem. Finally, the multiple time scales with the HPM is used to judge the stability criteria. The analyses include the resonance as well as nonresonance cases. Numerical estimations are performed to confirm, graphically, the perturbed solutions together with the stability examination. It is shown that the damped parameter and the cubic stiffness parameter have a destabilizing influence. In contrast, the natural and parametric frequencies are of stabilizing influences.
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Data Availability Statement
No data, models, or code were generated or used during the study.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 5 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Nov 19, 2018
Accepted: Dec 3, 2019
Published online: Mar 3, 2020
Published in print: May 1, 2020
Discussion open until: Aug 3, 2020
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