Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force
This paper delves into the dynamical, chaotic, and stability aspects of the Duffing oscillator (DO) under sinusoidal external excitation, underscoring its relevance in various scientific and engineering applications. The DO, with its complex behavior, poses a significant challenge to our understandi...
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2025-06-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/14613484241298998 |
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| author | MK Abohamer TS Amer A Arab AA Galal |
| author_facet | MK Abohamer TS Amer A Arab AA Galal |
| author_sort | MK Abohamer |
| collection | DOAJ |
| description | This paper delves into the dynamical, chaotic, and stability aspects of the Duffing oscillator (DO) under sinusoidal external excitation, underscoring its relevance in various scientific and engineering applications. The DO, with its complex behavior, poses a significant challenge to our understanding. A unique perturbation technique, the multiple-scales (MS), is harnessed to tackle this challenge and enrich our knowledge. The analysis entails determining third-order expansions, exploring resonant cases, and factoring in the influence of viscous damping. The accuracy of the analytical solution is cross-validated with numerical results using the Runge–Kutta fourth-order (RK4). The paper also employs effective methods to assess the obtained results qualitatively. As a result, Visual figures, such as bifurcation diagrams and Lyapunov exponents’ spectra (LES), have been presented to illustrate diverse system motions and demonstrate Poincaré diagrams. Moreover, stability analysis has been investigated via resonance curves showing the stable and unstable regions. These aids facilitate our comprehension of the system’s complex behavior and its variations under different conditions. The results are elucidated through displayed curves, offering insights into the dynamics of the DO under sinusoidal excitation and damping effects. The influence of excitation and the quadratic parameter on bifurcation diagrams, LES, and Poincaré maps helps us understand the intricate behavior of nonlinear oscillatory systems, such as DO. The presented oscillator is a compelling example of elucidating the nonlinear behavior observed in numerous engineering and physics phenomena. |
| format | Article |
| id | doaj-art-9b54bd281e304614aba90713cb680d63 |
| institution | DOAJ |
| issn | 1461-3484 2048-4046 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj-art-9b54bd281e304614aba90713cb680d632025-08-20T02:39:58ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462025-06-014410.1177/14613484241298998Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external forceMK AbohamerTS AmerA ArabAA GalalThis paper delves into the dynamical, chaotic, and stability aspects of the Duffing oscillator (DO) under sinusoidal external excitation, underscoring its relevance in various scientific and engineering applications. The DO, with its complex behavior, poses a significant challenge to our understanding. A unique perturbation technique, the multiple-scales (MS), is harnessed to tackle this challenge and enrich our knowledge. The analysis entails determining third-order expansions, exploring resonant cases, and factoring in the influence of viscous damping. The accuracy of the analytical solution is cross-validated with numerical results using the Runge–Kutta fourth-order (RK4). The paper also employs effective methods to assess the obtained results qualitatively. As a result, Visual figures, such as bifurcation diagrams and Lyapunov exponents’ spectra (LES), have been presented to illustrate diverse system motions and demonstrate Poincaré diagrams. Moreover, stability analysis has been investigated via resonance curves showing the stable and unstable regions. These aids facilitate our comprehension of the system’s complex behavior and its variations under different conditions. The results are elucidated through displayed curves, offering insights into the dynamics of the DO under sinusoidal excitation and damping effects. The influence of excitation and the quadratic parameter on bifurcation diagrams, LES, and Poincaré maps helps us understand the intricate behavior of nonlinear oscillatory systems, such as DO. The presented oscillator is a compelling example of elucidating the nonlinear behavior observed in numerous engineering and physics phenomena.https://doi.org/10.1177/14613484241298998 |
| spellingShingle | MK Abohamer TS Amer A Arab AA Galal Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force Journal of Low Frequency Noise, Vibration and Active Control |
| title | Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force |
| title_full | Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force |
| title_fullStr | Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force |
| title_full_unstemmed | Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force |
| title_short | Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force |
| title_sort | analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force |
| url | https://doi.org/10.1177/14613484241298998 |
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