Highly accurate analytical solution for free vibrations of strongly nonlinear Duffing oscillator. Issue 1 (March 2022)

• Record Type: Journal Article
• Authors: Ismail, Gamal Mohamed; Abul-Ez, Mahmoud; Zayed, Mohra; Ahmad, Hijaz; El-Moshneb, Maha
• Is Part Of: Journal of low frequency noise, vibration, and active control. Volume 41:Issue 1(2022)
• Page Start: 223
• Page End: 229
• Publication Date: 2022-03
• Subjects: Analytical solution -- perturbation technique -- nonlinear Duffing oscillator -- energy balance method -- frequency amplitude formulation; Vibration -- Periodicals; Noise -- Periodicals; Sound -- Periodicals; Damping (Mechanics) -- Periodicals; Damping (Mechanics); Noise; Sound; Vibration; Periodicals; 620.205
• DOI: 10.1177/14613484211034009
• Languages: English
• ISSNs: 1461-3484

Abstract

Based on the suggested parameter, a new analytical perturbation technique is presented to obtain highly ordered accurate analytical solutions for nonlinear Duffing oscillator with nonlinearity of high order. Comparing the obtained results with the numerical and other previously published results reveals the usefulness and correctness of the present technique. It is shown that the results are valid for small and large amplitudes. Indeed, it is found that our proposed technique produces more accurate and computationally results than the rival known methods. The obtained results show the efficiency and capability of the present perturbation technique to be applied to various strongly nonlinear differential equations.