Results 81 to 90 of about 7,901 (195)
VibrationIn the paper, we first develop a novel automatically energy-preserving scheme (AEPS) for the undamped and unforced single and multi-coupled Duffing equations by recasting them to the Lie-type systems of ordinary differential equations.
Chein-Shan Liu +2 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2010 In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation.
Lequn Peng, Wentao Wang
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Ninety years of Duffing’s equation
Theoretical and Applied Mechanics, 2013 In the paper the origin of the so named ?Duffing?s equation? is shown. The author?s generalization of the equation, her published papers dealing with Duffing?s equation and some of the solution methods are presented. Three characteristic approximate solution procedures based on the exact solution of the strong cubic Duffing?s equation are ...
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Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators
Journal of Low Frequency Noise, Vibration and Active Control, 2019 A brief introduction to the development of the homotopy perturbation method is given, and the main milestones are elucidated with more than 90 references.
Dan-Ni Yu, Ji-Huan He, Andres G Garcıa
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Chaos and limit cycle in Duffing's equation
Journal of the Franklin Institute, 1990 The authors present in several figures the chaotic behavior and the limit cycles which correspond to different values of parameters entering Duffing's equation.
Ku, Y. H., Sun, Xiaoguang
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Journal of Low Frequency Noise, Vibration and Active Control, 2019 Fractional oscillators can effectively deal with noise in the vibration. This paper adopts He’s fractional derivative, which is defined through the variational iteration algorithm.
Yan Wang, Jian-Ye An
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AxiomsTwo nonlinear Duffing equations are numerically treated in this article. The nonlinear fractional-order Duffing equations and the second-order nonlinear Duffing equations are handled.
Waleed Mohamed Abd-Elhameed +3 more
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Advances in Mathematical Physics, 2014 This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions ...
Changjin Xu, Maoxin Liao
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Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017 stract This paper includes studying (dynamic of double chaos) in two steps: First Step:- Applying ordinary differential equation have behaved chaotically such as (Duffing's equation) on (double pendulum) equation system to get new system of ...
A. M. Ahmed, S. Noori
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Periodic Duffing equations with delay
Electronic Journal of Differential Equations, 2004 The paper is devoted to find sufficient conditions for the existence of a \(T\)-periodic solution for the Duffing equation with delay \[ x''(t)+cx'(t)+g(t-\tau, x(t-\tau), x'(t-\tau))=p(t), \] where \(c\in \mathbb{R}\), \(g\) is a continuous function and \(T\)-periodic in its first argument, and \(p\) is \(T\)-periodic.
Jean-Marc Belley, Michel Virgilio
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