Journal ArticleDOI
Accurate approximate analytical solutions for multi-degree-of-freedom coupled van der Pol-Duffing oscillators by homotopy analysis method
TLDR
In this article, the homotopy analysis method (HAM) is presented to establish the accurate approximate analytical solutions for multi-degree-of-freedom (MDOF) nonlinear coupled oscillators.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2010-10-01. It has received 26 citations till now. The article focuses on the topics: Homotopy analysis method & Homotopy.read more
Citations
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Journal ArticleDOI
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review
TL;DR: In this article, a survey of recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones, is presented.
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Influence of thermal radiation and Joule heating in the Eyring–Powell fluid flow with the Soret and Dufour effects
TL;DR: In this article, a two-dimensional magnetohydrodynamic boundary layer flow of the Eyring-Powell fluid on a stretching surface in the presence of thermal radiation and Joule heating is analyzed.
EXISTENCE OF LIMIT CYCLES FOR COUPLED VAN DER POL EQUATIONS (Mathematical Economics)
TL;DR: In this paper, the existence of limit cycles of coupled van der Pol equations by using S1-degree theory due to Dylawerski et al. was considered, and it was shown that limit cycles can be found in the limit cycle of the coupled Van der Pol equation.
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Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator
TL;DR: In this article, the residue harmonic balance is developed for coupled systems exemplified by the damped Duffing resonator driven by a van der Pol oscillator, which combines the features of harmonic balance and parameter bookkeeping to obtain approximate solutions to any desired accuracy.
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Fractional derivative and time delay damper characteristics in Duffing–van der Pol oscillators
TL;DR: The residue harmonic balance method is presented to find periodic solutions of Duffing–van der Pol oscillators having damping terms described by fractional derivative and time delay respectively to investigate the damping effects of these two oscillators.
References
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Journal ArticleDOI
On the homotopy analysis method for non-linear vibration of beams
TL;DR: In this paper, the homotopy analysis method (HAM) is used to investigate non-linear vibration behavior of Euler-Bernoulli beams subjected to axial loads, and the effect of vibration amplitude on the nonlinear frequency and buckling load is discussed.
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Derivation of the Adomian decomposition method using the homotopy analysis method
TL;DR: The mathematical derivation of the Adomian decomposition method using the homotopy analysis method is presented and an error analysis is addressed as well as the convergence criteria.
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A one-step optimal homotopy analysis method for nonlinear differential equations
TL;DR: In this article, a one-step optimal approach is proposed to improve the computational efficiency of the homotopy analysis method (HAM) for nonlinear problems, which is first expressed by means of a unknown embedding function in Taylor series, whose coefficient is then determined one by one by minimizing the square residual error of the governing equation.
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An analytic approximate approach for free oscillations of self-excited systems
TL;DR: In this article, the homotopy analysis method is employed to control the convergence of approximation series and adjust convergence regions when necessary, unlike other analytic techniques, this approach provides us with a convenient way to adjust convergence region when necessary.