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.
Journal ArticleDOI
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
Homotopy analysis method for limit cycle flutter of airfoils
Y.M. Chen,Jun Liu +1 more
TL;DR: An analytical approximate method for non-linear problems, namely the homotopy analysis method, is for the first time employed to propose a new approach for the flutter system of a two-dimensional airfoil with a cubic structural nonlinearity.
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Uniformly valid solution of limit cycle of the Duffing–van der Pol equation
Y.M. Chen,J.K. Liu +1 more
TL;DR: In this paper, the authors studied the limit cycle of the Duffing-van der Pol equation and derived an algebraic equation for ω using homotopy analysis and obtained an analytical approximation for the frequency.
Journal ArticleDOI
Solution of coupled system of nonlinear differential equations using homotopy analysis method
Mehdi Ganjiani,Hossein Ganjiani +1 more
TL;DR: In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion-reaction equations, and the results obtained by this method have a good agreement with one obtained by other methods.
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Sub-harmonic resonances of nonlinear oscillations with parametric excitation by means of the homotopy analysis method
Jianmin Wen,Zhengcai Cao +1 more
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A new method for homoclinic solutions of ordinary differential equations
TL;DR: Liao et al. as mentioned in this paper used the homotopy analysis method to obtain a homoclinic solution for a differential equation with zero perturbation parameter and with hyperbolic equilibrium.