Journal ArticleDOI
A generalization of the method of harmonic balance
TLDR
In this paper, a procedure for generalizing harmonic balance to obtain higher-order approximations to the periodic solutions of differential equations for two systems, one a conservative system and the other non-conservative, is presented.About:
This article is published in Journal of Sound and Vibration.The article was published on 1986-12-22. It has received 164 citations till now. The article focuses on the topics: Harmonic balance & Nonlinear system.read more
Citations
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Journal ArticleDOI
Homotopy–perturbation method for pure nonlinear differential equation
TL;DR: In this paper, the homotopy-perturbation method was adopted for solving pure strong nonlinear second-order differential equation, where the initial approximate solution was assumed in the form of Jacobi elliptic function.
Journal ArticleDOI
An analytical approximate technique for a class of strongly non-linear oscillators
Baisheng Wu,W. P. Sun,C.W. Lim +2 more
TL;DR: In this article, an analytical approximate technique for large amplitude oscillations of a class of conservative single degree-of-freedom systems with odd non-linearity is proposed, which incorporates salient features of both Newton's method and the harmonic balance method.
Journal ArticleDOI
A new analytical approach to the Duffing-harmonic oscillator
C.W. Lim,Baisheng Wu +1 more
TL;DR: In this article, a new approach to solving the nonlinear Duffing-harmonic oscillator is presented, which combines the linearization of the governing equation with the method of harmonic balance.
Journal ArticleDOI
Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance
Albert C. J. Luo,Jianzhe Huang +1 more
TL;DR: In this article, the generalized harmonic balance method is used for approximate, analytical solutions of periodic motions in nonlinear dynamical systems, such as the periodic motion of a forced Duffing oscillator, and the stability and bifurcation analysis of the HB2 approximate solution of period-1 motions.
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ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS
Albert C. J. Luo,Jianzhe Huang +1 more
TL;DR: The analytical solutions for period-m flows and chaos in nonlinear dynamical systems are presented through the generalized harmonic balance method and the stable and unstable chaotic motions can be achieved analytically.
References
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Journal ArticleDOI
Comments on the method of harmonic balance
TL;DR: In this article, the advantages and limitations of the harmonic-balance or describing-function approximation scheme for solving nonlinear ordinary differential equations of oscillatory motion are discussed; the limitation rules are essentially those described by Mickens (1983).
Journal ArticleDOI
Approximate analytic solutions for singular non-linear oscillators
K. B. Bota,Ronald E. Mickens +1 more
TL;DR: In this paper, the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations was investigated for systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot).
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Rational-Fourier-series Approximations for Periodic Boundary-value Problems
TL;DR: On generalise la methode d'approximation de Galerkin this article for des problemes aux valeurs limites periodiques for permettre l'utilisation de rapports ou d'autres fonctions de 2 series de Fourier.