A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators

Cheung, Y.K.; Chen, S.H.; Lau, S.L.

doi:10.1016/0020-7462(91)90066-3

Cited by 221 publications

(174 citation statements)

References 5 publications

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“…Nayfeh [31] derived higher order amplitude equations for the Duffing equation by the method of multiple scales in response to some uncertainty that existed at that time in the literature [32,33,34,35,36]. In particular, one can identify the results of [31] and [33] with our amplitude equation (3.4) and renormalized expansion (3.7), respectively.…”

Section: Wave Propagation In Nonlinear Mediamentioning

confidence: 99%

The Renormalization Group: A Perturbation Method for the Graduate Curriculum

Kirkinis¹

2012

SIAM Rev.

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Abstract. In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp. 1311-1315 Phys. Rev. E, 54 (1996), pp. 376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum. The method is illustrated by some linear and nonlinear singular perturbation problems.

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Section: Wave Propagation In Nonlinear Mediamentioning

confidence: 99%

The Renormalization Group: A Perturbation Method for the Graduate Curriculum

Kirkinis¹

2012

SIAM Rev.

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“…This well-known remark has been verified in [1] through a comparison between the exact free oscillation period of the Duffing oscillator (1.1) and that given by the Poincare method.…”

Section: Introductionmentioning

confidence: 79%

A note on the method of harmonic balance

Định¹

2001

Vietnam J. Mech.

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“…Dowell (1986) has used the IHB method to investigate the boundary supports of clamped beams and plates. Cheung et al (1991) derived a formulation for third-order general nonlinear systems. Progressive research has established the usability of the IHB method especially because of its sophistication in problem formulation and computational implementation.…”

Section: Modelling Of Frictionally Damped Systemsmentioning

confidence: 99%

Dynamics of dry friction damping in gas turbines: literature survey

Rizvi

Smith

Rajasekaran

et al. 2014

Journal of Vibration and Control

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Vibrating structures, such as gas turbine engines, are assemblages of multiple components interfaced with each other through physical contact. The friction produced at these contact interfaces, by sliding or slipping at the interface, is a source of energy dissipation, resulting in damping effects. This passive approach to damping is exploited by engineers to provide optimal energy dissipation to attenuate vibration in a variety of systems (such as bladed disc assemblies and airfoils), to prevent wear and premature failure. However, the highly nonlinear nature of friction renders accurate predictive modeling of such a problem challenging. This article gives an overview of the current state of the art, and the methods used for mathematical and predictive computational modeling of vibrating systems under the influence of dry friction.

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A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators

Cited by 221 publications

References 5 publications

The Renormalization Group: A Perturbation Method for the Graduate Curriculum

The Renormalization Group: A Perturbation Method for the Graduate Curriculum

A note on the method of harmonic balance

Dynamics of dry friction damping in gas turbines: literature survey

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