VARIATIONAL APPROACH METHOD FOR NONLINEAR OSCILLATIONS OF THE MOTION OF A RIGID ROD ROCKING BACK AND CUBIC-QUINTIC DUFFING OSCILLATORS

被引：26

作者：

Ganji, S. S. ^{[1
]}

Ganji, D. D. ^{[1
]}

Babazadeh, H. ^{[1
]}

Karimpour, S. ^{[1
]}

机构：

[1] Babol Univ Technol, Dept Civil Mech & Elect Engn, Babol Sar, Iran

来源：

PROGRESS IN ELECTROMAGNETICS RESEARCH M | 2008年 / 4卷

关键词：

D O I：

10.2528/PIERM08061007

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

This paper deals with Approximate Analytical Solutions to nonlinear oscillations of a conservative, non-natural, single-degree-of-freedom system with odd nonlinearity. By extending the Variational approach proposed by He, we established approximate analytical formulas for the period and periodic solution. To illustrate the applicability and accuracy of the method, two examples are presented: (i) the motion of a rigid rod rocking back and forth on the circular surface without slipping, and (ii) Cubic-Quintic Duffing Oscillators. Comparison of the result which is obtained by this method with the obtained result by the Exact solution reveals that the He's Variational approach is very effective and convenient and can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other sciences.

引用

页码：23 / 32

页数：10

共 42 条

[1] An Approximation of the Analytical Solution of the Linear and Nonlinear Integro-Differential Equations by Homotopy Perturbation Method [J].

Alizadeh, S. R. Seyed ;

Domairry, G. G. ;

Karimpour, S. .

ACTA APPLICANDAE MATHEMATICAE, 2008, 104 (03) :355-366

[2] Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable [J].

Belendez, A. ;

Mendez, D. I. ;

Belendez, T. ;

Hernandez, A. ;

Alvarez, M. L. .

JOURNAL OF SOUND AND VIBRATION, 2008, 314 (3-5) :775-782

[3] Application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire [J].

Belendez, A. ;

Hernandez, A. ;

Belendez, T. ;

Alvarez, M. L. ;

Gallego, S. ;

Ortuno, M. ;

Neipp, C. .

JOURNAL OF SOUND AND VIBRATION, 2007, 302 (4-5) :1018-1029

[4] Determination of limit cycles for a modified van der Pol oscillator [J].

D'Acunto, M .

MECHANICS RESEARCH COMMUNICATIONS, 2006, 33 (01) :93-98

[5]

Ganji DD, 2006, INT J NONLIN SCI NUM, V7, P411

[6] The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer [J].

Ganji, D. D. .

PHYSICS LETTERS A, 2006, 355 (4-5) :337-341

[7] Harmonic balance approach to limit cycles for nonlinear jerk equations [J].

Gottlieb, H. P. W. .

JOURNAL OF SOUND AND VIBRATION, 2006, 297 (1-2) :243-250

[8] On the large amplitude free vibrations of a restrained uniform beam carrying an intermediate lumped mass [J].

Hamdan, MN ;

Shabaneh, NH .

JOURNAL OF SOUND AND VIBRATION, 1997, 199 (05) :711-736

[9]

Hashemi K. S. H. A., 2008, IST C TORQ IN PRESS

[10]

He J.-H., 2006, NONPERTURBATIVE METH

← 1 2 3 4 5 →