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Technical Briefs

Analytical Approximations to Conservative Oscillators With Odd Nonlinearity Using the Variational Iteration Method

[+] Author and Article Information
A. Khosrozadeh

Department of Mechanical Engineering,
Marvdasht Branch, Islamic Azad University,
Marvdasht, Iran
e-mail: alkhosro@gmail.com

M. A. Hajabasi

Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman, Iran

H. R. Fahham

Department of Mechanical Engineering,
Marvdasht Branch, Islamic Azad University,
Marvdasht, Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 11, 2011; final manuscript received April 12, 2012; published online July 23, 2012. Assoc. Editor: Eric A. Butcher.

J. Comput. Nonlinear Dynam 8(1), 014502 (Jul 23, 2012) (5 pages) Paper No: CND-11-1241; doi: 10.1115/1.4006789 History: Received December 11, 2011; Revised April 12, 2012

In this article, a new technique is introduced for establishing analytical approximate solutions to conservative oscillators with strong odd nonlinearity using the variational iteration method and the Fourier series. The illustrated examples show that only a few iterations can provide very accurate approximate solutions for the whole range of oscillation amplitude even for longer time ranges.

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References

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Figures

Grahic Jump Location
Fig. 1

Comparison of the approximate solutions with the numeric one for example 1 (w = 1, A = 1.5)

Grahic Jump Location
Fig. 2

Comparison of the approximate solutions with the numeric one for example 1 (w = 1, A = 2.5)

Grahic Jump Location
Fig. 3

Phase plane plot for example 1 (w = 1)

Grahic Jump Location
Fig. 4

Comparison of the approximate solutions with the numeric one for example 2 (λ = 1, A = 100)

Grahic Jump Location
Fig. 5

Comparison of the approximate solutions with the numeric one for example 2 (λ = 1, A = 0.5), (a) t = 0-25, (b) t = 50-90

Grahic Jump Location
Fig. 6

Comparison of the approximate solutions with the numeric one for example 3 (A = 0.1)

Grahic Jump Location
Fig. 7

Comparison of the approximate solutions with the numeric one for example 3 (A = 1)

Grahic Jump Location
Fig. 8

Comparison of the approximate solutions with the numeric one for example 3 (A = 10)

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