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Article

Analytical Solution to Determine Displacement of Nonlinear Oscillations with Parametric Excitation by Differential Transformation Method

by
A. Fereidoon
1,*,
N. Kordani
1,
Y. Rostamiyan
1,* and
D. D.Ganji
2,*
1
Department of Mechanical Engineering, Semnan University, Semnan, Iran
2
Department of Mechanical Engineering, Babol University of Technology Babol, P. O. Box 484, Iran
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2010, 15(5), 810-815; https://doi.org/10.3390/mca15050810
Submission received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
Versions Notes

Abstract

In this study, sub-harmonic displacement of nonlinear oscillations with parametric excitation is solved using a simulation method called the Differential Transformation Method (DTM). We employed this method to derive solutions of nonlinear oscillations with parametric excitation equation. Also Runge-Kutta as numerical method is exerted to this equation too. The obtained results from DTM are compared with those from the numerical solution to verify the accuracy of the proposed method. The results specify that the technique introduced here is accurate and achieve suitable results in predicting the solution of such problems.
Keywords: Differential Transformation Method (DTM); Numerical Solution (NS); Runge-Kutta; Sub-harmonic; Nonlinear oscillations; parametric excitation Differential Transformation Method (DTM); Numerical Solution (NS); Runge-Kutta; Sub-harmonic; Nonlinear oscillations; parametric excitation

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MDPI and ACS Style

Fereidoon, A.; Kordani, N.; Rostamiyan, Y.; D.Ganji, D. Analytical Solution to Determine Displacement of Nonlinear Oscillations with Parametric Excitation by Differential Transformation Method. Math. Comput. Appl. 2010, 15, 810-815. https://doi.org/10.3390/mca15050810

AMA Style

Fereidoon A, Kordani N, Rostamiyan Y, D.Ganji D. Analytical Solution to Determine Displacement of Nonlinear Oscillations with Parametric Excitation by Differential Transformation Method. Mathematical and Computational Applications. 2010; 15(5):810-815. https://doi.org/10.3390/mca15050810

Chicago/Turabian Style

Fereidoon, A., N. Kordani, Y. Rostamiyan, and D. D.Ganji. 2010. "Analytical Solution to Determine Displacement of Nonlinear Oscillations with Parametric Excitation by Differential Transformation Method" Mathematical and Computational Applications 15, no. 5: 810-815. https://doi.org/10.3390/mca15050810

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