Open Access

ARTICLE

Application of the Differential Transform Method for Solving Periodic Solutions of Strongly Non-linear Oscillators

Hsin-Ping Chu¹, Cheng-Ying Lo²

1 Kao Yuan University, Department of Mechanical and Automation Engineering, Kaohsiung, Taiwan
2 National Formosa University, Department of Aeronautical Engineering, Yulin, Taiwan (Corresponding author)

Computer Modeling in Engineering & Sciences 2011, 77(3&4), 161-172. https://doi.org/10.3970/cmes.2011.077.161

Abstract

This paper presents the application of the differential transform method to solve strongly nonlinear equations with cubic nonlinearities and self-excitation terms. First, the equations are transformed by the differential transform method into the algebra equations in terms of the transformed functions. Secondly, the higher-order transformed functions are calculated in terms of other lower-order transformed functions through the iterative procedure. Finally, the solutions are approximated by the n-th partial sum of the infinite series obtained by the inverse differential transform. Two strongly nonlinear equations with different coefficients and initial conditions are given as illustrative examples.

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Keywords

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