Journal
RESULTS IN PHYSICS
Volume 7, Issue -, Pages 3962-3967Publisher
ELSEVIER
DOI: 10.1016/j.rinp.2017.10.008
Keywords
Approximate frequency; Harmonic balance method; Cubic-quintic Duffing oscillator; Analytical solutions; Truncation principle
Funding
- International Islamic University Malaysia, Malaysia by the Ministry of Higher Education Malaysia [FRGS-15-228-0469]
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In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.
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