Chowdhury, Md. Sazzad Hossien and Hosen, Md. Alal and Ahmad, Kartini and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2017) High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method. Results in Physics, 7. pp. 3962-3967. E-ISSN 2211-3797
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Abstract
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.
| Item Type: | Article (Journal) |
|---|---|
| Additional Information: | 5807/60636 |
| Uncontrolled Keywords: | Approximate frequency, Harmonic balance method, Cubic-quintic Duffing oscillator, Analytical solutions, Truncation principle |
| Subjects: | T Technology > T Technology (General) T Technology > TJ Mechanical engineering and machinery T Technology > TS Manufactures |
| Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): | Kulliyyah of Engineering |
| Depositing User: | Prof. Ir. Dr. Mohammad Yeakub Ali |
| Date Deposited: | 24 Dec 2017 22:17 |
| Last Modified: | 10 Jul 2018 17:37 |
| URI: | http://irep.iium.edu.my/id/eprint/60636 |
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