A modified harmonic balance method to obtain higher-order approximations to strongly nonlinear oscillators

Md. Alal, Hosen and Chowdhury, Md. Sazzad Hossien and Ismail, Gamal M. and Yıldırım, Ahmet (2020) A modified harmonic balance method to obtain higher-order approximations to strongly nonlinear oscillators. Journal of Interdisciplinary Mathematics, 23 (7). pp. 1325-1345. ISSN 0972-0502 E-ISSN 2169-012X

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Abstract

We propose a new method, namely, the modified harmonic balance method. This paper also analyses and offers the high-order approximate periodic solutions to the strongly nonlinear oscillator with cubic and harmonic restoring force. The existing harmonic balance method cannot be applied directly to such kind of nonlinear oscillators in the presence of forcing term. It is possible if we rewrite the original form of the nonlinear oscillators. If we do so, the results are valid only for small values of amplitude of the oscillation. Moreover, after applying the existing harmonic balance method, a set of complicated higher-order nonlinear algebraic equations are obtained. Analytical investigation of these equations is cumbersome especially when the amplitude of the oscillation is large. These limitations are removed in the proposed method. In addition, a suitable truncation principle has also been used in which the solution achieves better results than existing solutions. The approximate results agree well with numerically obtained exact solutions. Highly accurate results and a simple solution procedure are the advantages of this proposed method, which could be applied to other nonlinear oscillatory problems arising in nonlinear science and engineering.

Item Type:	Article (Journal)
Additional Information:	5807/86636
Uncontrolled Keywords:	Approximate solutions, Cubic and harmonic restoring force oscillator, Harmonic balance method, Iteration method, Homotopy perturbation method
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA297 Numerical Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering Kulliyyah of Engineering > Department of Science
Depositing User:	Dr. Md Sazzad Hossien Chowdhury
Date Deposited:	23 Dec 2020 15:54
Last Modified:	23 Dec 2020 15:54
URI:	http://irep.iium.edu.my/id/eprint/86636

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