A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method

Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2016) A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method. Results in Physics, 6. pp. 496-504. ISSN 2211-3797

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Abstract

In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude Ao = 100 , the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique.

Item Type:	Article (Journal)
Additional Information:	5807/51653
Uncontrolled Keywords:	Highly nonlinear oscillator, energy balance method, analytical approximate technique, duffing-relativistic oscillator
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Manufacturing and Materials Engineering Kulliyyah of Engineering > Department of Mechanical Engineering Kulliyyah of Engineering > Department of Science
Depositing User:	Prof Dr Ahmad Faris Ismail
Date Deposited:	17 Aug 2016 15:38
Last Modified:	30 May 2017 11:53
URI:	http://irep.iium.edu.my/id/eprint/51653

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