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Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2018) Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity. In: 4th International Conference on Mathematical Applications in Engineering 2017 (ICMAE'17), 8th–9th August 2017, Kuala Lumpur, Malaysia.

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Abstract

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Item Type: Conference or Workshop Item (Plenary Papers)
Additional Information: 5807/61802
Uncontrolled Keywords: Analytical approximations, oscillators, antisymmetric quadratic nonlinearity
Subjects: Q Science > QA Mathematics > QA297 Numerical Analysis
Kulliyyahs/Centres/Divisions/Institutes: Kulliyyah of Engineering > Department of Manufacturing and Materials Engineering
Kulliyyah of Engineering > Department of Mechanical Engineering
Kulliyyah of Engineering > Department of Science
Depositing User: Dr. Md Sazzad Hossien Chowdhury
Date Deposited: 02 Feb 2018 15:08
Last Modified: 26 Jun 2018 15:03
URI: http://irep.iium.edu.my/id/eprint/61802

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