Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method

Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien (2015) Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method. In: 2nd International Conference on Mathematical Sciences & Computer Engineering (ICMSCE 2015), 5th-6th February 2015, Langkawi, Malaysia. (In Press)

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Abstract

We introduce an analytical technique to solve strongly nonlinear oscillators with cubic and harmonic restoring force by using harmonic balance method (HBM). A set of nonlinear algebraic equations is appeared when HBM is imposed. In this paper, a power series solutions of these nonlinear algebraic equations gives desired results and to avoid numerical complexity. A very good agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. We found that, a second order HBM works very well and the excellent agreement of the approximate solutions with the numerical solutions. The advantage of this method is its simple procedure and applicable for many oscillatory problems arising in science and engineering.

Item Type:	Conference or Workshop Item (Full Paper)
Additional Information:	5807/44869
Uncontrolled Keywords:	Analytical Technique, Strongly Nonlinear oscillator, Approximate solutions, Harmonic balance method, Power series solution.
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Science
Depositing User:	Dr. Md Sazzad Hossien Chowdhury
Date Deposited:	05 Oct 2015 09:11
Last Modified:	05 Oct 2015 09:12
URI:	http://irep.iium.edu.my/id/eprint/44869

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