Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method

Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method

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 eq...

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Main Authors: Hosen, Md. Alal, Chowdhury, Md. Sazzad Hossien
Format: Conference or Workshop Item
Language:English
Published: 2015
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/44869/
http://irep.iium.edu.my/44869/
http://irep.iium.edu.my/44869/1/44869.pdf
id iium-44869
recordtype eprints
spelling iium-448692015-10-05T01:12:49Z http://irep.iium.edu.my/44869/ Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien QA Mathematics 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. 2015 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/44869/1/44869.pdf 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) http://www.icmsce.net/cms/
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Hosen, Md. Alal
Chowdhury, Md. Sazzad Hossien
Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
description 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.
format Conference or Workshop Item
author Hosen, Md. Alal
Chowdhury, Md. Sazzad Hossien
author_facet Hosen, Md. Alal
Chowdhury, Md. Sazzad Hossien
author_sort Hosen, Md. Alal
title Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
title_short Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
title_full Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
title_fullStr Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
title_full_unstemmed Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
title_sort approximate solutions for strongly nonlinear oscillators by using harmonic balance method
publishDate 2015
url http://irep.iium.edu.my/44869/
http://irep.iium.edu.my/44869/
http://irep.iium.edu.my/44869/1/44869.pdf
first_indexed 2023-09-18T21:03:48Z
last_indexed 2023-09-18T21:03:48Z
_version_ 1777410799044657152

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