An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator

In this paper, an analytical technique has been proposed to obtain higher-order approximate periods for the nonlinear oscillator with the square of the angular frequency depends quadratically on the velocity which is based on the harmonic balance method (HBM). Analytical investigation of the appeare...

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Main Authors:	Chowdhury, Md. Sazzad Hossien, Hosen, Md. Alal, Ali, Mohammad Yeakub, Ismail, Ahmad Faris
Format:	Article
Language:	English English English
Published:	Kulliyyah of Engineering, International Islamic University Malaysia 2018
Subjects:	QA297 Numerical Analysis
Online Access:	http://irep.iium.edu.my/67432/ http://irep.iium.edu.my/67432/ http://irep.iium.edu.my/67432/ http://irep.iium.edu.my/67432/1/67432_An%20analytical%20technique%20to%20obtain%20higher-order.pdf http://irep.iium.edu.my/67432/7/67432_An%20analytical%20technique%20to%20obtain%20higher-order%20approximate_scopus.pdf http://irep.iium.edu.my/67432/12/67432%20AN%20ANALYTICAL%20TECHNIQUE%20TO%20OBTAIN%20HIGHER-ORDER%20WOS.pdf

id	iium-67432
recordtype	eprints
spelling	iium-674322019-01-27T07:48:13Z http://irep.iium.edu.my/67432/ An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ali, Mohammad Yeakub Ismail, Ahmad Faris QA297 Numerical Analysis In this paper, an analytical technique has been proposed to obtain higher-order approximate periods for the nonlinear oscillator with the square of the angular frequency depends quadratically on the velocity which is based on the harmonic balance method (HBM). Analytical investigation of the appeared set of nonlinear algebraic equations is usually cumbersome, which is addressed by the proposed technique in a novel way. In this paper, this limitation is eradicated and provides desired results without much numerical complexity. Besides, a new suitable truncation formula has been introduced in which the approximate periods measures much better results than existing periods. The proposed technique is applied to the benchmark nonlinear oscillatory problem with the square of the angular frequency depends quadratically on the velocity to illustrate its novelty, reliability and wider applicability. Remarkableyimprotant that using the proposed technique a third-order approximate period gives an excellent agreement as compared with the exact ones. ********************************************************** Penulisan ini berkenan simulasi pengaruh pelbagai nilai indeks modulasi ( ) dalam strategi PWM berasaskan aplikasi dalam menghasilkan bentuk gelombang yang bertingkat. Bentuk gelombang ini diuji untuk aplikasi dalam topologi MMCs. Penilaian dan hasil dari artikle ini termasuk variasi komponen asas (50 Hz) dalam voltan keluar. Ia juga meneliti jumlah penyelarasan harmonik voltan keluar (THDv) dan arus keluaran (THDi) apabila indeks modulasi ditukar dalam rantau modulasi linear, 0 < <1. Ia juga meneroka kesan indeks modulasi lebih daripada 1. Selain itu, bentuk voltan keluar yang berbeza sebagai akibat dari pelbagai pada MMCs juga digambarkan untuk menunjukkan kesan berbeza-beza nilai pada sub-modul MMCs. Kulliyyah of Engineering, International Islamic University Malaysia 2018-12-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/67432/1/67432_An%20analytical%20technique%20to%20obtain%20higher-order.pdf application/pdf en http://irep.iium.edu.my/67432/7/67432_An%20analytical%20technique%20to%20obtain%20higher-order%20approximate_scopus.pdf application/pdf en http://irep.iium.edu.my/67432/12/67432%20AN%20ANALYTICAL%20TECHNIQUE%20TO%20OBTAIN%20HIGHER-ORDER%20WOS.pdf Chowdhury, Md. Sazzad Hossien and Hosen, Md. Alal and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2018) An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator. IIUM Engineering Journal, 19 (2). pp. 182-191. ISSN 1511-788X E-ISSN 2289-7860 http://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/943 10.31436/iiumej.v19i2.943
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA297 Numerical Analysis
spellingShingle	QA297 Numerical Analysis Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ali, Mohammad Yeakub Ismail, Ahmad Faris An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
description	In this paper, an analytical technique has been proposed to obtain higher-order approximate periods for the nonlinear oscillator with the square of the angular frequency depends quadratically on the velocity which is based on the harmonic balance method (HBM). Analytical investigation of the appeared set of nonlinear algebraic equations is usually cumbersome, which is addressed by the proposed technique in a novel way. In this paper, this limitation is eradicated and provides desired results without much numerical complexity. Besides, a new suitable truncation formula has been introduced in which the approximate periods measures much better results than existing periods. The proposed technique is applied to the benchmark nonlinear oscillatory problem with the square of the angular frequency depends quadratically on the velocity to illustrate its novelty, reliability and wider applicability. Remarkableyimprotant that using the proposed technique a third-order approximate period gives an excellent agreement as compared with the exact ones. ********************************************************** Penulisan ini berkenan simulasi pengaruh pelbagai nilai indeks modulasi ( ) dalam strategi PWM berasaskan aplikasi dalam menghasilkan bentuk gelombang yang bertingkat. Bentuk gelombang ini diuji untuk aplikasi dalam topologi MMCs. Penilaian dan hasil dari artikle ini termasuk variasi komponen asas (50 Hz) dalam voltan keluar. Ia juga meneliti jumlah penyelarasan harmonik voltan keluar (THDv) dan arus keluaran (THDi) apabila indeks modulasi ditukar dalam rantau modulasi linear, 0 < <1. Ia juga meneroka kesan indeks modulasi lebih daripada 1. Selain itu, bentuk voltan keluar yang berbeza sebagai akibat dari pelbagai pada MMCs juga digambarkan untuk menunjukkan kesan berbeza-beza nilai pada sub-modul MMCs.
format	Article
author	Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_facet	Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_sort	Chowdhury, Md. Sazzad Hossien
title	An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
title_short	An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
title_full	An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
title_fullStr	An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
title_full_unstemmed	An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
title_sort	analytical technique to obtain higher-order approximate periods for the nonlinear oscillator
publisher	Kulliyyah of Engineering, International Islamic University Malaysia
publishDate	2018
url	http://irep.iium.edu.my/67432/ http://irep.iium.edu.my/67432/ http://irep.iium.edu.my/67432/ http://irep.iium.edu.my/67432/1/67432_An%20analytical%20technique%20to%20obtain%20higher-order.pdf http://irep.iium.edu.my/67432/7/67432_An%20analytical%20technique%20to%20obtain%20higher-order%20approximate_scopus.pdf http://irep.iium.edu.my/67432/12/67432%20AN%20ANALYTICAL%20TECHNIQUE%20TO%20OBTAIN%20HIGHER-ORDER%20WOS.pdf
first_indexed	2023-09-18T21:35:43Z
last_indexed	2023-09-18T21:35:43Z
_version_	1777412807218692096

An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator

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