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

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

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5807/67432
Uncontrolled Keywords:	Approximate periods, truncation principle, Harmonic balance method,Nonlinear oscillator, Analytical technique.
Subjects:	Q Science > QA Mathematics > QA297 Numerical Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering 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:	15 Nov 2018 11:47
Last Modified:	27 Jan 2019 15:48
URI:	http://irep.iium.edu.my/id/eprint/67432

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