A modified two-variable expansion method for a nonlinear Jerk equation

Zheng, MY; Zhang, N; Sun, GY

A modified two-variable expansion method for a nonlinear Jerk equation

Zheng, MY Zhang, N

Sun, GY

Permalink

Publication Type:: Journal Article
Citation:: Zhendong yu Chongji/Journal of Vibration and Shock, 2012, 31 (23), pp. 118 - 122
Issue Date:: 2012-12-15

Closed Access

	Filename	Description	Size
	Ò»Àà·ÇÏßÐÔJerk·½³ÌµÄ¸Ä½øÁ½±äÁ¿Õ¹¿ª·¨.pdf	Published Version	338.04 kB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Zheng, MY	en_US
dc.contributor.author	Zhang, N https://orcid.org/0000-0001-6408-0044	en_US
dc.contributor.author	Sun, GY	en_US
dc.date.issued	2012-12-15	en_US
dc.identifier.citation	Zhendong yu Chongji/Journal of Vibration and Shock, 2012, 31 (23), pp. 118 - 122	en_US
dc.identifier.issn	1000-3835	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114902
dc.description.abstract	A modified two-variable expansion method was used to determine approximate frequencies and approximate analytical periodic solutions to a third-order differential equation with cubic nonlinearterms. This method combining Lindstedt-Poincare technique and the two-variable expansion method was not only valid for weakly nonlinear oscillations but also for strongly nonlinear oscillations. Here, a nonlinear Jerk equation excluding linear part of velocity term as an example was calculated. Its second-order approximate period and second-order approximate analytical periodic solution were obtained. A comparison of the first and second approximate analytical periodic solutions with the numerically exact solutions showed that the second order approximate analytical periodic solution is much more accurate than the first one. The result showed that the modified two-variable expansion method is suitable for solving a nonlinear Jerk equation, moreover, when the Jerk equation doesn't have linear part of velocity term, this method is still effective.	en_US
dc.relation.ispartof	Zhendong yu Chongji/Journal of Vibration and Shock	en_US
dc.subject.classification	Mechanical Engineering & Transports	en_US
dc.title	A modified two-variable expansion method for a nonlinear Jerk equation	en_US
dc.type	Journal Article
utslib.citation.volume	23	en_US
utslib.citation.volume	31	en_US
utslib.for	0902 Automotive Engineering	en_US
utslib.for	091304 Dynamics, Vibration and Vibration Control	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access
pubs.issue	23	en_US
pubs.publication-status	Published	en_US
pubs.volume	31	en_US

Abstract:

A modified two-variable expansion method was used to determine approximate frequencies and approximate analytical periodic solutions to a third-order differential equation with cubic nonlinearterms. This method combining Lindstedt-Poincare technique and the two-variable expansion method was not only valid for weakly nonlinear oscillations but also for strongly nonlinear oscillations. Here, a nonlinear Jerk equation excluding linear part of velocity term as an example was calculated. Its second-order approximate period and second-order approximate analytical periodic solution were obtained. A comparison of the first and second approximate analytical periodic solutions with the numerically exact solutions showed that the second order approximate analytical periodic solution is much more accurate than the first one. The result showed that the modified two-variable expansion method is suitable for solving a nonlinear Jerk equation, moreover, when the Jerk equation doesn't have linear part of velocity term, this method is still effective.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/114902