Nonlinear vibrations of a slightly curved beam with nonlinear boundary conditions

Ye, SQ; Mao, XY; Ding, H; Ji, JC; Chen, LQ

Nonlinear vibrations of a slightly curved beam with nonlinear boundary conditions

Ye, SQ Mao, XY Ding, H Ji, JC Chen, LQ

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Publisher:: PERGAMON-ELSEVIER SCIENCE LTD
Publication Type:: Journal Article
Citation:: International Journal of Mechanical Sciences, 2020, 168
Issue Date:: 2020-02-15

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Field	Value	Language
dc.contributor.author	Ye, SQ
dc.contributor.author	Mao, XY
dc.contributor.author	Ding, H
dc.contributor.author	Ji, JC
dc.contributor.author	Chen, LQ
dc.date.accessioned	2021-03-19T06:17:08Z
dc.date.available	2021-03-19T06:17:08Z
dc.date.issued	2020-02-15
dc.identifier.citation	International Journal of Mechanical Sciences, 2020, 168
dc.identifier.issn	0020-7403
dc.identifier.issn	1879-2162
dc.identifier.uri	http://hdl.handle.net/10453/147382
dc.description.abstract	© 2019 The existing studies of nonlinear vibration of elastic structures are usually focused on straight structures with homogeneous linear boundaries. Differently, this paper investigates the nonlinear transverse vibrations of a slightly curved beam with nonlinear boundary conditions. By using the generalized Hamilton's principle, the governing equation with geometric nonlinearity is obtained for the dynamics of the curved beam. A method of dealing with nonlinear boundaries is proposed, which is considered as a nonlinear concentrated force at the boundary. The normal modes and natural frequencies of the curved beam are determined using two different hypothetical modes based on the derived system. The harmonic balance method in combination with the pseudo arc-length method is employed to obtain the primary resonance response and 1/2 super-harmonic resonance response of the slightly curved beam. It is found that the initial curvature plays a significant role in the characteristics of the nonlinear vibrations of the curved beam. With an increase of the initial curvature, the nonlinear characteristics of softening and hardening types can coexist in the steady-state amplitude-frequency response. Moreover, the results show that the initial curvature can induce 1/2 super-harmonic resonance. Furthermore, it is also found that the nonlinear boundary has a significant influence on the nonlinear vibration of the curved structure. Therefore, the obtained results provide useful information for further studying the nonlinear vibrations of the curved beam with nonlinear and time-dependent boundary conditions.
dc.language	English
dc.publisher	PERGAMON-ELSEVIER SCIENCE LTD
dc.relation.ispartof	International Journal of Mechanical Sciences
dc.relation.isbasedon	10.1016/j.ijmecsci.2019.105294
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0905 Civil Engineering, 0910 Manufacturing Engineering, 0913 Mechanical Engineering
dc.subject.classification	Mechanical Engineering & Transports
dc.title	Nonlinear vibrations of a slightly curved beam with nonlinear boundary conditions
dc.type	Journal Article
utslib.citation.volume	168
utslib.for	0905 Civil Engineering
utslib.for	0910 Manufacturing Engineering
utslib.for	0913 Mechanical Engineering
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	*
dc.date.updated	2021-03-19T06:17:07Z
pubs.publication-status	Published
pubs.volume	168

Abstract:

© 2019 The existing studies of nonlinear vibration of elastic structures are usually focused on straight structures with homogeneous linear boundaries. Differently, this paper investigates the nonlinear transverse vibrations of a slightly curved beam with nonlinear boundary conditions. By using the generalized Hamilton's principle, the governing equation with geometric nonlinearity is obtained for the dynamics of the curved beam. A method of dealing with nonlinear boundaries is proposed, which is considered as a nonlinear concentrated force at the boundary. The normal modes and natural frequencies of the curved beam are determined using two different hypothetical modes based on the derived system. The harmonic balance method in combination with the pseudo arc-length method is employed to obtain the primary resonance response and 1/2 super-harmonic resonance response of the slightly curved beam. It is found that the initial curvature plays a significant role in the characteristics of the nonlinear vibrations of the curved beam. With an increase of the initial curvature, the nonlinear characteristics of softening and hardening types can coexist in the steady-state amplitude-frequency response. Moreover, the results show that the initial curvature can induce 1/2 super-harmonic resonance. Furthermore, it is also found that the nonlinear boundary has a significant influence on the nonlinear vibration of the curved structure. Therefore, the obtained results provide useful information for further studying the nonlinear vibrations of the curved beam with nonlinear and time-dependent boundary conditions.

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http://hdl.handle.net/10453/147382