Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales

Gao, K; Gao, W; Wu, B; Wu, D; Song, C

Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales

Gao, K Gao, W Wu, B Wu, D

Song, C

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Publisher:: Elsevier BV
Publication Type:: Journal Article
Citation:: Thin-Walled Structures, 2018, 125, pp. 281-293
Issue Date:: 2018-04-01

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Field	Value	Language
dc.contributor.author	Gao, K
dc.contributor.author	Gao, W
dc.contributor.author	Wu, B
dc.contributor.author	Wu, D https://orcid.org/0000-0002-7284-5024
dc.contributor.author	Song, C
dc.date.accessioned	2022-09-03T03:59:17Z
dc.date.available	2022-09-03T03:59:17Z
dc.date.issued	2018-04-01
dc.identifier.citation	Thin-Walled Structures, 2018, 125, pp. 281-293
dc.identifier.issn	0263-8231
dc.identifier.uri	http://hdl.handle.net/10453/161252
dc.description.abstract	An analytical method is proposed for the nonlinear primary resonance analysis of cylindrical shells made of functionally graded (FG) porous materials subjected to a uniformly distributed harmonic load including the damping effect. The Young's modulus, shear modulus and density of porous materials are assumed to vary through the thickness direction based on the assumption of a common mechanical feature of the open-cell foam. Three types of FG porous distributions, namely symmetric porosity distribution, non-symmetric porosity stiff or soft distribution and uniform porosity distribution are considered in this paper. Theoretical formulations are derived based on Donnell shell theory (DST) and accounting for von-Kármán strain-displacement relation and damping effect. The first mode of deflection function that satisfies the boundary conditions is introduced into this nonlinear governing partial differential equation and then a Galerkin-based procedure is utilized to obtain a Duffing-type nonlinear ordinary differential equation with a cubic nonlinear term. Finally, the governing equation is solved analytically by conducting the method of multiple scales (MMS) which results in frequency-response curves of FG porous cylindrical shells in the presence of damping effect. The detailed parametric studies on porosity distribution, porosity coefficient, damping ratio, amplitude and frequency of the external harmonic excitation, aspect ratio and thickness ratio, shown that the distribution type of FG porous cylindrical shells significantly affects primary resonance behavior and the response presents a hardening-type nonlinearity, which provides a useful help for the design and optimize of FG porous shell-type devices working under external harmonic excitation.
dc.language	en
dc.publisher	Elsevier BV
dc.relation	http://purl.org/au-research/grants/arc/IH150100006
dc.relation.ispartof	Thin-Walled Structures
dc.relation.isbasedon	10.1016/j.tws.2017.12.039
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0901 Aerospace Engineering, 0905 Civil Engineering, 0913 Mechanical Engineering
dc.subject.classification	Civil Engineering
dc.title	Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales
dc.type	Journal Article
utslib.citation.volume	125
utslib.for	0901 Aerospace Engineering
utslib.for	0905 Civil 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 Civil and Environmental Engineering
utslib.copyright.status	closed_access	*
dc.date.updated	2022-09-03T03:59:13Z
pubs.publication-status	Published
pubs.volume	125

Abstract:

An analytical method is proposed for the nonlinear primary resonance analysis of cylindrical shells made of functionally graded (FG) porous materials subjected to a uniformly distributed harmonic load including the damping effect. The Young's modulus, shear modulus and density of porous materials are assumed to vary through the thickness direction based on the assumption of a common mechanical feature of the open-cell foam. Three types of FG porous distributions, namely symmetric porosity distribution, non-symmetric porosity stiff or soft distribution and uniform porosity distribution are considered in this paper. Theoretical formulations are derived based on Donnell shell theory (DST) and accounting for von-Kármán strain-displacement relation and damping effect. The first mode of deflection function that satisfies the boundary conditions is introduced into this nonlinear governing partial differential equation and then a Galerkin-based procedure is utilized to obtain a Duffing-type nonlinear ordinary differential equation with a cubic nonlinear term. Finally, the governing equation is solved analytically by conducting the method of multiple scales (MMS) which results in frequency-response curves of FG porous cylindrical shells in the presence of damping effect. The detailed parametric studies on porosity distribution, porosity coefficient, damping ratio, amplitude and frequency of the external harmonic excitation, aspect ratio and thickness ratio, shown that the distribution type of FG porous cylindrical shells significantly affects primary resonance behavior and the response presents a hardening-type nonlinearity, which provides a useful help for the design and optimize of FG porous shell-type devices working under external harmonic excitation.

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http://hdl.handle.net/10453/161252