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Article: Three-dimensional vibrations of annular thick plates with linearly varying thickness

TitleThree-dimensional vibrations of annular thick plates with linearly varying thickness
Authors
Keywords3-D Elasticity Solution
Annular Plate
Variable Thickness
Vibration
Issue Date2012
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00419/index.htm
Citation
Archive Of Applied Mechanics, 2012, v. 82 n. 1, p. 111-135 How to Cite?
AbstractThe free vibration of annular thick plates with linearly varying thickness along the radial direction is studied, based on the linear, small strain, three-dimensional (3-D) elasticity theory. Various boundary conditions, symmetrically and asymmetrically linear variations of upper and lower surfaces are considered in the analysis. The well-known Ritz method is used to derive the eigen-value equation. The trigonometric functions in the circumferential direction, the Chebyshev polynomials in the thickness direction, and the Chebyshev polynomials multiplied by the boundary functions in the radial direction are chosen as the trial functions. The present analysis includes full vibration modes, e.g.; flexural, thickness-shear, extensive, and torsional. The first eight frequency parameters accurate to at least four significant figures for five vibration categories are obtained. Comparisons of present results for plates having symmetrically linearly varying thickness are made with others based on 2-D classical thin plate theory, 2-D moderate thickness plate theory, and 3-D elasticity theory. The first 35 natural frequencies for plates with asymmetrically linearly varying thickness are compared to the finite element solutions; excellent agreement has been achieved. The asymmetry effect of upper and lower surface variations on the frequency parameters of annular plates is discussed in detail. The first four modes of axisymmetric vibration for completely free circular plates with symmetrically and asymmetrically linearly varying thickness are plotted. The present results for 3-D vibration of annular plates with linearly varying thickness can be taken as benchmark data for validating results from various plate theories and numerical methods. © 2011 Springer-Verlag.
Persistent Identifierhttp://hdl.handle.net/10722/150653
ISSN
2015 Impact Factor: 1.103
2015 SCImago Journal Rankings: 0.865
ISI Accession Number ID
Funding AgencyGrant Number
University of Hong Kong2009 11159054
Funding Information:

The financial support of the Seed Funding Programming for Basic Research (2009 11159054), of the University of Hong Kong is acknowledged.

References

 

DC FieldValueLanguage
dc.contributor.authorZhou, Den_US
dc.contributor.authorLo, SHen_US
dc.date.accessioned2012-06-26T06:06:29Z-
dc.date.available2012-06-26T06:06:29Z-
dc.date.issued2012en_US
dc.identifier.citationArchive Of Applied Mechanics, 2012, v. 82 n. 1, p. 111-135en_US
dc.identifier.issn0939-1533en_US
dc.identifier.urihttp://hdl.handle.net/10722/150653-
dc.description.abstractThe free vibration of annular thick plates with linearly varying thickness along the radial direction is studied, based on the linear, small strain, three-dimensional (3-D) elasticity theory. Various boundary conditions, symmetrically and asymmetrically linear variations of upper and lower surfaces are considered in the analysis. The well-known Ritz method is used to derive the eigen-value equation. The trigonometric functions in the circumferential direction, the Chebyshev polynomials in the thickness direction, and the Chebyshev polynomials multiplied by the boundary functions in the radial direction are chosen as the trial functions. The present analysis includes full vibration modes, e.g.; flexural, thickness-shear, extensive, and torsional. The first eight frequency parameters accurate to at least four significant figures for five vibration categories are obtained. Comparisons of present results for plates having symmetrically linearly varying thickness are made with others based on 2-D classical thin plate theory, 2-D moderate thickness plate theory, and 3-D elasticity theory. The first 35 natural frequencies for plates with asymmetrically linearly varying thickness are compared to the finite element solutions; excellent agreement has been achieved. The asymmetry effect of upper and lower surface variations on the frequency parameters of annular plates is discussed in detail. The first four modes of axisymmetric vibration for completely free circular plates with symmetrically and asymmetrically linearly varying thickness are plotted. The present results for 3-D vibration of annular plates with linearly varying thickness can be taken as benchmark data for validating results from various plate theories and numerical methods. © 2011 Springer-Verlag.en_US
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00419/index.htmen_US
dc.relation.ispartofArchive of Applied Mechanicsen_US
dc.subject3-D Elasticity Solutionen_US
dc.subjectAnnular Plateen_US
dc.subjectVariable Thicknessen_US
dc.subjectVibrationen_US
dc.titleThree-dimensional vibrations of annular thick plates with linearly varying thicknessen_US
dc.typeArticleen_US
dc.identifier.emailLo, SH:hreclsh@hkucc.hku.hken_US
dc.identifier.authorityLo, SH=rp00223en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s00419-011-0543-yen_US
dc.identifier.scopuseid_2-s2.0-84856596351en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84856596351&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume82en_US
dc.identifier.issue1en_US
dc.identifier.spage111en_US
dc.identifier.epage135en_US
dc.identifier.isiWOS:000299171500008-
dc.publisher.placeGermanyen_US
dc.identifier.scopusauthoridZhou, D=7403395115en_US
dc.identifier.scopusauthoridLo, SH=7401542444en_US
dc.identifier.citeulike9202175-

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