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Article: Three-dimensional vibration analysis of a torus with circular cross section
Title | Three-dimensional vibration analysis of a torus with circular cross section |
---|---|
Authors | |
Keywords | Physics - sound |
Issue Date | 2002 |
Publisher | Acoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.html |
Citation | Journal of the Acoustical Society of America, 2002, v. 112 n. 6, p. 2831-2839 How to Cite? |
Abstract | The free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, θ) at each circular cross section and the circumferential coordinate φ around the ring, is developed. Each of the displacement components ur, vτ, and wφ in the r, θ, and φ directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the θ and φ directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem. © 2002 Acoustical Society of America. |
Persistent Identifier | http://hdl.handle.net/10722/42648 |
ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 0.687 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Zhou, D | en_HK |
dc.contributor.author | Au, FTK | en_HK |
dc.contributor.author | Lo, SH | en_HK |
dc.contributor.author | Cheung, YK | en_HK |
dc.date.accessioned | 2007-03-23T04:28:49Z | - |
dc.date.available | 2007-03-23T04:28:49Z | - |
dc.date.issued | 2002 | en_HK |
dc.identifier.citation | Journal of the Acoustical Society of America, 2002, v. 112 n. 6, p. 2831-2839 | - |
dc.identifier.issn | 0001-4966 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/42648 | - |
dc.description.abstract | The free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, θ) at each circular cross section and the circumferential coordinate φ around the ring, is developed. Each of the displacement components ur, vτ, and wφ in the r, θ, and φ directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the θ and φ directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem. © 2002 Acoustical Society of America. | en_HK |
dc.format.extent | 188978 bytes | - |
dc.format.extent | 25088 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.format.mimetype | application/msword | - |
dc.language | eng | en_HK |
dc.publisher | Acoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.html | en_HK |
dc.relation.ispartof | Journal of the Acoustical Society of America | en_HK |
dc.rights | Copyright 2002 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in Journal of the Acoustical Society of America, 2002, v. 112 n. 6, p. 2831-2839 and may be found at https://doi.org/10.1121/1.1509429 | - |
dc.subject | Physics - sound | en_HK |
dc.title | Three-dimensional vibration analysis of a torus with circular cross section | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0001-4966&volume=112&issue=6&spage=2831&epage=2839&date=2002&atitle=Three-dimensional+vibration+analysis+of+a+torus+with+circular+cross+section | en_HK |
dc.identifier.email | Au, FTK:francis.au@hku.hk | en_HK |
dc.identifier.email | Lo, SH:hreclsh@hkucc.hku.hk | en_HK |
dc.identifier.email | Cheung, YK:hreccyk@hkucc.hku.hk | en_HK |
dc.identifier.authority | Au, FTK=rp00083 | en_HK |
dc.identifier.authority | Lo, SH=rp00223 | en_HK |
dc.identifier.authority | Cheung, YK=rp00104 | en_HK |
dc.description.nature | published_or_final_version | en_HK |
dc.identifier.doi | 10.1121/1.1509429 | en_HK |
dc.identifier.pmid | 12509004 | - |
dc.identifier.scopus | eid_2-s2.0-0038590393 | en_HK |
dc.identifier.hkuros | 76154 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0038590393&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 112 | en_HK |
dc.identifier.issue | 6 | en_HK |
dc.identifier.spage | 2831 | en_HK |
dc.identifier.epage | 2839 | en_HK |
dc.identifier.isi | WOS:000179824900032 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Zhou, D=7403395115 | en_HK |
dc.identifier.scopusauthorid | Au, FTK=7005204072 | en_HK |
dc.identifier.scopusauthorid | Lo, SH=7401542444 | en_HK |
dc.identifier.scopusauthorid | Cheung, YK=7202111065 | en_HK |
dc.identifier.citeulike | 919473 | - |
dc.identifier.issnl | 0001-4966 | - |