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 | Zhou, D1 Au, FTK2 Lo, SH2 Cheung, YK2 |
| 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?] DOI: http://dx.doi.org/10.1121/1.1509429 |
| 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. |
| ISSN | 0001-4966 2011 Impact Factor: 1.55 2011 SCImago Journal Rankings: 0.075 |
| DOI | http://dx.doi.org/10.1121/1.1509429 |
| ISI Accession Number ID | WOS:000179824900032 |
| References | References in Scopus |
| dc.contributor.author | Zhou, D |
|---|---|
| dc.contributor.author | Au, FTK |
| dc.contributor.author | Lo, SH |
| dc.contributor.author | Cheung, YK |
| dc.date.accessioned | 2007-03-23T04:28:49Z |
| dc.date.available | 2007-03-23T04:28:49Z |
| dc.date.issued | 2002 |
| 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. |
| dc.description.nature | published_or_final_version |
| dc.format.extent | 188978 bytes |
| dc.format.extent | 25088 bytes |
| dc.format.mimetype | application/pdf |
| dc.format.mimetype | application/msword |
| dc.identifier.citation | Journal Of The Acoustical Society Of America, 2002, v. 112 n. 6, p. 2831-2839 [How to Cite?] DOI: http://dx.doi.org/10.1121/1.1509429 |
| dc.identifier.citeulike | 919473 |
| dc.identifier.doi | http://dx.doi.org/10.1121/1.1509429 |
| dc.identifier.epage | 2839 |
| dc.identifier.hkuros | 76154 |
| dc.identifier.isi | WOS:000179824900032 |
| dc.identifier.issn | 0001-4966 2011 Impact Factor: 1.55 2011 SCImago Journal Rankings: 0.075 |
| dc.identifier.issue | 6 |
| dc.identifier.openurl | ![]() |
| dc.identifier.pmid | 12509004 |
| dc.identifier.scopus | eid_2-s2.0-0038590393 |
| dc.identifier.spage | 2831 |
| dc.identifier.uri | http://hdl.handle.net/10722/42648 |
| dc.identifier.volume | 112 |
| dc.language | eng |
| dc.publisher | Acoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.html |
| dc.publisher.place | United States |
| dc.relation.ispartof | Journal of the Acoustical Society of America |
| dc.relation.references | References in Scopus |
| dc.rights | Creative Commons: Attribution 3.0 Hong Kong License |
| dc.subject | Physics - sound |
| dc.title | Three-dimensional vibration analysis of a torus with circular cross section |
| dc.type | Article |
Author Affiliations
- Nanjing University of Information Science and Technology
- The University of Hong Kong


