Article: Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections
| Title | Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections | ||||
|---|---|---|---|---|---|
| Authors | Zhou, D1 Cheung, YK2 Lo, SH2 | ||||
| Keywords | Chebyshev polynomial Elasticity solution Ritz method Three-dimensional vibration Toroidal sector | ||||
| Issue Date | 2010 | ||||
| Publisher | A S M E International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanics | ||||
| Citation | Journal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8 [How to Cite?] DOI: http://dx.doi.org/10.1115/1.4000906 | ||||
| Abstract | This paper studies the free vibration of circular toroidal sectors with circular crosssections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted. © 2010 by ASME. | ||||
| ISSN | 0021-8936 2011 Impact Factor: 0.949 2011 SCImago Journal Rankings: 0.051 | ||||
| DOI | http://dx.doi.org/10.1115/1.4000906 | ||||
| ISI Accession Number ID | WOS:000276867700002
Funding Information: The work described in this paper was supported by the CAS membership "structural vibrations in three-dimensional solids" from the University of Hong Kong. | ||||
| References | References in Scopus |
| dc.contributor.author | Zhou, D | ||||
|---|---|---|---|---|---|
| dc.contributor.author | Cheung, YK | ||||
| dc.contributor.author | Lo, SH | ||||
| dc.date.accessioned | 2011-09-23T05:44:52Z | ||||
| dc.date.available | 2011-09-23T05:44:52Z | ||||
| dc.date.issued | 2010 | ||||
| dc.description.abstract | This paper studies the free vibration of circular toroidal sectors with circular crosssections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted. © 2010 by ASME. | ||||
| dc.description.nature | Link_to_subscribed_fulltext | ||||
| dc.identifier.citation | Journal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8 [How to Cite?] DOI: http://dx.doi.org/10.1115/1.4000906 | ||||
| dc.identifier.doi | http://dx.doi.org/10.1115/1.4000906 | ||||
| dc.identifier.epage | 8 | ||||
| dc.identifier.hkuros | 195762 | ||||
| dc.identifier.isi | WOS:000276867700002
Funding Information: The work described in this paper was supported by the CAS membership "structural vibrations in three-dimensional solids" from the University of Hong Kong. | ||||
| dc.identifier.issn | 0021-8936 2011 Impact Factor: 0.949 2011 SCImago Journal Rankings: 0.051 | ||||
| dc.identifier.issue | 4 | ||||
| dc.identifier.scopus | eid_2-s2.0-77955290209 | ||||
| dc.identifier.spage | 1 | ||||
| dc.identifier.uri | http://hdl.handle.net/10722/139086 | ||||
| dc.identifier.volume | 77 | ||||
| dc.language | eng | ||||
| dc.publisher | A S M E International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanics | ||||
| dc.publisher.place | United States | ||||
| dc.relation.ispartof | Journal of Applied Mechanics, Transactions ASME | ||||
| dc.relation.references | References in Scopus | ||||
| dc.subject | Chebyshev polynomial | ||||
| dc.subject | Elasticity solution | ||||
| dc.subject | Ritz method | ||||
| dc.subject | Three-dimensional vibration | ||||
| dc.subject | Toroidal sector | ||||
| dc.title | Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections | ||||
| dc.type | Article |
Author Affiliations
- Nanjing University of Technology
- The University of Hong Kong