File Download
 
Links for fulltext
(May Require Subscription)
 
Supplementary

Article: 3D vibration analysis of solid and hollow circular cylinders via Chebyshev-Ritz method
  • Basic View
  • Metadata View
  • XML View
Title3D vibration analysis of solid and hollow circular cylinders via Chebyshev-Ritz method
 
AuthorsZhou, D2
Cheung, YK1
Lo, SH1
Au, FTK1
 
Issue Date2003
 
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cma
 
CitationComputer Methods In Applied Mechanics And Engineering, 2003, v. 192 n. 13-14, p. 1575-1589 [How to Cite?]
DOI: http://dx.doi.org/10.1016/S0045-7825(02)00643-6
 
AbstractA general approach is presented for solving the free vibration of solid and hollow circular cylinders. The analysis procedure is based on the small-strain, linear and exact elasticity theory. By taking the Chebyshev polynomial series multiplied by a boundary function to satisfy the geometric boundary conditions as the admissible functions, the Ritz method is applied to derive the frequency equation of the cylinder. According to the axisymmetric geometrical property of a circular cylinder, the vibration modes are divided into three distinct categories: axisymmetric vibration, torsional vibration and circumferential vibration. Moreover, for a cylinder with the same boundary conditions at the two ends, the vibration modes can be further divided into antisymmetric and symmetric ones in the length direction. Convergence and comparison studies demonstrate the high accuracy and small computational cost of the present method. A significant advantage over other Ritz solutions is that the present method can guarantee stable numerical operation even when a large number of terms of admissible functions are used. Not only the lower-order but also the higher-order frequencies can be obtained by using a few terms of the Chebyshev polynomials. Finally, the first several frequencies of circular cylinders with different boundary conditions, with respect to various parameters such as the length-radius ratio and the inside-outside radius ratio, are given. © 2003 Elsevier Science B.V. All rights reserved.
 
ISSN0045-7825
2013 Impact Factor: 2.626
2013 SCImago Journal Rankings: 3.252
 
DOIhttp://dx.doi.org/10.1016/S0045-7825(02)00643-6
 
ISI Accession Number IDWOS:000181896300001
 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorZhou, D
 
dc.contributor.authorCheung, YK
 
dc.contributor.authorLo, SH
 
dc.contributor.authorAu, FTK
 
dc.date.accessioned2012-06-26T06:02:37Z
 
dc.date.available2012-06-26T06:02:37Z
 
dc.date.issued2003
 
dc.description.abstractA general approach is presented for solving the free vibration of solid and hollow circular cylinders. The analysis procedure is based on the small-strain, linear and exact elasticity theory. By taking the Chebyshev polynomial series multiplied by a boundary function to satisfy the geometric boundary conditions as the admissible functions, the Ritz method is applied to derive the frequency equation of the cylinder. According to the axisymmetric geometrical property of a circular cylinder, the vibration modes are divided into three distinct categories: axisymmetric vibration, torsional vibration and circumferential vibration. Moreover, for a cylinder with the same boundary conditions at the two ends, the vibration modes can be further divided into antisymmetric and symmetric ones in the length direction. Convergence and comparison studies demonstrate the high accuracy and small computational cost of the present method. A significant advantage over other Ritz solutions is that the present method can guarantee stable numerical operation even when a large number of terms of admissible functions are used. Not only the lower-order but also the higher-order frequencies can be obtained by using a few terms of the Chebyshev polynomials. Finally, the first several frequencies of circular cylinders with different boundary conditions, with respect to various parameters such as the length-radius ratio and the inside-outside radius ratio, are given. © 2003 Elsevier Science B.V. All rights reserved.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationComputer Methods In Applied Mechanics And Engineering, 2003, v. 192 n. 13-14, p. 1575-1589 [How to Cite?]
DOI: http://dx.doi.org/10.1016/S0045-7825(02)00643-6
 
dc.identifier.doihttp://dx.doi.org/10.1016/S0045-7825(02)00643-6
 
dc.identifier.epage1589
 
dc.identifier.hkuros76269
 
dc.identifier.isiWOS:000181896300001
 
dc.identifier.issn0045-7825
2013 Impact Factor: 2.626
2013 SCImago Journal Rankings: 3.252
 
dc.identifier.issue13-14
 
dc.identifier.scopuseid_2-s2.0-0037470761
 
dc.identifier.spage1575
 
dc.identifier.urihttp://hdl.handle.net/10722/150232
 
dc.identifier.volume192
 
dc.languageeng
 
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cma
 
dc.publisher.placeNetherlands
 
dc.relation.ispartofComputer Methods in Applied Mechanics and Engineering
 
dc.relation.referencesReferences in Scopus
 
dc.title3D vibration analysis of solid and hollow circular cylinders via Chebyshev-Ritz method
 
dc.typeArticle
 
<?xml encoding="utf-8" version="1.0"?>
<item><contributor.author>Zhou, D</contributor.author>
<contributor.author>Cheung, YK</contributor.author>
<contributor.author>Lo, SH</contributor.author>
<contributor.author>Au, FTK</contributor.author>
<date.accessioned>2012-06-26T06:02:37Z</date.accessioned>
<date.available>2012-06-26T06:02:37Z</date.available>
<date.issued>2003</date.issued>
<identifier.citation>Computer Methods In Applied Mechanics And Engineering, 2003, v. 192 n. 13-14, p. 1575-1589</identifier.citation>
<identifier.issn>0045-7825</identifier.issn>
<identifier.uri>http://hdl.handle.net/10722/150232</identifier.uri>
<description.abstract>A general approach is presented for solving the free vibration of solid and hollow circular cylinders. The analysis procedure is based on the small-strain, linear and exact elasticity theory. By taking the Chebyshev polynomial series multiplied by a boundary function to satisfy the geometric boundary conditions as the admissible functions, the Ritz method is applied to derive the frequency equation of the cylinder. According to the axisymmetric geometrical property of a circular cylinder, the vibration modes are divided into three distinct categories: axisymmetric vibration, torsional vibration and circumferential vibration. Moreover, for a cylinder with the same boundary conditions at the two ends, the vibration modes can be further divided into antisymmetric and symmetric ones in the length direction. Convergence and comparison studies demonstrate the high accuracy and small computational cost of the present method. A significant advantage over other Ritz solutions is that the present method can guarantee stable numerical operation even when a large number of terms of admissible functions are used. Not only the lower-order but also the higher-order frequencies can be obtained by using a few terms of the Chebyshev polynomials. Finally, the first several frequencies of circular cylinders with different boundary conditions, with respect to various parameters such as the length-radius ratio and the inside-outside radius ratio, are given. &#169; 2003 Elsevier Science B.V. All rights reserved.</description.abstract>
<language>eng</language>
<publisher>Elsevier BV. The Journal&apos;s web site is located at http://www.elsevier.com/locate/cma</publisher>
<relation.ispartof>Computer Methods in Applied Mechanics and Engineering</relation.ispartof>
<title>3D vibration analysis of solid and hollow circular cylinders via Chebyshev-Ritz method</title>
<type>Article</type>
<description.nature>Link_to_subscribed_fulltext</description.nature>
<identifier.doi>10.1016/S0045-7825(02)00643-6</identifier.doi>
<identifier.scopus>eid_2-s2.0-0037470761</identifier.scopus>
<identifier.hkuros>76269</identifier.hkuros>
<relation.references>http://www.scopus.com/mlt/select.url?eid=2-s2.0-0037470761&amp;selection=ref&amp;src=s&amp;origin=recordpage</relation.references>
<identifier.volume>192</identifier.volume>
<identifier.issue>13-14</identifier.issue>
<identifier.spage>1575</identifier.spage>
<identifier.epage>1589</identifier.epage>
<identifier.isi>WOS:000181896300001</identifier.isi>
<publisher.place>Netherlands</publisher.place>
</item>
Author Affiliations
  1. The University of Hong Kong
  2. Nanjing University of Information Science and Technology