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Article: Free vibration of a type of tapered beams

TitleFree vibration of a type of tapered beams
Authors
Issue Date2000
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cma
Citation
Computer Methods In Applied Mechanics And Engineering, 2000, v. 188 n. 1, p. 203-216 How to Cite?
AbstractThis paper studies the vibrational characteristics of tapered beams with continuously varying rectangular cross-section of depth and breadth proportional to xs and xt, respectively, where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co-ordinate measured from the sharp end of the beam. The Bernoulli-Euler theory of bending is used to describe the motion of the beam. A new set of beam functions are developed as the admissible functions, which are the complete solution of the tapered beam under an arbitrary static load expanded into a Taylor series. The eigenfrequency equation is obtained by the Rayleigh-Ritz method. The accuracy is assured from the convergency and comparison studies. The effect of the location of the Taylor series expanding point on the convergency is discussed. The analysis shows that the present approach is convergent for arbitrary truncation factor by taking the midpoint of the beam as the expanding point of the Taylor series. Numerical results are tabulated for three different tapered beams with various boundary conditions and truncation factors. It is shown that the eigenfrequencies can be obtained with high accuracy by using only a small number of terms of the static beam functions.
Persistent Identifierhttp://hdl.handle.net/10722/150162
ISSN
2015 Impact Factor: 3.467
2015 SCImago Journal Rankings: 2.952
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZhou, Den_US
dc.contributor.authorCheung, YKen_US
dc.date.accessioned2012-06-26T06:01:57Z-
dc.date.available2012-06-26T06:01:57Z-
dc.date.issued2000en_US
dc.identifier.citationComputer Methods In Applied Mechanics And Engineering, 2000, v. 188 n. 1, p. 203-216en_US
dc.identifier.issn0045-7825en_US
dc.identifier.urihttp://hdl.handle.net/10722/150162-
dc.description.abstractThis paper studies the vibrational characteristics of tapered beams with continuously varying rectangular cross-section of depth and breadth proportional to xs and xt, respectively, where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co-ordinate measured from the sharp end of the beam. The Bernoulli-Euler theory of bending is used to describe the motion of the beam. A new set of beam functions are developed as the admissible functions, which are the complete solution of the tapered beam under an arbitrary static load expanded into a Taylor series. The eigenfrequency equation is obtained by the Rayleigh-Ritz method. The accuracy is assured from the convergency and comparison studies. The effect of the location of the Taylor series expanding point on the convergency is discussed. The analysis shows that the present approach is convergent for arbitrary truncation factor by taking the midpoint of the beam as the expanding point of the Taylor series. Numerical results are tabulated for three different tapered beams with various boundary conditions and truncation factors. It is shown that the eigenfrequencies can be obtained with high accuracy by using only a small number of terms of the static beam functions.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cmaen_US
dc.relation.ispartofComputer Methods in Applied Mechanics and Engineeringen_US
dc.rightsComputer methods in applied mechanics and engineering. Copyright © Elsevier BV.-
dc.titleFree vibration of a type of tapered beamsen_US
dc.typeArticleen_US
dc.identifier.emailCheung, YK:hreccyk@hkucc.hku.hken_US
dc.identifier.authorityCheung, YK=rp00104en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/S0045-7825(99)00148-6en_US
dc.identifier.scopuseid_2-s2.0-0034226292en_US
dc.identifier.hkuros56593-
dc.identifier.volume188en_US
dc.identifier.issue1en_US
dc.identifier.spage203en_US
dc.identifier.epage216en_US
dc.identifier.isiWOS:000088661700013-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridZhou, D=7403395115en_US
dc.identifier.scopusauthoridCheung, YK=7202111065en_US

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