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Article: Riesz basis property of serially connected Timoshenko beams

TitleRiesz basis property of serially connected Timoshenko beams
Authors
Issue Date2007
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207179.asp
Citation
International Journal Of Control, 2007, v. 80 n. 3, p. 470-485 How to Cite?
AbstractIn this paper we study the Riesz basis property of serially connected Timoshenko beams with joint and boundary feedback controls. Suppose that the left end of the whole beam is clamped and the right end is free. At intermediate nodes, the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous. The collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system. We prove that the operator determined by the closed loop system has compact resolvent and generates a C0 semigroup in an appropriate Hilbert space. We also show that there is a sequence of the generalized eigenvectors of the operator that forms a Riesz basis with parentheses. Hence the spectrum determined growth condition holds. Therefore if the imaginary axis is not an asymptote of the spectrum, then the closed loop system is exponentially stable. Finally, we give a conclusion remark to explain that our result can be applied not only on the serially connected Timoshenko beams.
Persistent Identifierhttp://hdl.handle.net/10722/75325
ISSN
2015 Impact Factor: 1.88
2015 SCImago Journal Rankings: 1.494
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorXu, GQen_HK
dc.contributor.authorHan, ZJen_HK
dc.contributor.authorYung, SPen_HK
dc.date.accessioned2010-09-06T07:10:03Z-
dc.date.available2010-09-06T07:10:03Z-
dc.date.issued2007en_HK
dc.identifier.citationInternational Journal Of Control, 2007, v. 80 n. 3, p. 470-485en_HK
dc.identifier.issn0020-7179en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75325-
dc.description.abstractIn this paper we study the Riesz basis property of serially connected Timoshenko beams with joint and boundary feedback controls. Suppose that the left end of the whole beam is clamped and the right end is free. At intermediate nodes, the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous. The collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system. We prove that the operator determined by the closed loop system has compact resolvent and generates a C0 semigroup in an appropriate Hilbert space. We also show that there is a sequence of the generalized eigenvectors of the operator that forms a Riesz basis with parentheses. Hence the spectrum determined growth condition holds. Therefore if the imaginary axis is not an asymptote of the spectrum, then the closed loop system is exponentially stable. Finally, we give a conclusion remark to explain that our result can be applied not only on the serially connected Timoshenko beams.en_HK
dc.languageengen_HK
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207179.aspen_HK
dc.relation.ispartofInternational Journal of Controlen_HK
dc.titleRiesz basis property of serially connected Timoshenko beamsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0020-7179&volume=80 no 3&spage=470&epage=485&date=2007&atitle=Riesz+basis+property+of+serially+connected+Timoshenko+beamsen_HK
dc.identifier.emailYung, SP:spyung@hkucc.hku.hken_HK
dc.identifier.authorityYung, SP=rp00838en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/00207170601100904en_HK
dc.identifier.scopuseid_2-s2.0-33847082156en_HK
dc.identifier.hkuros136673en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33847082156&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume80en_HK
dc.identifier.issue3en_HK
dc.identifier.spage470en_HK
dc.identifier.epage485en_HK
dc.identifier.isiWOS:000244983500012-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridXu, GQ=7404263948en_HK
dc.identifier.scopusauthoridHan, ZJ=35188970400en_HK
dc.identifier.scopusauthoridYung, SP=7006540951en_HK

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