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Article: The free vibrations of tapered rectangular plates using a new set of beam functions with the RayleighRitz method
Title  The free vibrations of tapered rectangular plates using a new set of beam functions with the RayleighRitz method 

Authors  
Issue Date  1999 
Publisher  Elsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/jsvi 
Citation  Journal Of Sound And Vibration, 1999, v. 223 n. 5, p. 703722 How to Cite? 
Abstract  In this paper, the free vibrations of a wide range of nonuniform rectangular plates in one or two directions are considered. The domain of the plate is bounded by x = α1a, a and y = β1b, b in rectangular coordinates. The thickness of the plate is continuously varying and proportional to the power function xsyt. A variety of tapered rectangular plates can be described by giving the taper factors, s and t, different values, s and t may be given arbitrary real numbers if both α1 ≠ 0 and β1 ≠ 0 or arbitrary nonnegative numbers if α1 = 0 or β1 = 0. The uniform rectangular plate is a special case by letting both s and t equal to zero. A new set of admissible functions which are the static solutions of the tapered beam (or a strip taken from the tapered rectangular plate), under an arbitrary static load expanded into a Taylor series, is developed. Unlike conventional admissible functions, the set of static beam functions will vary appropriately with the thickness variation of the plate. The eigenfrequency equation is obtained by the use of the RayleighRitz method. A general computer program has been compiled and some numerical results are tabulated. On the basis of comparison with available results in the literature, it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions. © 1999 Academic Press. 
Persistent Identifier  http://hdl.handle.net/10722/71015 
ISSN  2015 Impact Factor: 2.107 2015 SCImago Journal Rankings: 1.494 
References 
DC Field  Value  Language 

dc.contributor.author  Cheung, YK  en_HK 
dc.contributor.author  Zhou, D  en_HK 
dc.date.accessioned  20100906T06:28:09Z   
dc.date.available  20100906T06:28:09Z   
dc.date.issued  1999  en_HK 
dc.identifier.citation  Journal Of Sound And Vibration, 1999, v. 223 n. 5, p. 703722  en_HK 
dc.identifier.issn  0022460X  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/71015   
dc.description.abstract  In this paper, the free vibrations of a wide range of nonuniform rectangular plates in one or two directions are considered. The domain of the plate is bounded by x = α1a, a and y = β1b, b in rectangular coordinates. The thickness of the plate is continuously varying and proportional to the power function xsyt. A variety of tapered rectangular plates can be described by giving the taper factors, s and t, different values, s and t may be given arbitrary real numbers if both α1 ≠ 0 and β1 ≠ 0 or arbitrary nonnegative numbers if α1 = 0 or β1 = 0. The uniform rectangular plate is a special case by letting both s and t equal to zero. A new set of admissible functions which are the static solutions of the tapered beam (or a strip taken from the tapered rectangular plate), under an arbitrary static load expanded into a Taylor series, is developed. Unlike conventional admissible functions, the set of static beam functions will vary appropriately with the thickness variation of the plate. The eigenfrequency equation is obtained by the use of the RayleighRitz method. A general computer program has been compiled and some numerical results are tabulated. On the basis of comparison with available results in the literature, it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions. © 1999 Academic Press.  en_HK 
dc.language  eng  en_HK 
dc.publisher  Elsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/jsvi  en_HK 
dc.relation.ispartof  Journal of Sound and Vibration  en_HK 
dc.title  The free vibrations of tapered rectangular plates using a new set of beam functions with the RayleighRitz method  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0022460X&volume=223 &issue=5&spage=703 &epage= 722&date=1999&atitle=The+free+vibrations+of+tapered+rectangular+plates+using+a+new+set+of+beam+functions+with+the+RayleighRitz+Method  en_HK 
dc.identifier.email  Cheung, YK:hreccyk@hkucc.hku.hk  en_HK 
dc.identifier.authority  Cheung, YK=rp00104  en_HK 
dc.description.nature  link_to_subscribed_fulltext   
dc.identifier.scopus  eid_2s2.00001626475  en_HK 
dc.identifier.hkuros  42830  en_HK 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.00001626475&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  223  en_HK 
dc.identifier.issue  5  en_HK 
dc.identifier.spage  703  en_HK 
dc.identifier.epage  722  en_HK 
dc.publisher.place  United Kingdom  en_HK 
dc.identifier.scopusauthorid  Cheung, YK=7202111065  en_HK 
dc.identifier.scopusauthorid  Zhou, D=7403395115  en_HK 