Author s response.pdf

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1、InternationalJournalofMechanicalSciences44(2002)447–449Author’sresponseReplyto‘Commentson“Onthemethodstoderivefrequencyequationsofbeamscarryingmultiplemasses”’
Twocommonlyusedmethodstoderivetheeigenfrequencyequationofabeamcarryingmultipleconcentratedmassesat

2、anarbitrarylocationwereconsideredinarecentworkbyLow[1].TheresultsattainedbyusingthemethodofthefrequencydeterminantandthemethodofLaplacetransformwerecomparedanddiscussed.ThisfurthernoteistoclarifysomeissuesraisedbyNaguleswaran[2]ontheresultspresentedinRef.[1]

3、.Firstofall,thepresentauthorwouldliketothankNaguleswaranforhisinterestintheworkandhiscomments.Asanexampleofthemultiple-massloadedbeam,themodelconsideredinRef.[1]wasabeamcarryingtwoconcentratedmasseslocatedatx=a1andx=a2,respectively,wherexisthespatialco-ordin

4、atealongthebeamlengthl.TheresultantexpressionindimensionlessformwaslistedinTable1[1]intermsofeigenparameter,positionparameters:1=a1=l;2=a2=l,andmassratios:1=M1=(Al);2=M2=(Al).Toverifythevalidityofthegeneratedfrequencyequation,the5rstthreeeigenvalues(i=

5、kil;i=1–3)wereobtainedfordi7erentpositionparameters1,2,andmassratios1,2,assummarizedinTable2[1].Itisnotedthatthe117-termfrequencyequationlistedinTable1[1]didcontaintwotypo-errors.Theerrors,however,wouldnota7ectthenumericalresultsgeneratedfromtheoriginale

6、quation.Theoriginalfrequencyequationshouldreadasfreq-eqn2mcc(117terms)[1]:224(coscosh−1)+12[cch(2)shch(1)sh(2)2−cch(2)shch(1)sh(1)+s(1)cc(2)chc(1)s(2)−···+2s(2)ch(2)c(1)sh(
1)]+21[s(1)ch(1)−···22−s(1)cchch(1)

7、]+22[c(2)csh+···−schch(2)]=0inwhichthetwoerrorshavebeencorrectedinbold.Itshouldbenotedthatthefrequencyequationforclamped–clampedbeamswouldreducetoEq.(5e)inRef.[3]containing16termsasfollows:222(1−coscosh)+[sincoshcosh−cossinhcos+coscosh

8、(sincosh−cossinh)
PIIsoforiginalarticles:S0020-7403(00)00052-7,S0020-7403(01)00078-9.0020-7403/02/$-seefrontmatter?2002ElsevierScienceLtd.Allrightsreserved.PII:S0020-7403(01)00079-0448A