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1、MathematicalandComputerModelling55(2012)480–489ContentslistsavailableatSciVerseScienceDirectMathematicalandComputerModellingjournalhomepage:www.elsevier.com/locate/mcmDynamicmodeloflargeamplitudenon-linearoscillationsarisinginthestructuralengineering:AnalyticalsolutionsM.Akbarzadea,Y.Kha
2、nb,∗aDepartmentofMechanicalEngineering,QuchanBranch,IslamicAzadUniversity,Quchan,IranbDepartmentofMathematics,ZhejiangUniversity,Hangzhou310027,ChinaarticleinfoabstractArticlehistory:AmathematicalmodeldescribingtheprocessoflargeamplitudevibrationofauniformReceived2May2011cantileverbeamar
3、isinginthestructuralengineeringisproposed.SixdifferentanalyticalReceivedinrevisedform25July2011methodsareappliedtosolvethedynamicmodelofthelargeamplitudenon-linearAccepted25July2011oscillationequation.Periodicsolutionsareanalyticallyverified,andconsequentlytherelationshipbetweenthenatura
4、lfrequencyandtheinitialamplitudeisobtainedinanKeywords:analyticalform.ComparisonofthepresentsolutionsismadewiththeexactsolutionandLargeamplitudeexcellentagreementisnoted.Nonlinearoscillation©2011ElsevierLtd.Allrightsreserved.AnalyticalmethodsNaturalfrequencyPeriodicsolution1.Introduction
5、Structuralengineeringtheoryisbaseduponphysicallawsandempiricalknowledgeofthestructuralperformanceofdifferentlandscapesandmaterials.Manyengineeringstructurescanbemodelledasaslender,flexiblecantileverbeamcarryingalumpedmasswithrotaryinertiaatanintermediatepointalongitsspan;hencetheyexperie
6、ncelarge-amplitudevibration[1–5].Ingeneral,suchproblemsarenotamenabletoexacttreatmentbecauseoftheircomplexity,andapproximatetechniquesmustberesortedto[1–5].Amongstthese,theperturbationmethods[6–8]areincommonuse.Perturbationmethodsarebasedontheexistenceofsmallparameters,theso-calledpertur
7、bationquantity.Recently,considerableattentionhasbeenpaidtowardsapproximatesolutionsforanalyticallysolvingthenonlineardifferentialequation.Manynonlinearproblemsdonotcontainsuchaperturbationquantity.So,inordertoovercometheshortcomings,manynewtechniqueshaveappearedintheopenl
