资源描述：
《IJNN_Volume 11_Issue 3_Pages 159-166》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Int.J.Nanosci.Nanotechnol.,Vol.11,No.3,Sept.2015,pp.159-166AnalyticalSolutionfortheForcedVibrationsofaNano-ResonatorwithCubicNonlinearitiesUsingHomotopyAnalysisMethod112*3E.MaaniMiandoab,F.Tajaddodianfar,H.NejatPishkenariandH.M.Ouakad1.SchoolofMechanicalEngineering,CollegeofEngineering,Univers
2、ityofTehran,Tehran,I.R.Iran.2.MechanicalEngineeringDepartment,SharifUniversityofTechnology,Tehran,I.R.Iran.3.DepartmentofMechanicalEngineering,KingFahdUniversityofPetroleumandMinerals,31261,Dhahran,KingdomofSaudiArabia,SaudiArabia(*)Correspondingauthor:nejat@sharif.edu(Received:25Dec2014andAcc
3、epted:10Sep.2015)AbstractManyofnonlinearsystemsinthefieldofengineeringsuchasnano-resonatorandatomicforcemicroscopecanbemodeledbasedonDuffingequation.Analyticalfrequencyresponseofthissystemhelpsusanalyzedifferentinterestingnonlinearbehaviorsappearinginitsresponseduetoitsrichdynamics.Inthispaper
4、,thegeneralformofDuffingequationwithcubicnonlinearityaswellasparametricexcitationsisconsideredanditsfrequencyresponseisderivedutilizingHomotopyAnalysisMethod(HAM)forthefirsttime.AlthoughtimeresponseofdifferentDuffingsystemshasbeenanalyzedusingHAM,derivationofitsfrequencyresponseequationbyapply
5、ingthispowerfulmethodhasnotbeenpresented.Themainadvantageofproposedsimpleclosed-formsolutionisthatitisnotrestrictedtoweaklynonlinearsystemsincontrastwithperturbationmethods.BecauseofnumerousapplicationsofMicro-electro-mechanicalresonatoranditsrichandnonlineardynamics,itisconsideredasacasestudy
6、inthispaperandtheobtainedanalyticalequationisappliedtofinditsfrequencyresponse.Thevalidationofanalyticalmethodisverifiedbycomparingtheresultswithnumericalsimulations.Itisalsoshownthatproposedclosed-formequationfornano-resonatorfrequencyresponsecancapturebothhardeningandsofteningbehaviorofnano-
7、resonatoraswellasjumpphenomenon.TheresultsofthispapercanbeusefulinanalysisofdifferentengineeringsystemsmodeledbygeneralDuffingequation.Keywords:Duffingequation,Frequencyresponse,Homotopyanalysismethod,Nano-resonators.1.INRODUCTIONNonlin
