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1、兰州交通大学硕士学位论文AbstractVibrationSystemasacommondynamicsystemiscloselyrelatedtopeople’sdailylife,whichplaysaveryimportantroleinthefieldofengineeringandindustry.Especiallyinrecentyears,itwasfocusedforresearchingandattractedextensiveattentionofmanyscholars,engineeringsandtechnical
2、personnels.Asacommonnonlineardynamicalsystem,ithasnonlinearandsingularityproblemswhichcausedbyfactorssuchasthecollisionandimpact,makingthedynamicresponseofthesystembecomesquitecomplex.Becauseofitsnon-smoothvectorfield,whichmakingsometraditionalresearchmethodsinsmoothsystemar
3、enolongerapplicabletosuchsystems.Thusitneedstoexploresomenewtheoreticalapproachestostudyitsperiodicsolutionsandbifurcationbehavior.Therefore,ithassomedifficultiesintheorystudy.Firstly,thepapergivesastudyforaclassoftwodegreesoffreedomrigidcollisionvibrationsystemswithclearanc
4、e,andanalysisthedynamicbehaviorwhichnearthegrazingorbitalofthesystem,whichcombiningthecharacteristicsofthemovementobtainedtheanalyticalconditionsofthevibrationsystemthathasgrazingorbitalbyanalyticalmethod,anddeducedthezerotimediscontinuousmapping(ZDM)andthePoincaresectiondis
5、continuousmappingwithmappingandseriesexpansionmethod,andgavefurthercompoundtothesmoothmapcorrespondingtonocollisionperiodictrajectorieswithdiscontinuousmappingpushed,thengetsegmentmappingexpressionsofthegrazingbifurcation,andgivesamoredetailedanalysisforitssingularityofJacob
6、ianmatrix,whichfoundsingularityitemsonlyexistinthetraceofsystemJacobianmatrix,andsingularityitemsappearwhensatisfythecorrespondingconditionsonly.Finally,numericalsimulationwasgivedforthesystembythefourth-orderRunge-Kuttaalgorithm.Itwascombinedbifurcationdiagramandphasediagra
7、mtofindthatparameterbifurcationwillappeardiscontinuousfromaconstantcycletracktothetransitionpointinnext,andsystemcorrespondinggrazingmotioncollisionwilloccurinthesediscontinuouspoints.Thenonthebasisofthefirstsystemmodel,addingtheelastictotheconstraint,namelytwodegreesoffreed
8、omelasticcollisionvibrationsystem,whichisstudiedthesecondbasicmodelinthispa
