柔性连接杆的非线性动力学分析

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1、Non-lineardynamicsofaflexibleconnectingrodAbstract:Thepresentstudyinvestigatesthedynamicresponseofsingle-cylinderreciprocatingengine.Inparticular,simplifiedmodelsoftheclassicalslider–crankmechanismareexamined,whichtakeintoaccounttheflexibilityoftheconnectingrod.Moreover,amainnewfeatu

2、reofthesemodelsisthatboththedrivingandtheresistingmomentsareexpressedasfunctionsofthecrankshaftmotion,insteadofprescribingtherotationofthecrank.TheequationsofmotionarefirstderivedbyapplicationofHamilton’sprinciple.Theseequationsarethendiscretizedgeometricallyandputintheirfinalformbya

3、pplyingGalerkin’smethod.Owingtothelargerotationsexhibitedbythemechanismmembersandtheformofthedrivingandtheresistingmoments,theresultingequationsofmotioninvolvestrongnon-linearities.Asaconsequence,theirsolutionisobtainedinboththetimeandthefrequencydomainbyemployingappropriatenumerical

4、methodologies.Inparticular,thesemethodologiesincludeeitherdeterminationoftransientresponsebyemployingdirectintegrationtechniquesordirectdeterminationofcompletebranchesofperiodicsteadystateresponsebyapplyingsuitablemethodologies.Thefirstsetofnumericalresultsreferstothespecialcasewhere

5、theangularvelocityoftheenginecrankcanbeconsideredasvirtuallyconstant.Thiscasecanbeanalysedmoreeasilyandprovidesvaluableinsightintosomeimportantaspectsofthesystemdynamics.Then,theemphasisisshiftedtothegeneralcase,correspondingtonon-idealforcingconditions.Inallcases,theattentionisfocus

6、edonexaminingtheinfluenceoftheparametersofthesystemonitsdynamicsduringintervalswithtransientorunderperiodicsteadystateconditions.Keywords:enginemechanisms,flexiblerod,non-idealforcing,periodicsteadystate,chaoticresponse,Sommerfeldphenomena1INTRODUCTIONDuringthelastthreedecades,therap

7、idandcontinuousimprovementsinthelevelofcomputingpowerhaveresultedinconsiderablebenefitsinmanytechnologicalfields.Theavailabilityofpowerfulcomputingmachinesandthedevelopmentofefficientnumericalcodeshavemadepossibletheanalysisoflarge-scalemechanicalmodels,includingthoseemployedintheare

8、aofenginedyn