简介：

简介：Thenonlinearnormalmodes(NNMs)associatedwithintegrnalresonancecanbeclassifiedintotwokinds:uncoupledandcoupled.ThebifurcationproblemofthecoupledNNMofsystemswith1:2:5dualinternalresonanceisintwovariables.ThesingularanalysisofitispresentedafterseparatingthetwovariablesbytakingadvantageofMaplealgebra,andsomenewbifurcationpatternsarefound.DifferentfromtheNNMsofsystemswithsingleinternalresonance,thenumberoftheNNMsofsystemswithdualinternalresonancemaybemoreorlessthanthenumberofthedegreesoffreedom.Atlast,itispointedoutthatbifurcationproblemsintwovariablescanbeconvenientlysolvedbyseparatingvariablesaswellasusingcouplingequations.

简介：Theresonancesofparametricvibrationwithforcedvibrationisanalyzed,thebifurca-tionequationofthesystemisobtainedandthesinsularityanalysisismade.Someofthelawsandphe-nomenaarerevealed.Thetransitionvarietyandbifurcationdiagramofthephysicalparametricplanearegiven.Theresultscanbeusedinensinecrins.

简介：Thenonlinearbehaviorofacantileveredfluidconveyingpipesubjectedtoprincipalparametricandinternalresonancesisinvestigatedinthispaper.Theflowvelocityisdividedintoconstantandsinusoidaiparts.Thevelocityvalueoftheconstantpartissoadjustedsuchthatthesystemexhibits3:1internalresonancesforthefirsttwomodes.Themethodofmultiplescalesisemployedtoobtaintheresponseofthesystemandasetoffourfirst-ordernonlinearordinary-differentialequationsforgoverningtheamplitudeoftheresponse.TheeigenvaluesoftheJacobianmatrixareusedtoassessthestabilityoftheequilibriumsolutionswithvaryingparameters.Thecodimension2derivedfromthedouble-zeroeigenvaiuesisanalyzedindetail.Theresultsshowthattheresponseamplitudemayundergosaddle-node,pitchfork,Hopf,homoclinicloopandperiod-doublingbifurcationsdependingonthefrequencyandamplitudeofthesinusoidalflow.Whenthefrequencyofthesinusoidalflowequalsexactlyhalfofthefirst-modefrequency,thesystemhasaroutetochaosbyperiod-doublingbifurcationandthenreturnstoaperiodicmotionastheamplitudeofthesinusoidalflowincreases.

简介：Harmonic,subharmonic,superharmonic,simultaneoussub/superharmonic,andcombinationresonancesoftheadditivetypeofself-excitedtwocoupled-secondordersystemstomulti-frequencyexcitationareinvestigated.Thetheoreticalresultsareobtainedbythemultiple-scalesmethod.Thesteadystateamplitudesforeachresonanceareplotted,showingtheinfluenceofthedifferentparameters.Analysisforeachfigureisgiven.Approximatesolutioncorrespondingtoeachtypeofresonanceisdetermined.Stabilityanalysesarecarriedoutforeachcase.