CO-DIMENSION 2 BIFURCATIONS AND CHAOS IN CANTILEVERED PIPE CONVEYING TIME VARYING FLUID WITH THREE-TO-ONE INTERNAL RESONANCES-中国期刊网

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

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CO-DIMENSION 2 BIFURCATIONS AND CHAOS IN CANTILEVERED PIPE CONVEYING TIME VARYING FLUID WITH THREE-TO-ONE INTERNAL RESONANCES

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CO-DIMENSION 2 BIFURCATIONS AND CHAOS IN CANTILEVERED PIPE CONVEYING TIME VARYING FLUID WITH THREE-TO-ONE INTERNAL RESONANCES

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