简介:ThepreviouspaperreportedanewderivativeintheEuleriandescriptioninflatspace—thegeneralizedcovariantderivativeofgeneralizedEuleriancomponentwithrespecttotime.ThispaperextendsthethoughtfromtheEuleriandescriptiontotheLagrangiandescription:onthebasisofthepostulateofcovariantforminvariabilityintimefield,wedefineanewderivativeintheLagrangiandescriptioninflatspace—thegeneralizedcovariantderivativeofgeneralizedLagrangiancomponentwithrespecttotime.Besides,thecovariantdifferentialtransformationgroupissetup.ThecovariantforminvariabilityofLagrangianspace-timeisascertained.
简介:ThispaperreportsanewderivativeintheEuleriandescriptioninflatspace-thegeneralizedcovariantderivativewithrespecttotime.Thefollowingcontentsareincluded:(a)therestrictedcovariantderivativewithrespecttotimeforEuleriancomponentisdefined;(b)thepostulateofthecovariantforminvariabilityintimefieldissetup;(c)thegeneralizedcovariantderivativewithrespecttotimeforgeneralizedEuleriancomponentisdefined;(d)thealgebraicstructureofthegeneralizedcovariantderivativewithrespecttotimeismadeclear;(e)thecovariantdifferentialtransformationgroupintimefiledisderived.TheseprogressesrevealthecovariantforminvariabilityofEulerianspaceandtime.
简介:Stress-dependenceoftheintrinsictimeofviscoelasticmaterialsisinvestigated.Theinfluenceofstresslevelontheintrinsictimeisconsideredtobesimilartothatoflemperature,pressure,solventcon-centration,damageandphysicalaging.Thetime-lemperature-stressequivalenceprincipleisproposed,byemployingwhich,thecreepcurvesatdifferenttemperaturesandstresslevelscanbeshiftedintoamastercurveatreferencetemperatureandstresslevel.Thusthelong-termcreepbehaviorofviscoelasticmaterialsatalowertemperatureandstresscanbepredictedfromtheshort-termoneatahighertemperatureandstress.Asanexample,thenonlinearcreepbehaviorofhigh-densitypolyethylene(HDPE)atroomtemperatureisstudiedusingthetime-temperature-stressequivalenceprinciplepresented.
简介:Thenonlinearbehaviorofacantileveredfluidconveyingpipesubjectedtoprincipalparametricandinternalresonancesisinvestigatedinthispaper.Theflowvelocityisdividedintoconstantandsinusoidaiparts.Thevelocityvalueoftheconstantpartissoadjustedsuchthatthesystemexhibits3:1internalresonancesforthefirsttwomodes.Themethodofmultiplescalesisemployedtoobtaintheresponseofthesystemandasetoffourfirst-ordernonlinearordinary-differentialequationsforgoverningtheamplitudeoftheresponse.TheeigenvaluesoftheJacobianmatrixareusedtoassessthestabilityoftheequilibriumsolutionswithvaryingparameters.Thecodimension2derivedfromthedouble-zeroeigenvaiuesisanalyzedindetail.Theresultsshowthattheresponseamplitudemayundergosaddle-node,pitchfork,Hopf,homoclinicloopandperiod-doublingbifurcationsdependingonthefrequencyandamplitudeofthesinusoidalflow.Whenthefrequencyofthesinusoidalflowequalsexactlyhalfofthefirst-modefrequency,thesystemhasaroutetochaosbyperiod-doublingbifurcationandthenreturnstoaperiodicmotionastheamplitudeofthesinusoidalflowincreases.