EMBED Equation.docx

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EMBEDEquation

THEORETICALSTUDYOFTRANSMITTIVlTYOF

ELECTROMAGNETICWAVEINMAGNETORHEOLOGICALFLUIDS

FANJi-jun，YUNan—hui，XUYa—qian

（1．DepartmentofMathematicsandPhysics，WuhanPolytechnicUniversity，Wuhan430023，China；

2．DepartmentofMechanicalEngineering，WuhanPolytechnicUniversity，Wuhan430023，China）

Abstract:

theuseofmagnetorheologicalfluidinadditionalmagneticfieldfunction,itsinternalstructuretochange,thedielectricconstantandmagneticconductancewillalsochange,establishedthroughtheelectromagneticwaveMRFtheorymodel,anddeducedtheelectromagneticwavetransmissionrateofthebasicformofexpression.Theoreticalmodelshowsthat:

theelectromagneticwavetransmissionratevarieswithmagnetorheologicalfluidofdielectricconstantincreaseanddecrease;Alongwiththemagnetorheologicalfluidmagneticpermeabilityincreaseandincrease;WiththeincreaseofMRFthicknessdecreases.Theoreticalanalysisinadditionalmagneticfieldthatfunction,magnetorheologicalfluidstructuretochange.

Dielectricpropertiesandmagneticpermeabilitychangeisaleadtotheelectromagneticwavetransmissionratecanbethemainreasonfortheregulation.

Keywords:

magnetorheologicalfluid;Theelectromagneticwavetransmissionrate;Intelligentmaterials

Chineseclassificationnumber:

O441.4;TB381literature

identificationcode:

A

0Introduction

Magnetorheologicalfluids（MRF,hereinafterreferredtoastheMRr'）isakindofbehaviorcancontrolofintelligentmaterial,.Itisbythecolloidtinyparticlesofscatteredsolubleininsulationinformationintheliquid.Withadditionalmagneticfieldcancontrolthechangeoftherheologicalbehaviorofstablesuspension.Inundertheactionofthemagneticfield.TheapparentviscosityofMRFwillquickyhaveasignificantchange,liquidincreaseyieldstress,whichchangestherheologicalcharacteristicshowsimilarsolidnature;whenadditionalmagneticfieldcancelled,fluidandrestoredtotheoriginalstate,theresponsetimeisveryshort,onlyforafew

Ills,thisphenomenoniscalledmagnetorheologicaleffect.

Sincethe1980s,peopleontheelectrorheologicalfluidopticalbehaviorresearchismore,suchasYostudowhostudiestheDCelectricfieldelectrorheologicalfluidpervioustolightquality;ZhouLuweiwhostudiestheelectrorheologicalfluidopticalsecondharmonic;ZhaoXiaopengwhostudiestheelectrorheologicalfluidopticaltransmission,rotaryTuopolarizedlightandcharacteristics,andtheelectrorheologicalfluidandmicrowareproperties.Inthelong¨.AreaFeinsteinkbasedontheclassicalelectromagnetictheoryelectrorheologicalfluidmicrowaveabsorptionandprojection,andpointsoutthatthemicrowavewavelengthgivenmicrowavesignal,thereisacertainparticlesizeandspaceorientationtoabsorbthebiggestreflection.Andaboutelectromagneticwarepropagationinmagnetorheologicalfluidbehavior.Inthisreseachrelatedtotheexperimentalstudyhasimportanttheoreticalsignificance.Magnetorheologicalfluidinadditionalmagneticfieldfunction,itsopticalbehaviorcanbealsotohavealotofregulatoryapplication,butsomeofitsbasicopticalresponselawhasnotyetunderstood.Sofurtherresearchcomplexfluidbasicopticalbehaviorappearsmoreurgentandnecessary.

TheauthorwasinvestigatedintheoryintheelectromagneticwaveMRFtransmissioncancontrolbehavior,anddeducesthemagnetorheologicalfluidelectromagnetictransmissionrateformulatheory,thispaperanalyzesthemagnetorheologicalwaveinthemagnetorheologicalfluidtransmissionoftheinfluencefactors.Computersimulationresultsaregiven.

Onetheoryis

Accordingtothetheoryofclassicalelectromagneticwave.Electromagneticwavesinthepropagationofthemediathatthemaincharacteristicofintroducedbythedielectricconstant

researchandmagneticconductivitytothe

.

Therefore,thestudyofelectromagnrticwavepropagationbehaviorinfactisthemediumofthedielectricconstant

researchandmagneticconductance

thistwoparameterswithtime,spaceandthechangeruleoffrequency.Hereisthemagnetorheologicalfluidselectromagneticwavepropagationofthebehaviorofthebasictheoreticalanalysis,andinfluencefactorsoftheelectromagneticwavetransmissionrate.

Noadditionalmagneticfield,magnetorheologicalfluidinternalgrainsdistribution,therefore,wecanthinkitisaquasiisotropicmedium.Afterbringingtobearsomearrangedinhappenedwithinthepolarizationchainorcylindricalstructure,atthetimeitisregardedasalateralanisotropicmedium,asshowninfigure1below.WithoutconsideringthecontinuityofMRF,itputsforwardthemodel.

（1）Boundaryproblem:

thinktheelectromagneticwaveinthevesselwallandtheairinterfaceinthetransmissionrateisconstant.

（2）Noadditionalmagneticfield（B=0）,thefluidofdielectricconstantis

magneticconductanceis

;Afterbringingtobearsomemagneticfield,magnetorheologicalfluidsdielectricconstantandmagneticcondutancewerespacecoordinatesandthemagneticfieldofthefunction

（x,y,z,B）and

（x,y,z,B）

Figure1theelectromagneticwaveinthemagnetorheologicalfluidinterfaceoftheincidentandtransmissionschemes

Electromagneticwavesinmaxwell'sequationsconservespacetosatisfy,willmagnetorheologicalfluidastheidealconductor,so

0;Isthestationarywaveindependentboundaryconditionfor:

1.1Withouttheexternalmagneticfield

Noadditionalmagneticfield,wecannotconsiderofMRFdiscontinuity,andwillitasunevenmedium.

1.1.1Theelectromagneticwaveinthemagnetorheologicalfluidinterfaceaction

Theelectromagneticwaveinthemagnetorheologicalfluidinterfacewilloccurreflectionandrefraction,becausethemagnetorheologicalfluidconductivityisverysmall,cannotconsiderofinterfaceabsorb,andonlyconsidermagnetorheologicalfluidtotheelectromagneticwaveabsorption.Whentheelectromagneticwaveelectricfieldvectorperpendiculartotheincidentsurface,basedontheelectromagneticwaveinthecontainerboxandmagnetorheologicalfluidinterfaceboundaryconditions,asshowninfigure2shows.

Figure2electromagneticwaveintheerdiagramoftheinterface

Thetwointerfacesoftransmissionrateallforthe:

Bytype（4）cangettheelectromagneticwavethroughthemagnetorheologicalfluidtotaltransmissionratefor:

Amongthem

forthecontainerboxofmaterialsandMRFwaveimpedance,amongthem

=

i=1,2,and

respectivelyfortheirmagneticconductanceanddielectricconstant.

Bytype（4）availableIlearnedtoaudit.MagneticLirecite1"magneticflow,liquidtotaltransmissionratefor:

Type,kasmagnetorheologicalfluidtotheelectromagneticwaveabsorption.

1.1.2Magnetorheologicalfluidtotheelectromagneticwaveoftransmissionandabsorption

Inthemagnetorheologicalfluidinternalestablishfig.03showscoordinatesystem,theyaxisasimplementingmagneticfielddirection,stoneaxesandmagneticfieldofverticaldirection,zaxisoftheelectromagneticwavepropagationdirection（inverticalpaper）

Figure3whennoadditionalmagneticfieldMRFinternalstructureschematicdrawing

Whenmagnetorheologicalfluidofelectricalconductivitynotzero,inthemagnetorheologicalfluidelectromagneticwavepropagationofthemeetnexttype:

（6）type,

forMRFdielectricconstant,

=

+j

forcomplexdielectricconstant,

forelectromagneticwaveJiaoPinLv,

asmagnetorheologicalfluidofelectricalconductivity.

Intheabsenceoftheelectromagneticwavesourceareaelectricityvectorhomogeneousmeethelmholtzequation:

Type,

=

forwavenumber,itisplural.Thisdefinition:

=j

forthetransmissionconstant,whichcanbedividedinto

=

+j

whichabsorbconstant

and

respectivelyis:

Becauseofelectromagneticenergyanditselectricityvectoramplitudeoftheflatisdirectly,somagnetorheologicalfluidtotheelectromagneticwaveabsorptionfor:

WhentheelectromagneticwavethroughthethicknessofdMRF,theabsorptionrateford,magnetorheologicalfluidtransmissionratefor:

1.1.3Electromagneticwavethroughthemagnetorheologicalfluidtotaltransmissionrate

Thetransmissionrateforinterfacetransmissionrateandmagnetorheologicalfluidtransmissionrateoftheproduct,butthetotaltransmissionratefor:

（11）type,dforelectromagneticwavesinthetransmissiondistanceofMRF,arealpartofthetransmissionconstantk.

1.2Haveadditionalmagneticfield

Inadditionalmagneticfieldeffect,frommagnetorheologicalfluidcanjudgetheformationmechanismofMRFinmagneticfieldmorethanthresholdmagneticfieldisanisotropic.

Figure4forelectromagneticwavepropagationdirectionandthemagnetorheologicalfluidparticleschaindirectionschematicdiagram,definetheyaxisdirectionforparticlechains,forthexaxisandgranularinthedirectionofverticalchain,theelectromagneticwavepropagationdirectionfor:

thezaxis（inverticalpaper）.Thefollowingdependingonthemagnetorheologicalfluidinthezaxisforuniformmedium,inxoyplanewithinisanunevenmedium.Canelectricityvectorplanewaveintoandmagneticfieldorparticlechainsofparallelandperpendiculardandk.Oxinthedielectricconstantdirectionsystemfore,inthedirectionofdevelopmentforthedielectricconstantk;Thecorrespondingconductivitywereyandx,qforelectricityvectorwavekandxaxisAngle.

Figure4electricityvectorwaveandmagnetorheologicalfluidparticleschaindirectionschemes

1．2．1Theelectromagneticwaveinthemagnetorheologicalfluidinterfacetransmission

Accordingtotheequation（4）,inthexaxisandYaxisoftotaltransmissionraterespectivelyis:

Therefo