1、弹性浮筏系统动力学建模及冲击响应分析第 9 卷第 6 期2005 年 12 月船舶力学JournalofShipMechanicsV01.9No.6Dec.2005ArticleID:10077294(2005)06011313DynamicModelingandResponseAnalysistoImpactofElasticFloatingRaftSystemWANGZhi-gang,FENGQi,WANGYu(1TheKeyLaboratoryofSofidMechanicsofMinistryofEducation,TongjiUniversity,Shanghai200092,Chi
2、na;2NavalResearchCenter,Bering100037,China)Abstract:Thefloatingraftisacomplexdynamicsystemcomposedofconcentratedmasses,springs,dampers,andelasticcontinuum,whichiswidelyusedinvibrationisolationoftheimportantequipmentonship.Inthispaper,theoriesofmulti-bodydynamicsandstructuraldynamicsarecombinedtoappl
3、ytothedynamicmodelingoftheelasticfloatingraftsystem.Thedynamicvibrationequationofthesystemisgiventakingaccountofthecouplingoftherigidmotionandtheelasticvibration.Bypracticalengineeringcase,numericalanalysisisdone,andthenaturalfrequencyandtheresponsetoimpactofthesystemareobtained.Thenumericalresultss
4、howthattheelasticdeformationoftheraftbodywillaffectthedynamiccharacterofthesystem,andtheproposedmodelismorepreciseandjudiciousinengineeringapplication.Theresearchwilldogoodtothedesignofthefloatingraftbyprovidingtheoreticalreferenceandjustification.Keywords:elasticfloatingraft;vibrationisolation;resp
5、onsetoimpactCICnumber:1J661.4Documentcode:A1IntroductionForalongtime,theanti-shockoftheimportantequipmentonshiphasbeenaproblemobsessingtheshipengineer.Theefficientwaytocontrolimpacttransmissionistoapplyvibrationisolationsystemonship.Thefloatingraftsystemhasgoodperformanceinisolatingimpacttransmissio
6、n,andiswidelyusedinthevibrationisolationoftheimportantequipmentonship.Therearemanymethodsformechanicalmodelinganddynamiccharacteranalysisforthefloatingraft,suchasstructuraldynamicstheory,multi-bodydynamicstheory,finiteelementmethod,impedancesynthesismethod,andsoonJ.Incustomaryanalysis,theelasticdefo
7、rmationofthefloatingraftisoftenneglected,andthecomponentbodiesofthesystemaretreatedasrigidbodies.Underspecialapplicationbackground,suchsimplificationcanmeetprecisionrequirementinengineering.Butwhenthelowerraftbodyofthesystemisthinnerandhasalargerareacomparedwiththeupperequipment,itisinappropriatedis
8、regardingthetransversalbendingvibrationforitselasticity.Otherwise,theinevitableerrorwilloccurintheprocessofdynamicalcharacteranalysisofthesystem.Receiveddate:2004 一】l-12Foundationitem:SupportedbytheNationalNaturalScienceFoundationofChinaunderGrantNo.10072040Biography:WANGZhigang(1977-),Male,Ph.D.stu
9、dentofTongjiUniversity.船舶力学第 9 卷第 6 期Soreeresearchersstudiedtheeffectoftheelasticityoftheraftondynamiccharacteroftheelasticfloatingraftsystembasedonthepowerflowmethod.ZhangWeiboandSongKongjiecalculatedthepowerflowthrougharaftvibrationisolatingsystemtransmittedintothefoundationbasedonthemobilitymetho
10、dt.FengDezhenandSongKongjiestudiedthetransmissi0nmechanismandcharacteristicofthepowerflowinthecomplexflexiblecoupledasymmetricmultisupportedelasticfloatingraftsystemn.Inthispaper,multi-bodytheoryandstructuraldynamicstheoryarecombinedtoapplytothemodelingofthesystem,withtheeouplingofrigidmotionandelas
11、ticvibrationofthesystemconsidered 圈.Theupperequipmentisthoughtofasrigidbodyforitshighrigidity,andonlyitsrigid-bodymotionisconsidered.Thelowerraftbodyisregardedasanelasticbodyforitscomplicatedstructureandmoreelasticityincomparisonwithrigidbody,andbothitsrigidmotionanditselasticbendingvibrationarecons
12、idered.Finally,thedynamicequationofthewholesystemisderived.Throughthepracticalengineeringcase,thenaturalequencyofthesystemandtheresponsetodifferentimpactincitementsareobtained.Thenumericalresultsshowthattheproposedmodelispracticalinengineeringapplication.Fig.1Themodelofthefloatingraft2Dynamicmodelof
13、theelasticfloatingraft2.1CoordinatesystemselectionUndertheframeoflineartheory,themotionstatusofthelowerraftbodycanbedescribedwiththesuperpositionofthemotionofanimaginaryrigidbody(B1)andtheelasticbendingvibrationsurroundingtherigidbody(B1).Theupperequipmentisregardedasrigidbody,whichisnotedwithB2.The
14、originoftheinertialframeistheintersectionoftheperpendicularbisectorofthelowerraftbodyandtheground.Theinertialbaseisdenotedwith,e.Theoriginsofbody-fixedbasesBe(=1,)i(:i2arelocatedinthecentroidsoftherigidbodiesB1,2).ThedisplacementvectorofthecentroidsoftherigidbodiesB;(i=1,2)intheinertialbase,eissigni
15、fiedwithr(.,r3.).TheCardanangle0ofbodyfixedbases8(1,2)relatiretoinertialbaseIeisadoptedastheattitudecoordinate,whichisdenotedwithott,8i,t.Thetransverseelasticdeformationofthelowerraftbodyisdenotedwithw.Sothecoordinatematrixofthesystemcanbewrittenas:y(rc1,01,r.2,02w)=(r1.1,r2c1,r3.1,o/,JE;1,1,r1.2,r2
16、c2,r3.2,o/2,JE;2,2,w)BecauseofthelittlerotatingangleoftherigidbodiesB;(i=1,2),accordingtoRefs.2,3theangularvelocityf(i=1,2)ofbody-fixedbasesB(=1,),i2relativetotheinertialbaseanbedescribedasfo11OWS.第 6 期 WANGZhigangetahDynamicModelingandResponse11509i=l,一withrespectt.theelasticdeformati.noftheraftbod
17、y,thelowerraftbodyisregardedasarbitrarypointinthemiddleplaneofthelowertionofthemiddleplaneofthethinplate,Y,z)=咖,q(t)raftbody,denotesthetransversedeforma.2.2DeterminationoftheforceandmomentduetospringsThespringbetweenthelowerraftbodyandthegroundisdenotedwith.andthenumberofwhichis1.Thejointofthespring
18、andthegroundisi,andthejointofthespringandthelowerraftbodyisi.Thespringbetweenthelowerraftbodyandtheupperequipmentisde.notedwithj,anditsnumberisn2.Thejointofthespringandthelowerraftbodyis,andthejointofthespringandtheupperequipmentisj.Thestiffnessmatrixofthespringiisandthestiffnessmatrixofthespringjis
19、.f-k00f-00KFj0k0l=100l【-00kj【-00j2.2.1TheforceandmomentduetospringbetweenthelowerraftbodyandthegroundTheforceofthespringactingonthelowerraftbody:F/=-KAI“i=一 KirlKiP,l+)where,isthecoordinatesquarematrixofthepointiinthebodyfixedbases.P.f10-p3,P,占,P.=IP3,0-pl.lIl【-,Plcl,0jldenotesthemomentactingonthece
20、ntroid(c1)ofthelowerraftbodydueto.Mcli=BP,T%=Fi+eP,=一,P.KirlBiP.KiP一+曰 P.Wi,P.0l01+,Kirc 一日.,Ki.,.O.O.O.O.r,L船舶力学第 9 卷第 6 期.:三.三=.-1 二:-=一一(rc:一.+.P.0l-KP.z,z 一 jB.Pc2j-0P3c2J-P2c2j,-,03c2JOP2cJ-PlcJP1.2j-0BPc10-p3PIP3.10-p1.1ID.ojThemomentofthespringsbetweenthelowerraftbodyandtheupperequipment:.Mc1
21、denotesthemomentactingonthecentroid(c1)ofthelowerraftbodydueto;8.Mc2denotesthemomentactingonthecentroid(c2)oftheupperequipmentdueto?MIj=-BATFi=-8,),-“-BIp,.0,Fj=一 BPnjKjrn+BPnjKjBPni01+BPniKir 以一 BlPniKiB|Pe2i02一Pclj0rc.+.,0rc2+B,P.0.一 0Pc2j02一(.+BL.0):广.TFj=-8(n,:,+;,=一I2-rc1+2Kjp_cljOl+Bpc2rc2 一 p
22、c2p2一Pc2,0;rc1+B2.:,;rc2-B2.:,.P 一1y0, 一:,;Pc2j,0:/1一【P 删,KW+2-02l0-y2 卢 2y:0 一 Ot:82Ot20A=1 一 y2 卢 2y21 一182O/22.3ElasticvibrationequationofthelowerraftbodySupposingthatthelowerraftbodyisanelasticthinplate,accordingtothetheoryofplateandshellt4,thetransversevibrationequationoftheplatecanbewrittenas:
23、2DY4(,y,)立=F(,y)6(X-Xi,)8(y-y,)+F()6(x.)8(y-ys)(1)第 6 期 WANGZhigangetahDynamicModelingandResponse117whereD=12(1)istheantibendingstiffnessoftheplate.Eistheelasticitym0dulus0fthemateria1.ftheplate.isPoiss.nsrati.histhethickness.ftheplate,and6areheirplanardimensi0n.Pisthedensity.fthematerla1.ftheplate,
24、wh.sedimensi.nisk 咖.F()istheforceduet.spring.,Y,)and(,)denotethepositi.ns.fthep.ints,inthelocalcoordinatesystem.W(x,y,t)=(x,y)q(t)where()isthevibrationmodeoftheplate.)=cos(T.丢)c0sintheabove,1isthemodalparametermeetingtheboundaryconditions4.whichmeetsthee.quation:tan+tanh()=0Multiplyingtheequation(1)
25、with()andintegratingthenewequationinthewholeplaneoftheplate,wehave州 p),ot/=(毗)+(圳(y-yj)dySubstitutingthegivenparameterintotheequation(2),wecangetthevibrationequation0ftheelasticthinplate:Alq( )+(1+2+3)g()1r3c.+D21+D31+pr3+D52+2=0佃十+圳?一搿z 一一,Yi)Kiz,=j=l():()一 2 一一 2n 一盟一 2D0,/,1l8 船舶力学第 9 卷第 6 期D.=i:1nlD:=i:1D3=一 lKf;(,)+JK;(;(;(,Yi)Plc1+i=1J:11
