外文资料--Effects of key parameters on energy distribution and kinetic.pdf外文资料--Effects of key parameters on energy distribution and kinetic.pdf

收藏 分享

资源预览需要最新版本的Flash Player支持。
您尚未安装或版本过低,建议您

JOURNALOFSOUNDANDVIBRATIONJOURNALOFSOUNDANDVIBRATION3082007548–562AMONGTHEENERGYSTATEAFTERCOLLISIONBETWEENABARANDABEAM,THERESTITUTIONSTATEANDTHESOUNDGENERATEDWHENATESTOFAWEIGHTANDREPORTEDINTERMITTENTTYPECOLLISIONWITHINASHORTTIME2WITHTHEADVANCEMENTOFARTICLEINPRESSWWWELSEVIERCOM/LOCATE/JSVI0022460X/SEEFRONTMATTERR2007ELSEVIERLTDALLRIGHTSRESERVEDDOI101016/JJSV200705008C3CORRESPONDINGAUTHOREMAILADDRESSNARAKEYAKICCUTOKAIACJPTNARABAYASHIBEAMANDABARCOLLIDETHEREFORE,ITISIMPORTANTTOANALYTICALLYSTUDYTHEEFFECTOFKEYPARAMETERSONVARIOUSENERGYSTATESTHUS,ASOURPRINCIPALRESULT,THECOMPLICATEDMOTIONOFASYSTEMINVOLVINGANINTERMITTENTCOLLISIONPHENOMENONNAMELY,ANELASTICBARANDANELASTICBEAMSUPPORTEDATBOTHENDS,WASCLARIFIEDTHEORETICALLYANDEXPERIMENTALLYR2007ELSEVIERLTDALLRIGHTSRESERVED1INTRODUCTIONWHENABARCOLLIDESPERPENDICULARLYWITHABEAM,LONGITUDINALVIBRATIONISGENERATEDINTHEBAR,WHILELATERALVIBRATIONISGENERATEDINTHEBEAMBOTHTHEBARANDBEAMHAVEADEFINITEELASTICPROPERTY;HOWEVER,COLLISIONPHENOMENABETWEENABARANDABEAMAREVERYCOMPLICATED,SINCETHEIRELASTICPROPERTIESINFLUENCEEACHOTHERREGARDINGCOLLISION,PARTICULARLYLATERALCOLLISION,OFABEAMHAVINGATYPICALSIMPLESTRUCTURE,TIMOSHENKOREPORTEDANALYTICALRESULTSFORAFALLINGSTEELBALLMANYYEARSAGO1MAJIMAANDNISHIDACARRIEDOUTADROPEFFECTSOFKEYPARAMETERSONENERGYDISTRIBUTIONANDKINETICCHARACTERISTICSINCOLLISIONOFBARANDBEAMTNARABAYASHIA,C3,KAZUOSHIBAIKEB,AISHIZAKAA,KOZAKICADEPARTMENTOFPRECISIONENGINEERING,SCHOOLOFENGINEERING,TOKAIUNIVERSITY,1117,KITAKANAME,HIRATSUKASI,KANAGAWA,JAPANBTOSHIBATECGOTANDA2172,SHINAGAWAKU,TOKYO,JAPANCDEPARTMENTOFPRIMEMOVERENGINEERING,SCHOOLOFENGINEERING,TOKAIUNIVERSITY,1117,KITAKANAME,HIRATSUKASI,KANAGAWA,JAPANACCEPTED3MAY2007THEPEERREVIEWOFTHISARTICLEWASORGANISEDBYTHEGUESTEDITORAVAILABLEONLINE10JULY2007ABSTRACTELASTICCOLLISIONPROBLEMSARETHEFOUNDATIONSOFALLCOLLISIONPROBLEMS,ANDABARANDABEAMCANREPRESENTATYPICALANDSIMPLESTRUCTUREHOWEVER,THEELASTICCOLLISIONOFABARANDABEAMISACOMPLICATEDPHENOMENONTHEPURPOSEOFTHISRESEARCHISTOCLARIFYTHERELATIONSHIPBETWEENTHEPRINCIPALPARAMETERANDTHEKINETICCHARACTERISTICSTHATINFLUENCETHISCOMPLICATEDELASTICCOLLISIONPHENOMENON,ANDTOEXPLAINTHESEONTHEBASISOFANIMPACTFORCEWAVEFORM,THEAPPARENTCOEFFICIENTOFRESTITUTION,ANDENERGYDISTRIBUTIONWEEMPLOYEDANANALYSISMETHODINWHICHTHEIMPACTFORCEASSUMESANEXPONENTIALFUNCTIONFORTHEBASICEQUATIONOFTHEONEDIMENSIONALELASTICVIBRATIONCORRESPONDINGTOTHELONGITUDINALVIBRATIONOFTHEBARANDTHELATERALVIBRATIONOFTHEBEAM,ANDINWHICHTHEFORCESATISFIESTHECONDITIONOFCONTINUITYOFTHEDISPLACEMENTINTHEEXPERIMENT,ASSUMINGFLATSURFACECONTACT,WEDIRECTLYDETECTEDCOLLISIONPHENOMENONELECTRICALLYUSINGPZTPASTEDONTOTHEENDSURFACEOFTHECOLLISIONBARONTHEBASISOFTHISSTUDY,THEKEYPARAMETERINTHEABOVEMENTIONEDCOLLISIONPHENOMENONISCLARIFIED,ANDANENERGYDISTRIBUTIONSITUATIONANDTHEINFLUENCEOFEACHPARAMETERCANNOWBECONSIDEREDFORARBITRARYCOMBINATIONSOFTHEBARANDBEAMFURTHERMORE,ITISASSUMEDTHATTHEREISACORRELATIONMEASUREMENTINSTRUMENTS,THENUMBEROFREPORTSONMEASUREMENTMETHODSUSINGSTRAINGAUGESANDPIEZOELECTRICELEMENTSPZTSHASBEENINCREASING3–5HOWEVER,DETAILEDDISCUSSIONHASNOTBEENCARRIEDOUTONINTERMITTENTTYPECOLLISIONBETWEENABARANDABEAMATTHEATEM’99ANDICEM12INTERNATIONALCONFERENCE,THEAUTHORSDEMONSTRATEDANDREPORTEDTHEEFFECTIVENESSOF1THEANALYTICALMETHODBASEDONAONEDIMENSIONALFUNDAMENTALEQUATIONONCOLLISIONPHENOMENABETWEENABARANDABEAMTOSATISFYTHECONDITIONOFCONTINUITYAND2ANEXPERIMENTALMETHODOFOBSERVINGTHECOLLISIONPHENOMENA6ANDRESTITUTIONCHARACTERISTICS7INTERMSOFELECTRICALCHARACTERISTICSINTHISANALYTICALMETHOD,ROTATORYINERTIAANDSHEARDEFORMATIONOFTHEBEAMAREDISREGARDEDFORSIMPLICITYINADDITION,ASSUMINGIMPACTFORCETOBEANEXPONENTIALFUNCTIONOFTIME8,9,THEEQUATIONSARESOLVEDSUCHTHATTHECONDITIONOFCONTINUITYBETWEENTHEBARANDTHEBEAMARESATISFIED,INORDERTOCLARIFYTHECOMPLICATEDMOTIONPHENOMENADURINGCOLLISIONINTHISPAPER,ABOTHENDSSUPPORTEDBEAM,WHICHISEASILYREALIZEDASASUPPORTINGCONDITION,ISUSED,ANDPZTISARTICLEINPRESSTNARABAYASHIETAL/JOURNALOFSOUNDANDVIBRATION3082007548–56254922EQUATIONOFMOTIONANDELASTICDISPLACEMENTOFBARINCOLLISIONIMPACTFORCEPTISAPPLIEDTOTHEENDOFTHEBARANDTHEBARISSUBJECTEDTOELASTICDEFORMATIONASSUMINGTHEELASTICDEFORMATIONOFTHEBARENDTOBEU1T,THEEQUATIONOFMOTIONISQ2U1TQT2C21Q2U1TQX22L2−L1,00,L2/20,−L2/20,00,LPYX21EQUATIONOFMOTIONFORCENTEROFGRAVITYOFBARASSUMINGIMPACTFORCEPTISAPPLIEDTOTHEENDOFTHEBARINTHELEFTWARDDIRECTIONDUETOCOLLISION,THECENTEROFGRAVITYOFTHEBARUTISOBTAINEDBYINTEGRATINGUNDERTHEINITIALCONDITIONOFU0ANDDU/DTVATT0R1L1A1D2UTDT2C0PT1PASTEDONTOTHEENDSURFACEOFTHECOLLIDINGBARANDTHECOLLISIONPHENOMENAAREOBSERVEDINTERMSOFELECTRICALCHARACTERISTICSACOMPARATIVESTUDYWASALSOCARRIEDOUTONTHEKEYPARAMETERSINTHEANALYSISANDEXPERIMENT,WHILECHANGINGCOLLISIONPOSITIONSINCETHEEXPERIMENTALANDTHEORETICALRESULTSGENERALLYWEREINGOODAGREEMENT,WECONCLUDEDTHATBOTHOURTHEORYANDEXPERIMENTALMETHODAREEFFECTIVEEVENUNDERTHECONDITIONTHATCOLLISIONPOSITIONCHANGESFURTHERMORE,THECHANGESOFINTHEKINETICCHARACTERISTICSOFTHEBARANDBEAMAREDISCUSSEDFROMTHEVIEWPOINTOFCHANGESINCOLLISIONPOSITION,RESTITUTIONCHARACTERISTICSANDENERGYDISTRIBUTION2SETTINGPROBLEMANDOUTLINEOFFUNDAMENTALEQUATIONSFORANALYSISACASEINWHICHANELASTICBARLENGTHL1,CROSSSECTIONALAREAA1,DENSITYR1,LONGITUDINALELASTICCOEFFICIENTE1,VELOCITYOFLONGITUDINALWAVEC1COLLIDEDPERPENDICULARLYWITHANELASTICBEAML2,A2,R2,E2ANDC2ATTHECENTEROFABEAMORATAPOSITIONLPFROMTHECENTERINTHESUPPORTEDENDDIRECTION,ATANINITIALVELOCITYOFV,ISCONSIDEREDFIG1THETIMEATWHICHTHEBARCOLLIDESWITHTHEBEAMISASSUMEDTOBETHEORIGINOFTIMETFIG1BARANDBEAMARTICLEINPRESSTNARABAYASHIETAL/JOURNALOFSOUNDANDVIBRATION3082007548–562550THEBOUNDARYCONDITIONSAREEXPRESSEDASATX0,E1A1QU1TQXC0PT0PTPT;0TOT3ATXC0L1,QU1TQX04THEINITIALCONDITIONISGIVENBYU1T0;QU1TQT05THEELASTICDEFORMATIONOFTHEBARENDCANBEDETERMINEDBYEXPANDINGTHEEQUATIONTOANINFINITESERIESUSINGTHENATURALANGULARFREQUENCYANDTHEEIGENFUNCTIONOFABOTHENDSFREEBARTHENATURALANGULARFREQUENCYANDEIGENFUNCTIONOFABOTHENDSFREEBARAREN1NNPC1L1;UNffiffiffiffiffiffiffiffiffi2L1PCOSNPXL16THEELASTICDEFORMATIONOFTHEBARENDISGIVENBYU1TC02R1A1L1X1N11N1NZT0PXSINN1NTC0XDX7CONSIDERINGTHEDISPLACEMENTATX0HERE,NISTHEMODENUMBER23EQUATIONOFMOTIONANDDEFLECTIONDISPLACEMENTOFBEAMATTIMEOFCOLLISIONTHEEQUATIONOFMOTIONOFTHEBEAMISEXPRESSEDBYQ2U2TQT2E2I2R2A2Q4U2TQY40,8WHEREI2ISTHEMOMENTOFINERTIAOFAREAANDU2TTHEDEFLECTIONDISPLACEMENTOFTHEBEAMTHEDEFLECTIONDISPLACEMENTOFTHEBEAMCANBECALCULATEDBYEXPANDINGTHEEQUATIONTOANINFINITESERIESUSINGEIGENFUNCTIONWVYFORBOTHENDSSUPPORTEDBEAMU2T1R2A2X1N11N2NWNLR2ZT0PZSINN2NTC0ZDZ9HERE,ASSUMINGTHEFIRSTMODENATURALANGULARFREQUENCYOFTHEBOTHENDSSUPPORTEDBEAMISN21,N2NN2N21HOLDSUNDERTHISCONDITION,THEEIGENFUNCTIONISEXPRESSEDASWNLPffiffiffiffi2L2RSINNPLPL212C18C1910ANDTHEDEFLECTIONDISPLACEMENTOFTHEBEAMATTHETIMEOFCOLLISIONISOBTAINEDHERE,LP/L2ISTHECOLLISIONPOSITIONRATIO,IE,THERATIOOFTHEDISTANCEBETWEENTHEBEAMCENTERANDTHECOLLISIONPOSITIONTOTHELENGTHBETWEENTHESUPPORTEDENDS24CONDITIONOFCONTINUITYANDAPPARENTCOEFFICIENTOFRESTITUTIONACASEINWHICHABARCOLLIDEDWITHABOTHENDSSUPPORTEDBEAMATAPOSITIONLPFROMTHECENTEROFTHEBEAMISCONSIDEREDTHEDISPLACEMENTOFTHEBARENDISTHESUMOFTHEDISPLACEMENTOFTHECENTEROFGRAVITYUTOBTAINEDBYINTEGRATINGEQ1ANDTHEELASTICDISPLACEMENTOFTHEBARENDU1T,ANDISGIVENBYUTU1T11NEXT,THEDISPLACEMENTOFTHEBEAMATTHECOLLISIONPOSITION,U2T,WHENTHEIMPACTFORCEPTISAPPLIEDTOTHECOLLISIONPOSITION,ISASSUMEDTOBEEQUALTOEQ11,SINCETHEDISPLACEMENTOFTHEBARENDANDTHATOFTHEBEAMATTHECOLLISIONPOSITIONAREEQUALDURINGCOLLISION,ANDHOLDSUTU1TU2T12ASSUMINGTHEDISPLACEMENTOFTHECENTEROFGRAVITYOFTHEBARBEFORECOLLISIONTOBEU0ANDTHATADDEDAFTERCOLLISIONTOBEU1,THEABOVEEQUATIONISEXPRESSEDEQ13ARTICLEINPRESSTNARABAYASHIETAL/JOURNALOFSOUNDANDVIBRATION3082007548–562551U0VTU2TC0U1U113BECAUSETHELEFTHANDSIDEOFEQ13CHANGESLINEARLYWITHTIME,THERIGHTHANDSIDESHOULDALSOCHANGESIMILARLYTHEIMPACTFORCEPTISAPPROXIMATEDUSINGTHEFOLLOWINGEQUATIONSUCHTHATTHERIGHTHANDSIDEOFEQ13CHANGESASLINEARLYASPOSSIBLEWITHTIME,ASSHOWNINFIG2B,ANDBOTHP1ANDM1AREADJUSTEDSOTHATTHECONTINUITYCONDITIONOFDISPLACEMENTISSATISFIEDPTP1EC0M1T14ONCEEQ14ISDETERMINED,BOTHTHEELASTICDEFORMATIONGENERATEDINTHEBARANDTHEDEFLECTIONDISPLACEMENTGENERATEDATTHECOLLISIONPOSITIONOFTHEBEAMCANBEOBTAINEDASINFINITESERIESUSINGTHEEIGENFUNCTIONSOFTHEBARANDBEAMHERE,THEEQUATIONSOFDISPLACEMENTOFTHEBARANDBEAMAREOBTAINEDASAFUNCTIONOFT,INWHICHTHEMASSRATIOANDNATURALFREQUENCYRATIOOFTHEBARANDBEAMAREUSEDASPARAMETERSANDM1ASANUNKNOWNBYCONSIDERINGTHECOLLISIONPOSITIONRATIOCONTAINEDINTHEEIGENFUNCTIONOFTHEBEAM,ITBECOMESPOSSIBLETOCALCULATETHEMOTIONOFTHEBARANDTHEBEAMBASEDONTHEEQUATIONFORTHEDISTANCEBETWEENTHEBARANDTHEBEAMU2TC0FUTU1TG40,ITISFOUNDTHATTHEBARENDSEPARATESFROMTHEBEAMCOLLISIONSCEASEATTHISPOINT,ANDTHEBARANDBEAMWILLNOTCOLLIDEAGAINUNLESSTHEDISTANCEBETWEENTHETWOBECOMES0BEFOREAPPROXIMATELY3/4OFTHEPERIODOFTHEBEAMINTHISCASE,THEBARANDTHEBEAMCOLLIDEONLYONCEINCONTRAST,WHENTHEYCOLLIDENTIMES,THEYCOMEINTOCONTACTAGAINATTIMETNATWHICHTHEDISTANCEBETWEENTHEBARANDTHEBEAMIS0ORLESSASSUMINGANIMPACTFORCEEXPRESSEDBYPTPNEC0MNTC0TN15ISAPPLIEDTOTHEBAR,PNANDMNAREDETERMINEDSUCHTHATTHECONDITIONOFCONTINUITYISSATISFIED,ANDTHEDISPLACEMENTISCALCULATEDFORTHENTHORLATERCOLLISIONSBYTHISPROCEDURE,VARIOUSIMPACTFORCEPATTERNSAREOBTAINEDUNDERVARIOUSCOMBINATIONSOFTHETHREEPARAMETERS,IE,1THENATURALFREQUENCYRATIOOFTHEBARTOTHEBEAMN11/N21,2THEMASSRATIOOFTHEBARTOTHEBEAMM1/M21AND2REFERTOTHEBARANDBEAM,RESPECTIVELY,AND3THECOLLISIONPOSITIONRATIOLP/L2WHERELPTHEDISTANCEBETWEENTHEBEAMCENTERANDTHECOLLISIONPOSITIONANDL2THELENGTHBETWEENTHESUPPORTEDENDSWHENTHEBARANDTHEBEAMCOLLIDENTIMES,B1N11TDRIGHTSIDEOFEQ13PTP1E−AFII98391TTIMEP1IMPACTFORCE0T0LEFTSIDEOFEQ1302ΠFIG2APPROXIMATIONOFIMPACTFORCEBYADJUSTINGM1/N11ANDCONTINUITYCONDITIONOFDISPLACEMENT8
编号:201311171715027729    类型:共享资源    大小:962.13KB    格式:PDF    上传时间:2013-11-17
  
5
关 键 词:
教育专区 外文翻译 精品文档 外文资料
  人人文库网所有资源均是用户自行上传分享,仅供网友学习交流,未经上传用户书面授权,请勿作他用。
关于本文
本文标题:外文资料--Effects of key parameters on energy distribution and kinetic.pdf
链接地址:http://www.renrendoc.com/p-97729.html

当前资源信息

4.0
 
(2人评价)
浏览:35次
英文资料库上传于2013-11-17

官方联系方式

客服手机:17625900360   
2:不支持迅雷下载,请使用浏览器下载   
3:不支持QQ浏览器下载,请用其他浏览器   
4:下载后的文档和图纸-无水印   
5:文档经过压缩,下载后原文更清晰   

精品推荐

相关阅读

人人文库
关于我们 - 网站声明 - 网站地图 - 资源地图 - 友情链接 - 网站客服客服 - 联系我们

网站客服QQ:2846424093    人人文库上传用户QQ群:460291265   

[email protected] 2016-2018  renrendoc.com 网站版权所有   南天在线技术支持

经营许可证编号:苏ICP备12009002号-5