2010_Dynamic motion of whirling rods with Coriolis effect

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1、AppliedMathematicalModelling34(2010)1203–1216ContentslistsavailableatScienceDirectAppliedMathematicalModellingjournalhomepage:www.elsevier.com/locate/apmDynamicmotionofwhirlingrodswithCorioliseffectWaiSunShum*,ZhangLinDivisionofBuildingScienceandTechnology,CityUniversityofHongKong,HongKong,Chin

2、aarticleinfoabstractArticlehistory:Longitudinalvibrationscoupledwithtransversevibrationsofwhirlingrodsareinvesti-Received13May2008gated.ItisknownthatlongitudinalandtransversevibrationsaregovernedbysecondReceivedinrevisedform31July2009andfourthorderdifferentialequations,respectively.DuetotheCori

3、oliseffect,asystemAccepted3August2009ofequationsthatgovernsthelongitudinalandtransversedisplacementswillbecon-Availableonline6August2009structedbycouplingthesetwoequationstogether.SolutionsoftheequationsassumesmalloscillationsofvibrationbeingsuperimposedonthesteadystateofthewhirlingKeywords:rod

4、.Exactandapproximatesolutionsareobtainedfromtheproposedgoverningequations,DynamicwhirlingrodswheretheapproximatesolutionsondisplacementsandnaturalfrequenciesareacquiredCorioliseffectNaturalmodesofvibrationsbyneglectingtheCorioliseffect.Aproposednumericalschemeknownascompletefunc-Resonancetionco

5、llocationmethodisimplementedtosolvethegoverningequationscoupledwithCoupleddifferentialequationslongitudinalandtransversedisplacements.TheapproximateresultsonbothlongitudinalCompletefunctioncollocationmethodandtransversenaturalfrequenciesshowthatnaturalfrequenciesaredecreasingwhiletheangularvelo

6、cityoftherodisincreasing.Exactandnumericalresultsonbothlongitu-dinalandtransversenaturalfrequenciesshowthattherearenopredictabletrendswhethernaturalfrequenciesareincreasingordecreasingwhiletheangularvelocityoftherodisincreasing.Ó2009ElsevierInc.Allrightsreserved.1.IntroductionLongitudinalandtra

7、nsversenaturalfrequenciesofarotatingrodareofinterestinthedesignofturbineblades,helicopterblades,centrifugalmachinesblades,fanbladesandpumpblades.Numerousresearchershaddelvedintotheinvestigationofeitherlongitudinalortransversevibra