Wind-rain-induced vibration and control of stay ca

STRUCTURALCONTROLANDHEALTHMONITORINGStruct.ControlHealthMonit.2007;14:1013–1033Publishedonline24November2006inWileyInterScience()DOI:10.1002/stc.190Wind–rain-inducedvibrationandcontrolofstaycablesinacable-stayedbridgeH.J.ZhouandY.L.Xu*,yDepartmentofCivilandStructuralEngineering,TheHongKongPolytechnicUniversity,HungHom,Kowloon,HongKongSUMMARYThispaperpresentsananalyticalmodelforinvestigatingwind–rain-inducedvibrationandcontrolofstaycablesinacable-stayedbridge.Thesingle-degree-of-freedom(SDOF)wind–rainexcitationmodeldevelopedfromasectionalcablemodelisappliedtoatautstaycable,takingintoconsiderationthevariationofmeanwindspeedalongthestaycableandtheeffectofmodeshapesofcablevibration.Thecomputedresultsfromtheanalyticalmodelarethencomparedwiththeavailablefieldmeasurementresults.Aftercomparison,theparameterstudiesareperformedtoexplorethemechanismofwind–rain-inducedvibrationofstaycables.Theanalyticalmodeldevelopedinthisstudycanalsoconsidercablevibrationcontrol,inwhichalinearviscousdamperisattachedtothestaycablenearitsanchorage.ClampedandunclampedmodeshapesofthestaycableandtheRunge–Kutta–Fehlbergmethodareusedtofindthenumericalsolutions.Thenumericalresultsshowthatthereisanoptimumdampingcoefficientoftheviscousdampertoachievethebestmitigationofwind–rain-inducedcablevibration.Thisoptimumdampingcoefficientisalmostthesameasthatobtainedfromthecomplexeigenvalueanalysisofthestaycablewithaviscousdamper.Copyright#2006JohnWiley&Sons,Ltd.KEYWORDS:analyticalmodel;staycable;wind–rain-inducedvibration;vibrationcontrol,viscousdamper1.INTRODUCTIONStaycablesareimportantstructuralcomponentsofalongspancable-stayedbridge.Becausestaycablesareofextremelysmallstructuraldampingandveryflexible,theyarepronetoenvironment-inducedvibration,especiallyunderthesimultaneousoccurrenceofwindandrain.*Correspondenceto:Y.L.Xu,DepartmentofCivilandStructuralEngineering,TheHongKongPolytechnicUniversity,HungHom,Kowloon,HongKong.yE-mail:[e-mail]/grantsponsor:ResearchGrantsCouncilofHongKong;contract/grantnumber:PolyU1/02CReceived6April2006Revised3September2006Accepted22September2006Copyright#2006JohnWiley&Sons,Ltd.Largeamplitudecablevibrationsduetowindandrainoftencausefatiguedamageandcorrosiontostrandsinsurprisinglyshortperiods.Manystudieshavebeenconductedtofindthereasonsbehindwind–rain-inducedcablevibrationandthemeasuresformitigatingsuchavibration.Thesestudiesincludefieldmeasurementsofwind–rain-inducedvibrationofstaycableswithout/withcontrol[1–2],wind–raintunneltestsofsectionalcablemodels[3–5]andanalyticalstudiesforexploringthemechanismofwind–rain-inducedcablevibration[6–9].Fromfieldmeasurements,itwasfoundthatexcessivewind–rain-inducedcablevibrationcouldoccurwhenacableisdowninclinedalongwinddirection,withacertainwindyawangleandatameanwindspeedrangingfrom7to15m/s.Thefieldmeasurementsandwind–raintunneltestsfurtherhighlightedthattherivuletformedalongtheuppersurfaceofacableunderthejointactionofwindandrainchangedtheoriginalcablecross-sectionandresultedinexcessivecablevibrationinthecableplane.Althoughsomeanalyticalmodelscouldpredictmajorfeaturesofwind–rain-inducedcablevibrationobservedfromfieldmeasurementsandwind–raintunneltests,theyarebasedonsectionalcablemodelswithoutconsideringthevariationofmeanwindspeedalongastaycableandtheeffectofmodeshapesofcablevibration.Thecomparisonbetweentheanalyticalandfieldmeasurementresultscannotbeperformedsatisfactorilyandwind–raintunneltestresultscannotbefullyusedfortheprototype.Furthermore,dampingdevicessuchasviscousdampershavebeeninstalledonstaycablesnearanchoragestomitigatewind–rain-inducedcablevibrationalthoughthemechanismofwind–rain-inducedcablevibrationhasnotbeenfullyunderstood.Noanalyticalmodelhasbeenestablishedtoevaluatetheeffectivenessofviscousdampersforvibrationcontrolofstaycablesunderwind–rainexcitationtothebestoftheauthors’recollection.Thecurrentpracticeforusingviscousdampersisratherempirical.Thesupplementaldampingratiorequiredfromtheinstallationofviscousdampersformitigatingwind–rain-inducedcablevibrationisestimatedbasedonwind–raintunneltestresultsorfieldobservations.Theamountofsupplementaldampingwhichcanbeprovidedbyviscousdampersisthenestimatedusingtheso-calleduniversaldesigncurveobtainedfromacomplexeigenvalueanalysis[10–12].Noanalyticalmodelisavailabletoprovideadirectestimationofwind–rain-inducedvibrationofastaycablewithout/withviscousdamper.Thispaperthuspresentsananalyticalmodelforinvestigatingwind–rain-inducedvibrationandcontrolofstaycablesinacable-stayedbridge.Thesingle-degree-of-freedom(SDOF)wind–rainexcitationmodeldevelopedfromasectionalcablemodelisappliedtoatautstaycable,takingintoconsiderationthevariationofthemeanwindspeedalongthestaycableandtheeffectofmodeshapesofcablevibration.Thecomputedresultsfromtheanalyticalmodelarethencomparedwiththeavailablefieldmeasurementresults.Aftercomparison,theparameterstudiesareperformedtoexplorethemechanismofwind–rain-inducedvibrationofstaycables.Theanalyticalmodeldevelopedinthisstudycanalsoconsidercablevibrationcontrol,inwhichalinearviscousdamperisattached