Modified complex mode superposition design respons

EarthquakesandStructures,Vol.4,No.4(2013)1-0001 Modifiedcomplexmodesuperpositiondesignresponsespectrummethodandparametersoptimizationforlinearseismicbase-isolationstructuresDong-MeiHuang1,2,Wei-XinRen1,2andYunMao31SchoolofCivilEngineering,CentralSouthUniversity,Changsha,Hunan,410075,China2NationalEngineeringLaboratoryforHighSpeedRailwayConstruction,CentralSouthUniversity,Changsha,Hunan,410075,China3DepartmentofCivilEngineering,HubeiUniversityofTechnology,Hubei,Wuhan,China(ReceivedMarch12,2012,RevisedMay20,2012,AcceptedJuly11,2012)Abstract.  Earthquakeresponsecalculation,parametricanalysisandseismicparameteroptimizationofbase-isolatedstructuresaresomecriticalissuesforseismicdesignofbase-isolatedstructures.Tocalculatetheearthquakeresponsesforsuchnon-symmetricandnon-classicaldampinglinearsystemsandtoimplementtheearthquakeresistantdesigncodes,amodifiedcomplexmodesuperpositiondesignresponsespectrummethodisputforward.Furthermore,todoparameteroptimizationforbase-isolationstructures,agraphicalapproachisproposedbyanalyzingtherelationshipbetweenthebaseshearratioofaseismicbase-isolationfloortonon-seismicbase-isolationoneandfrequencyratio-dampingratio,aswellastherelationshipbetweentheseismicbase-isolationfloordisplacementandfrequencyratio-dampingratio.Inaddition,theinfluencesofmodenumberandsiteclassificationontheseismicbase-isolationstructureandcorrespondingoptimumparametersareinvestigated.Itisdemonstratedthatthemodifiedcomplexmodesuperpositiondesignresponsespectrummethodismorepreciseandmoreconvenienttoengineeringapplicationsforutilizingthedampingreductionfactorsandthedesignresponsespectrum,andtheproposedgraphicalapproachforparameteroptimizationofseismicbase-isolationstructuresiscompendiousandfeasible.Keywords:  seismicbase-isolation;modifiedcomplexmodessuperpositionresponsespectrummethod;graphicalapproach;parameteroptimization;earthquakeresponse1.IntroductionBaseisolationisananti-seismictechnologythatcansignificantlyreducetheseismicresponsesofasuperstructurebysettingseismicbase-isolationdevicestoextendthesystemnaturalperiodandtoincreasethesystemdamping(BuckleandMayes1990,Skinneretal.1993,HongandKim2004,Fanetal.1991,NaeimandKelly1999,Komodromos2000,Eurocode2004,Takewaki2008).Atpresent,therearethreemainmethodstocalculatetheearthquakeresponsesofseismicbase-isolationstructures.Oneisthetimedomainmethodthattakesatypicalseismicwaveastheseismicexcitationtocalculatetheseismicresponsesintimedomain(Heatonetal.1995,Matsagar                                                       Correspondingauthor,Professor,E-mail:[e-mail]-MeiHuang,Wei-XinRenandYunMao andJangid2004).Thesecondisthefrequencydomainmethodthattakestherandomearthquakegroundmotionmodelastheseismicexcitationtocalculatetherandomseismicresponsesinfrequencydomain(ConstantinouandTadjbakhsh1983,JangidandDatta1995,TakewakiandFujita2009).Thethirdisthemodedecompositionresponsespectrummethodthatcalculatesthemaximumseismicresponsesaccordingtothemodedecompositionanddesignresponsespectrum(GB50011-2010)(Igusaetal.1984,GuptaandJaw1986,MahendraandBarbara1986,Yangetal.1990,Zhouetal.2004).Thetimedomainmethodwhichadoptsonlyoneseismicwaveasanexcitationisdifficulttoreflectthestatisticalcharacteristicsastheearthquakeisarandomprocess.Thefrequencymethodwhichadoptstheseismicrandommodelasanexcitationisuncertainfortheuncertaintiesinthemodelparameters.Themodedecompositionresponsespectrummethod,ontheotherhand,isonthebasisofdesignresponsespectrum,whichisastatisticalresultaccordingtohundredsofseismicwaveexcitationsandisadoptedbytheearthquakeresistantdesigncode(GB50011-2010)forengineeringapplication.Asiswell-known,theseismicbase-isolationstructureisanon-symmetricandnon-classicaldampingsystem,therefore,theforcedrealmodedecompositionresponsespectrummethodshouldbesubstitutedbythecomplexmodesuperpositiondesignresponsespectrummethodformoreaccurateresults.Withawideuseofseismicbase-isolationstructures,theparameteroptimizationdesignontheseismicbase-isolationdevicesisofinterest(AlessandroandIleana2004,ZhouandHan1996,ConstantinouandTadjbakhsh1984,CenkandHenri2004,Takewaki2005).Nowadays,manyconstrainedoptimizationmethodsforparameteroptimizationhavebeenproposedsuchasconjugategradientmethods(HorisbergerandBelanger1974),mathematicalprogrammingapproach(Ballingetal.1983),geneticalgorithm(Yoshietal.1999),GA-fuzzyoptimizationmethod(HyunandPaul2007)andsoon.Allthesemethodsareperformedbyconstantiterating,whichareeithertime-consumingornon-intuitive.Inthispaper,amodifiedcomplexmodesuperpositiondesignresponsespectrummethodisimplementedtocalculatetheseismicresponsesandagraphicalapproachforparameteroptimizationoftheseismicbase-isolationdevicesisproposed.Moreover,theinfluencesofmodenumberandsiteclassificationontheseismicbase-isolationstructureandcorrespondingoptimumparametersareinvestigated.2.Modifiedcomplexmodessuperpositiondesignresponsespectrummethod2.1MotionequationandsolutionTocalculatetheearthquakeresponsesofseismicbase-isolationstructures,thecomputationalmodelthatnotonlyreflectstheactualdeformationbehaviorbu