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1、Stabilityofaverageaccelerationmethodforstructureswithnonlineardamping,,o1.5.No.1EARTHQUAKEENGINEERINGANDENGINEERINGVIBRATIONJune,2006ArticleID:1671-3664(2006)0l-0087-06StabilityofaverageaccelerationmethodforstructureswithnonlineardampingLiYan(李妍),WuBin(吴斌)andOuJinping(欧进萍)Schoo
2、lofCivilEngineering,HarbinInstituteofTechnology,Harbin15009&ChinaAbstract:TheenergyapproachisusedtotheoreticallyveilfythattheaverageaccelerationmethodfAAM1,whichisunconditionallvstableforlineardynamicsystems.isalsounconditionallystableforstructureswithtypicalnonlineardampin
3、g,includingthespecialcaseofvelocitypowertypedampingwithabilinearrestoringforcemode1.Basedontheenergyapproach.thestabilityoftheAAMisprovenforSDOFstructm'esusingthemathematicalfeaturesofthevelocitypowerfunctionandforMDOFstructuresbyapplyingthevirtualdisplacementtheorem.Finally,nu
4、mericalexamplesaregiventodemonstratetheaccuracyofthetheoreticalanalysis.Keywords:unconditionalstability;averageaccelerationmethod;nonlinearsystems;nonlineardamping1IntroductiOilNumericalstabilityisoneofthemajorconcernsforintegrationcalculation,whichisrequiredinmostnonlineardyna
5、micresponseanalyses.TherearedifierentdefinitionsofstabilityfCheng,1988)indifferentresearchfields.Unconditionalstabilityhasbecomeamajorresearchtopicoftimeintegrationschemesfornonlineardynamicsystemssincethebeginningofthe1990's(KuhlandRamm.1999).Thetimeintegrationschemescanbedivi
6、dedintotwocategories:explicitandimplicit.Theformerincludesthecentraldifferencemethod.explicitNewmark一method,theprecisetime.integrationmethod(Zhong,l994;Zhaoeta1.,2004;WangandZhou,2005;ShenandSong,l996;ZhangandCao,1999),CDM.RSTalgorithmfWua1.,2005),OSmethodandOSM.RSTalgorithm(Wu
7、andⅥg,2006),etc.:whilethelatterincludesthelinearaccelerationmethod.implicitNewmark.method,WiIson.0method,HiIber8.0methodthehighorderonestep一8method(Wangeta1..1996)andthegeneralized—methods(Erlichereta1.,2002),etc.Asamatteroffact,mostintegrationschemesareA.stable(Erlichereta1.,2
8、002),i…ealgorithmsused,C0rresp0ndencet0:WuBin,Schoolof
