基于结构图的建筑结构振动控制系统建模与仿真

33320116EarthquakeResistantEngineeringandRetrofittingVol.33No.3Jun．2011EarthquakeResistantEngineeringandRetrofittingJune20111002-8412201103-0064-06123111．7340002．7300503．730050。Newmark-β。TU352．1AModelingandSimulationofStructuralVibrationControlSystemBasedonBlockDiagramLiChun-feng1DuYong-feng23ShiJun1HuangJin11．DepartmentofMechanicalandElectricalEngineeringHexiUniversityZhangye734000China2．WesternCenterofDisasterMitigationinCivilEngineeringMinistryofEducationLanzhou730050China3．InstituteofEarthquakeProtectionandDisasterMitigationLanzhouUniversityofTechnologyLanzhou730050ChinaAbstractBlockdiagramcanbeseenasthecombinationofschematicstructurediagramandthetwodifferentialequationsvariouslinksofthecontrolsystemcanbebetterdistinguishinordertofacilitatestudytheimpactofparametersofvariouslinksonthesystemnotonlythequantitativedescriptionofschematicdiagramcanbecomplementedbutalsothepuremathematicsabstractioncalculationcanbeavoided．ThemodelingmethodofstructuralvibrationcontrolsystemisintroducedindetailbasedontheblockdiagramthesimulationanalysisiscarriedoutthroughestablishingtheblockdiagramaimingatanexamplewhichembodiessimplicityofthemethodthesimulationresultsbasedonblockdiagramareverifieduseoftheclassicNewmark-βnumericalalgorithmwhichshowsthecorrectnessofthegivenmethodinthispaper．Keywordsblockdiagr[e-mail]2010-04-1250978130qn201019。、、。1～68～97AMDBenchmarkLQG/LTR。MATLABSimulink。Simulink。333·65·EarthquakeResistantEngineeringandRetrofittingVol.33No.320111。。1．1M¨X+CX·+KX=－ME¨xgt1MCK、XE¨xgt。。M=m10m2mn－10mnC=c1+c2－c20－c2c2+c3－c3－c3－cn－1cn－1+cn－cn0－cncnK=k1+k2－k20－k2k2+k3－k3－k3－kn－1kn－1+kn－kn0－knkn1．21。5。、m1¨x1+c1+c2x1+k1+k2x1－c2x2－k2x2=m1¨xgtmi¨xi+ci+ci+1xi+ki+ki+1xi－ci+1xi+1－ki+1xi+1－cixi-1－kixi-1=mi¨xgt2≤i＜nmn¨xn+cnxn+knxn－cnxn-1－knxn-1=mn¨xgt22。。。。。2m1¨x1+c1x1+k1x1+c2x1+k2x1=m1¨xgt+c2x2+k2x2mi¨xi+cixi+kixi+ci+1xi+ki+1xi=mi¨xgt+ci+1xi+1+ki+1xi+1+cixi-1+kixi-12≤i＜nmn¨xn+cnxn+knxn=mn¨xgt+cnxn-1+knxn-13Laplacem1s2+c1s+k1+c2s+k2X1=m1Xgs+c2s+k2X2mis2+cis+ki+ci+1s+ki+1Xi=miXgs+ci+1s+ki+1Xi+1+cis+kiXi-12≤i＜nmns2+cns+knXn=mnXgs+cns+knXn－14·66·20116EarthquakeResistantEngineeringandRetrofittingJune2011。、、、、1PD。2。3PD。4PD。5PD。6PD。ikiici+1s+ki+1i+1PDii+1i+1iii－1iPDi－1。、1。。1Fig．1Buildingstructurehierarchicalblockdiagrams33．1kd=AG1hvcd=AG2ωhv5AG1G2hvω。Kelvinp=kdx+cdx6ΔV=πcdωx2073．21MX¨+C+CdX·+K+KdX=－ME¨xgt88CdKd。PD。ii、i－1i－1。44．151.0×106kg2．0×108N/mc1=2．28×106Ns/m。333·67·EarthquakeResistantEngineeringandRetrofittingVol.33No.3201125°G1=1．50×107N/m2G2=2．01×107N/m2A=0.03m2h=0.013m。82《》GB50011-2001Ⅰ。4．2MATLAB、1VED2。2ABCD=linmod‘system’。3p=eigA。pi=－ζiωi±jωi1－ζ2槡i94VED。2Fig．2Structuralvibrationcontrolsystembasedonblockdiagram1。1sTable1Thenaturalvibrationperiodonvibrationmodelss123451．560.530.340.260.231．340.460.290.230.204．3、0.2gElCentro13。Newmark-βab1/21/4。4。3、4199．60mm3．87m/s2。242．01mm3．21m/s2。57．82%17．05%。34Newmark-β·68·20116EarthquakeResistantEngineeringandRetrofittingJune2011、1．95mm0.41m/s2、0.43mm0.29m/s2。3Fig．3Topfloordisplacementandaccelerationresponsecurvesbasedonblockdiagram4Fig．4Theresponsecurvescomparisonaboutthetwomethods5Simulink1。2Newmark-β。References1．J．200521357～62DuYong-fengLiHui．ComparisonandimprovementofmodelsofoptimalcontrolalgorithmsfordynamicalresponseofstructuresunderearthquakeJ．WorldEarthquakeEngineering200521357～62inChinese2．J．20072918～12DuYong-fengLiuYan-huiLiHui．AImprovedAlgorithmforInstantaneousOptimalControlofStructures333·69·EarthquakeResistantEngineeringandRetrofittingVol.33No.32011SubjectedtoSeismicExcitationJ．EarthquakeResistantEngineeringandRetrofitting20072918～12inChinese3．J．2005313109～113DuYong-fengetal．ObjectivefunctionandstabilityofoptimalcontrolalgorithmsforseismiccontrolofstructureJ．JournalofLanzhouUniversityofTechnology2005313109～113inChinese4．、M．2003OuJin-ping．ActiveSemi-activeandIntelligentControloftheStructureM．BeijingSciencePress2003inChinese5．M．2005LiHong-nanetal．StructureVibrationandControlM．BeijingChinaArchitectureandBuildingPress2005inChinese6．MATLABM．2004XuZhao-dongGuoYing-qing．TheApplicationofMATLABinBuildingAntiseismicEngineeringM．BeijingSciencePress2004inChinese7．LQG/LTRAMDBenchmarkJ．2006181248～250DuYong-fengetal．SimulationofStructureVibrationAMDControlBenchmarkModelBaseonLQG/LTRMethodJ．JournalofSystemSimulation2006181248～250inChinese8SoongTT．StateoftheartreviewActivestructuralcontrolincivilengineeringJ．EngineeringStructure19881074～849SuhardjoJSpencerJRBFSainMK．Feedback-feedforwardcontrolofstructuresunderseismicexcitationJ．StructuralSafety1990869～891978～檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶81J．200841968～75MenJin-jieShiQing-xuanZhouQi．MethodofperformancebasedseismicdesignforverticallyirregularreinforcedconcreteframestructuresJ．ChinaCivilEngineeringJournal200841968～75inChinese5．D．2007MenJin-jie．TheoryandMethodsofPerformanceBasedSeismieDesignforIrregularReinforeedConcreteFrameStructuresD．Xi’anXi’anUniversityofArchitecture