Hybrid Simulation:BasicsBozidar Stojadinovic, Associate ProfessorUniversity of California, Berkeley2Hybrid SimulationHybrid simulation is an experimentally basedmethod for investigating the response ofstructure to dynamic excitation using a hybridmodelA hybrid model is a an assemblage of one ormore physical and one or more numerical,consistently scaled, substructuresThe equation of motion of a hybrid modelunder dynamic excitation is solved during ahybrid simulation test3Response of Structuresto Dynamic LoadsDynamic loading excites a structure: Resistance Energy dissipation (damping) InertiaImportant dynamic excitations: Seismic Wind Blast( ) ( ) ( ( )) ( )Ma t Cv t R d t f t+ + =4A Comparison of Test MethodsMaybeYesNoStrain rateYesYesNoDynamicsHybridSimulationShakingTable TestQuasi-Static TestPseudo-dynamic test methodFor a short historic review of PDTM, seeMosqueda, Stojadinovic and Mahin EERCreport EERC-2005-025Hybrid Simulation ConceptDiscretize the structure:Discretize time:Assign: an actuator an excitation componentto each degree of freedom( ) ( ) ( ( )) ( )Ma t Cv t R d t f t+ + =; 1,it i t i N= ! =6Impose Dynamic EquilibriumAt each time instance:Use measured restoring forceUse computer models for: Excitation Inertia Energy dissipation, commonly known asdampingi i i iMa Cv r f+ + =7StepwiseSolutionStart from a knownstate at instance iUse a numericaltechnique tocompute a targetdisplacement atinstance (i+1)Using actuators,impose targetdisplacement andmeasure forceCompute state atinstance (i+1)8SDOF ExampleEQMCentral differencemethod for velocityand accelerationapproximationSolution:i i i ima cv r f+ + =1 12i iid dvt+ !!="1 122i i iid d dat+ !! +="1 12 221 222i i i i im m cd d d r fm ct t tt t+ !" #$ %= ! ! ! +& '( )* * *+ ,- .+* *9Initial ConditionsNot self-startingGiven state at timezero: Computeacceleration tosatisfy equilibrium Compute fictitiousdisplacement to startthe procedure10 0 0 0( )ma f cv r= ! !21 0 0 02td d tv a!"= ! " !10ExampleA SDOF system with two springsWork in 4-member teamsmd, fdrdrtft0f0kkr011ObserveTasks: Complexity Required time to completeData flowSources of errorOpportunities for doing work in parallelLimitations of the iteration process: Physical specimens cannot revert to aprevious state and restart12Solution: SDOF Response13IssuesSubstructuresSimilitudeErrorsIntegration methodsImplementation in the labThank you!Development and operation of the nees@berkeley equipment site issponsored by NSF.http://nees.berkeley.eduContributions to this presentation from Prof. Gilberto Mosqueda andMr. John-Michael Wong are gratefully