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Hybrid Simulation Basics Bozidar Stojadinovic Associate Professor University of California Berkeley Hybrid Simulation Hybrid simulation is an experimentally based method for investigating the response of structure to dynamic excitation using a hybrid model A hybrid model is a an assemblage of one or more physical and one or more numerical consistently scaled substructures The equation of motion of a hybrid model under dynamic excitation is solved during a hybrid simulation test 2 Response of Structures to Dynamic Loads Dynamic loading excites a structure Resistance Energy dissipation damping Inertia Ma t Cv t R d t f t Important dynamic excitations Seismic Wind Blast 3 A Comparison of Test Methods Dynamics QuasiShaking Hybrid Static Test Table Test Simulation No Yes Yes Strain rate No Yes Maybe Pseudo dynamic test method For a short historic review of PDTM see Mosqueda Stojadinovic and Mahin EERC report EERC 2005 02 4 Hybrid Simulation Concept Discretize the structure Ma t Cv t R d t f t Discretize time ti i t i 1 N Assign an actuator an excitation component to each degree of freedom 5 Impose Dynamic Equilibrium At each time instance Mai Cvi ri fi Use measured restoring force Use computer models for Excitation Inertia Energy dissipation commonly known as damping 6 Stepwise Solution Start from a known state at instance i Use a numerical technique to compute a target displacement at instance i 1 Using actuators impose target displacement and measure force Compute state at instance i 1 7 SDOF Example mai cvi ri fi EQM Central difference di 1 di 1 vi method for velocity 2 t and acceleration di 1 2di di 1 approximation ai 2 t Solution 1 2m c m di 1 d 2 di 1 ri fi 2 i m c t 2 t t t 2 2 t 8 Initial Conditions Not self starting Given state at time zero Compute acceleration to satisfy equilibrium Compute fictitious displacement to start the procedure a0 m1 f 0 cv0 r0 2 t d 1 d 0 tv0 a0 2 9 Example A SDOF system with two springs Work in 4 member teams f f0 t t0 d f m r r k d

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