Hybrid Simulation Workshop: SDOF ExampleHybrid Simulation Workshop: SDOF Example Compute the response of a SDOF system shown below using “hybrid simulation” and a four-member team. System properties: • Natural period 1 sec; damping ratio 5%: o Mass m=0.0761 kips-sec2/in o Stiffness k=1.5 kips/in (for each spring) o Damping coefficient c=0.0478 kips-sec/in • Spring yield force ry=0.5 kip. Excitation properties: • Duration t0=0.5 sec • Intensity f0=1.5 kips Roles: • First member: Left spring • Second member: Right spring • Third member: Given resistance and force, compute target displacement • Fourth member: Compute initial conditions, then, in each step assemble spring forces, request displacement target, disseminate displacement target to springs Complete system state (force and displacement) for 10 time-steps with 0.1sectΔ=Pre-compute: 1000()mafcv=−−0r 210 02tdd tv a−Δ=−Δ−0 2mtΔ 2ctΔ Iterate: 112221222iiimmcdddmcttttt+−⎡⎤⎛⎞=−−⎜⎟⎢⎥ΔΔΔ⎝⎠⎣⎦+ΔΔiirf−+ Results: Time (sec) Excitation f (kips) Total resistance r (kips) Mass displacement d (in) 0 1.5 0.1 1.5 0.2 1.5 0.3 1.5 0.4 1.5 0.5 1.5 0.6 0 0.7 0 0.8 0 0.9 0 1.0
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