1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness 7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 1 2 3 4 5 6 7 8 pendulum with opt. lin. viscous damping semi-active, CL #3 semi-active, CL #4 semi-active, CL #1 semi-active, CL #2 (e.g. DBE) (e.g. MCE) 0 200 400 600 800 1000 1200 max( | f | ) (kN) 0 1 2 3 4 5 6 7 8 (e.g. DBE) (e.g. MCE) FP, PGAopt=3.5m/s2 pendulum with opt. lin. viscous damping FP, PGAopt=5.0m/s2 FP, PGAopt=6.5m/s2 semi-active, CL #1 semi-active, CL #2 semi-active, CL #3 semi-active, CL #4 a b PGA (m/s2) PGA (m/s2) max( | üs+üg | ) (m/s 2) Fig. 1.5 Absolute structural acceleration (a) due to semi-active pendulums and (b) maximum total forces of all considered isolators max( | u | ) (mm) 0 50 100 150 200 250 300 350 400 450 500 0 1 2 3 4 5 6 7 8 (e.g. DBE) (e.g. MCE) FP, PGAopt=3.5m/s2 pendulum with opt. lin. viscous damping FP, PGAopt=5.0m/s2 FP, PGAopt=6.5m/s2 semi-active, CL #1 semi-active, CL #2 semi-active, CL #3 semi-active, CL #4 residual | u | (mm) 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 (e.g. DBE) (e.g. MCE) FP, PGAopt=3.5m/s2 pendulum with opt. lin. viscous damping FP, PGAopt=5.0m/s2 FP, PGAopt=6.5m/s2 semi-active, CL #1 semi-active, CL #2 semi-active, CL #3 semi-active, CL #4 a b PGA (m/s2) PGA (m/s2) Fig. 1.6 Maximum displacements (a) and residual displacements (b) of all considered isolators (costs!, Fig. 1.6a), the re-centering capability (Fig. 1.6b, re-centering error must not be larger than 50% of the bearing displacement capacity, i.e. 50% of 250 mm) and the maximum force of the semi-active damper (costs!, Figs. 1.7 and 1.8). The review of all these results reveals that CL #1 and CL #2 represent promising solutions. None of these two control laws can be denoted as superior as the project specifications alone determine if CL #1 or CL #2 is more appropriate for the isolation task, i.e. if the absolute structural acceleration should be minimized for PGAs corresponding to DBE and earthquakes beyond of DBE (CL #1) or for PGAs corresponding to DBE and earthquakes below DBE (CL #2). 1.6 Summary This paper presents a novel semi-active base isolator based on a pendulum with uncontrollable lubricated friction of 1.5% and a semi-active oil damper in parallel. Four different control laws are formulated that target to control the total stiffness of the semi-active isolator in real-time as function of the actual bearing displacement amplitude and to produce optimal viscous damping. The numerical results demonstrate that the semi-active isolator significantly improves the isolation of the structure
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