6 F. Weber et al. 1.5 Results 1.5.1 Optimized Friction Pendulums The effective radius of the passive FP is designed to produce the targeted isolation time period Tiso D3.5 s. Given this effective radius the friction coefficient is optimized for minimum max jRus C Rugj for the PGA of the DBE that is assumed to be 5 m/s2 (Fig. 1.4b). The optimization of is also performed for PGAD3.5 m/s2 and PGAD6.5 m/s2 (Fig. 1.4a, c) to demonstrate that the best performance of the optimized FP is only obtained at the PGA value used for optimization highlighted by the green circles Fig. 1.4e. 1.5.2 Pendulum with Optimized Linear Viscous Damping The effective radius of the pendulum is the same as for the FP in order to guarantee equal time periods. The viscous damping coefficient is optimized for minimum max jRus C Rugj (Fig. 1.4d) which does not depend on the PGA of the ground acceleration as can be seen from the linear behavior of max jRus C Rugj as function of PGA depicted in Fig. 1.4e. 1.5.3 Semi-Active Pendulum The isolation performance in terms of absolute structural acceleration of the semi-active pendulum with passive friction of 1.5% (lubricated) resulting from the four suggested control laws is depicted in Fig. 1.5a. The main observations are: • CL #1 and CL #2 perform better than CL #3 and CL #4 because the maximum controlled stiffness of CL #1 and CL #2 are only 50% of the maximum value due to CL #3 and CL #4 whereby the actual stiffness and actual damping produced by the semi-active damper are closer to their desired counterparts for CL #1 and CL #2 than for CL #3 and CL #4; further information on stiffness and damping emulations with semi-active dampers are available in [10]. • CL #1 performs better than CL #2 at large PGAs because CL #1 is formulated to produce zero dynamic stiffness at U Umax D0.25 m whereas CL #2 outperforms CL #1 at smaller PGAs because CL #2 produces zero dynamic stiffness at UD0. In order to select the “best performing control law” not only the maximum reduction of the absolute structural acceleration should be considered but also the maximum force of the isolator (costs!, Fig. 1.5b), the maximum bearing displacement 2.2 2.4 2.6 2.8 0.60 0.62 0.64 0.66 PGA=3.5m/s2 PGA=6.5m/s2 µ (%) 3.4 3.6 3.8 4.0 4.2 0.86 0.88 0.90 4.6 4.8 5.0 5.2 1.12 1.13 1.14 1.15 c (kNs/m) 650 700 750 0.76 0.77 0.78 0.79 3.0 µ (%) 3.2 µ (%) PGA=5.0m/s2 independent of PGA 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 FP, optimized @ PGA=3.5m/s2 pendulum with optimized linear viscous damping FP, optimized @ PGA=5.0m/s2 FP, optimized @ PGA=6.5m/s2 optimization points of FPs (e.g. DBE) (e.g. MCE) e a b c d PGA (m/s2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) Fig. 1.4 Optimal friction coefficients (a–c) of passive FPs and optimal viscous coefficient (d) of passive pendulum with viscous damping; absolute structural acceleration (e) due to optimized passive FPs and pendulum with optimized viscous damping
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