8 F. Weber et al. bearing displacement u (mm) 㻙300 −200 100 100 200 300 −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 0 negative kR-eff during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm positive stiffness due to U < 125 mm (plus kR-eff at U close to zero) control law #1 (CL #1) bearing displacement u (mm) −300 −200 100 100 200 300 −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 0 control law #1 (CL #1) zero dynamic stiffness during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm positive stiffness due to U < 125 mm (kR-eff-nominal at U close to zero) a b total isolator force f / W (−) fsemi-active / W (−) Fig. 1.7 Force displacement trajectories of (a) semi-active control force and (b) total force of semi-active isolator due to control law #1 bearing displacement u (mm) −300 −200 100 100 200 300 −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 0 bearing displacement u (mm) −300 −200 100 0 100 200 300 control law #2 (CL #2) −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 control law #2 (CL #2) kR-eff-nominal during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm zero dynamic stiffness during 1/2 cycle at U close to zero total isolator force f / W (−) positive kR-eff during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm negative kR-eff during 1/2 cycle due to U close to zero a b fsemi-active / W (−) Fig. 1.8 Force displacement trajectories of (a) semi-active control force and (b) total force of semi-active isolator due to control law #2 compared to optimized friction pendulums and a hypothetical pendulum without friction but optimal viscous damping. This result is achieved without getting larger bearing displacements and forces and the re-centering requirement is also fulfilled semi-active base isolator. Acknowledgements The authors gratefully acknowledge the financial support of MAURER SE. References 1. Tsai, C.S., Chiang, T.-C., Chen, B.-J.: Experimental evaluation of piecewise exact solution for predicting seismic responses of spherical sliding type isolated structures. Earthq. Eng. Struct. Dyn. 34, 1027–1046 (2005) 2. Weber, F., Boston, C.: Energy based optimization of viscous-friction dampers on cables. Smart Mater. Struct. 19, 045025 (11pp) (2010) 3. Fenz, D.M., Constantinou, M.C.: Spherical sliding isolation bearings with adaptive behavior: theory. Earthq. Eng. Struct. Dyn. 37, 163–183 (2008) 4. Feng, M.Q., Shinozuka, M., Fujii, S.: Friction-controllable sliding isolation system. J. Eng. Mech. (ASCE). 119(9), 1845–1864 (1993)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==