1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness 3 ms ks cs μ us u us .. ug .. semi-active damper controller disp. sensor ground ground cylinder piston spherical hinge valve m h R ground ground Fig. 1.1 Schematic of structure with semi-active isolator where ms, cs, ks denote the modal mass, the viscous damping coefficient and the stiffness of the building, Rus, Pus and us denote the acceleration, velocity and displacement of the structure relative to the ground, Pu and u are the velocity and displacement of the top bearing plate relative to the ground and Rug is the ground acceleration given by the accelerogram of the El Centro North-South earthquake. The mass ms is determined by the typical vertical load of WD6 MN on the isolator, cs D2 s pks ms is computed based on the damping ratio s D1%and ks D24.15 MN/m is selected such that the natural frequency of the building without isolator is 1 Hz representing a typical value for structures that require base isolation. The equation of motion of the top plate of the isolator with mass mand with actual forcef actual semi active of the semi-active oil damper is m RuCfh C W Reff u Dcs .Pus Pu/ Cks .us u/ f actual semi active ms Rug (1.2) where fh is the friction force of the curved sliding surface and W/Reff is the restoring stiffness due to the effective radius Reff DR h of the pendulum. The force fh is modelled by the hysteretic damper modelling approach [8] fh D kh u W pre sliding W sign.Pu/ W sliding (1.3) where kh is the pre-sliding stiffness that is selected two orders of magnitude greater than W/Reff . In case of the passive pendulum without any friction but linear viscous damping fh in (1.2) is replaced by the termc opt Pu where copt denotes the optimal viscous damping coefficient of the isolator. 1.4 Control Law 1.4.1 General Formulation The desired active control force is formulated as follows f desired active D kcontrol uC c opt c Pu W c c 0 kcontrol u W c c <0 (1.4)
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