# Model of Triple Friction Pendulum Bearing for General Geometric and Frictional Parameters and for Uplift Conditions

## A.A. Sarlis and M.C. Constantinou

### MCEER-13-0010 | 07/01/2013 | 382 pages

Keywords: seismic isolation; Triple FP isolator modeling; uplift, landing, rocking, bouncing, overturning, flying and contact of bearing components

Abstract: Current models that describe the behavior of the Triple Friction Pendulum bearing (Fenz and Constantinou, 2008a to 2008e; Morgan, 2007) are based on the assumption that the resultant force of the contact pressure acts at the center of each sliding surface. Accordingly, these models only rely on equilibrium in the horizontal direction to arrive at the equations describing its behavior. This is sufficient for most practical applications where certain constraints on the friction coefficient values apply. Moreover, none of the existing models is capable of describing the behavior of the bearing under uplift conditions.   This report presents a revised model of the behavior of the Triple Friction Pendulum bearing in which no assumptions are made on the location of the resultant forces at each sliding surface and no constraints on the values of the coefficient of friction are required, provided that all sliding surfaces are in full contact.  To accomplish this, the number of degrees of freedom describing the behavior of the bearing is increased to include the location of the resultant force at each sliding surface and equations of moment equilibrium are introduced to relate these degrees of freedom to forces.   Moreover, the inertia effects of each of the moving parts of the bearing are accounted for in the derivation of the equations describing its behavior. The model explicitly calculates the motion of each of the components of friction pendulum bearings so that any dependence of the coefficient of friction on the sliding velocity can be explicitly accounted for and calculations of heat flux and temperature increase at each sliding surface can be made.   In a further extension of this model, the uplift behavior of the Triple Friction Pendulum bearing is modeled by explicitly modeling the dynamic response of its internal components and the effect of the rubber seal stiffness while satisfying the conditions of compatibility and equilibrium.  Finally, an additional model is developed that can capture the Triple Friction Pendulum behavior when in compression and when in uplift. This model is useful in capturing more complicated phenomena such as flying, overturning, and point contact of the various parts of the isolator.