Analytical thermo-mechanics 3D model of friction pendulum bearings

Among the most effective seismic protection devices, friction pendulum (FP), whose conceptual basis lies inthe pendulum motion and its simple analytical description, has now gained a widespread acceptance. All thestudies carried out so far have explored almost all the remarkable features of this device. Among the mostappealing are constant stiffness, constant oscillation period, and recentering capability. These studies–and the authors found no exception–have systematically made reference to the classical gravity pendulumequation, whose motion occurs only in one dimension (1D), according to one DOF: the polar angleθ. Whenthe presence of bi-directional seismic excitation required a 2D model, authors have resorted to the vectorcombination of the response of two orthogonal 1D pendulums, which we refer to as‘1.5D’pendulum.Actually, FP is more correctly described as a 2D spherical pendulum, consisting of a mass moving on asphere with friction, according to two DOFs: the polar angleθand the azimuth angleφ. The relevantanalytical equations of motion are presented in this paper, also accounting for thermo-mechanical coupling,to model the friction-induced temperature on the contact surface. The so-developed equations have been theobject of an ample parametric study. This has allowed to observe some–sometimes notable–features inthe FP response, both in free oscillation state and underbi-directional or tri-directional earthquake-likeaction, which in some cases lead to a different response with respect to what is generally computed–anddesigned–under the simplified assumptions of 1D or‘1.5D’pendulum motion.