Lawrence Berkeley National Laboratory

Among the most effective seismic protection devices, friction pendulum (FP), whose conceptual basis lies in the pendulum motion and its simple analytical description, has now gained a widespread acceptance. All the studies carried out so far have explored almost all the remarkable features of this device. Among the most appealing 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 pendulum equation, whose motion occurs only in one dimension (1D), according to one DOF: the polar angle θ. When the presence of bi-directional seismic excitation required a 2D model, authors have resorted to the vector combination 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 a sphere with friction, according to two DOFs: the polar angle θ and the azimuth angle φ. The relevant analytical 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 the object of an ample parametric study. This has allowed to observe some - sometimes notable - features in the FP response, both in free oscillation state and under bi-directional or tri-directional earthquake-like action, which in some cases lead to a different response with respect to what is generally computed - and designed - under the simplified assumptions of 1D or '1.5D' pendulum motion.