Multibody Kinematics of the Double Concave Curved Surface Sliders: From Supposed Compliant Sliding to Suspected Stick-Slip

Abstract

The double-concave curved-surface slider isolators are tribological systems composed of the assemblage of three rigid bodies that include two concave spherical plates and a straight cylinder with convex bases coupled with the former two and placed in between themselves. They originally spread under the name of double friction pendula (DFP), and compliant sliding was expected to take place along the coupled surfaces, during an earthquake. Compliant sliding means that it would take place with uniform distribution of geometrical contact and stresses in compliance with a supposed pendulum behavior. However, since earthquakes impose a horizontal kinematic history to the lower plate, the fulfillment of geometrical compatibility suggests that the relative movement between those three rigid bodies may only take place by a recursive alternation of sticking and slipping. Where this latter, assuming that the three components remain rigid, would take place not in a compliant manner but, on the contrary, would be concentrated along the extremities of one diagonal only of the pad. Since the three constitutive components of the double-concave curved-surface slider devices are expected to remain rigid during their relative movement, multibody modeling techniques currently used to simulate machines and mechanisms can be applied to the case study. For this reason, and in order to have more arguments to appraise the validity of the suspect above, the multibody kinematic equations were developed and applied for both supposed compliant sliding and expected stick-slip for two prototypes, a flat and a squat one. With the objective to contribute to the optimization of these devices, parametric numerical studies were also carried out with both approaches to help figure out respectively if the stick-slip effect is to be expected and in which circumstances it can be minimized. The obtained results herein presented neglect acceleration and forces for the sake of brevity and for the time being, but the complete dynamics will be presented in another work.