Generic 3D formulation for sliding isolators with variable curvature and its experimental verification

Sliding isolators with variable curvature (SIVCs), whose isolation stiffness can be continuously varied along with isolator displacement, allow a passive isolation system to adapt to seismic excitations. The variable stiffness also has the advantage of mitigating the long-period resonance effect when the isolation system is subjected to ground motion with strong long-period components. However, most previous studies on SIVCs were theoretical and adopted simplified models that omit the tri-directional coupled motion due to the geometric effect of the concave sliding surface. In order to provide a more precise analytical tool, this study developed a set of three-dimensional formulas based on Lagrange's equation of motion to predict the complete dynamic forces of an SIVC system transmitted to the superstructure. The formulas, which are applicable to all types of axially symmetric SIVCs, were then verified experimentally using a shaking table test that involved an SIVC system consisting of four polynomial friction pendulum isolators (PFPIs). The derived formulas show that the horizontal and vertical forces of the SIVC include two high-order nonlinear terms related to the curvature and slope of the SIVC sliding surface. In conjunction with the three-dimensional sliding motion of the isolator, these high-order terms cause the tri-directional coupling effect. The experimental results of the shaking table test verified the presence of this dynamic coupling effect and validated the proposed analytical model. Using the isolator parametrical values obtained from the test, the peak responses of the PFPI system subjected to 165 sets of bidirectional horizontal ground motions with various intensity levels were simulated. The simulation results indicate that the high-order coupling terms have a limited influence on isolator drift, but have a notable effect on the shear and vertical forces of the PFPIs when the motion of the isolation system is enlarged by increased seismic intensity.