Analytical solutions of inerter-added sliding isolation structures to ground motions

Abstract

• Contribute unfulfilled analytical solutions of inerter-added sliding structures. • Reveal explicitly the role of additional inerter played in a sliding isolation system. • Derive explicit conditions for motion modes of inerter-added sliding isolation structures. • Recommend the trade-off between reduction of isolation displacement and acceleration. Previous studies have proven that adding an inerter to a sliding isolation structure can reduce the isolation displacement without compromising the control effect of the superstructure. However, due to the strong nonlinearity of the sliding isolator , approximate methods or numerical analyses are adopted to investigate inerter-added sliding isolation structures, which hinders the understanding of the inherent working mechanisms of such structures. This study derives exact analytical solutions during both sliding and stick motion states of inerter-added sliding isolation structures under harmonic ground motions and investigates the influence of an additional inerter on the motion states and responses of such structures. The main novelties of this paper are the employment of the inerter technique in a sliding system for performance improvement and explicit expressions of the dynamic responses and motion modes for inerter-added sliding isolation structures that assist in understanding the role of the additional inerter. Differential equations are established for both the stick and sliding motions of inerter-added sliding isolation structures subjected to harmonic ground excitations. The dynamic characteristics of the structure are analyzed, and accurate analytical solutions are derived for structural responses. The explicit forms for the occurrence conditions of three fundamental modes (i.e., the stick-stick, stick-slip and slip-slip modes) for the motion of the inerter-added sliding isolation structures are presented. Based on the derived analytical solutions, extensive parametric analyses are conducted to investigate the influences of the added inerter on the motion modes and responses of sliding isolation structures. By adding an inerter, a decreased natural frequency, a decreased damping ratio and a reduction in ground motion excitation are observed for the vibration of the superstructure in the inerter-added sliding isolation structure compared to that in the sliding isolation structure without an inerter. Furthermore, the inerter causes the slip-slip mode to occur more easily, which is preferred for sliding isolation structures when sliding occurs. An increasing inertance of the inerter is beneficial for reducing isolation displacement in general but contrary to reducing maximum acceleration in some frequency ranges and excitations with large amplitudes. The trade-off between the reduction of isolation displacement and acceleration is recommended for determining the inertance of the inerter in sliding isolation structures.