Displacement mitigation–oriented design and mechanism for inerter-based isolation system

Abstract

The inerter-based isolation system, which comprises an inerter, a dashpot, and a spring, has been shown to be effective for improving the dynamic performance of isolated structures. However, the underlying theoretical basis of its vibration control mechanism has not been studied for superstructures with inerter-based isolation system; in particular, the functionality of the inerter has not been explicitly demonstrated. In this study, the displacement mitigation mechanism is established by deriving a fundamental equation, designated as the displacement demand equation. The mechanism is explained by clarifying the functionality of the inerter-based isolation system to determine the theoretical relationship between the displacements of the superstructure and isolation layer. A nominal displacement demand ratio is defined to evaluate the overall displacement demand of the structure–inerter-based isolation system, by considering the contribution of the inerter-based isolation system. Following the displacement mitigation mechanism, design strategies are developed for inerter-based isolation system, where the isolation frequency ratio can be directly determined once the target displacement performance of the entire structure–inerter-based isolation system is prespecified. In addition, the inertance-mass ratio and damping ratio of the inerter-based isolation system can be obtained according to the target demand of the superstructure displacement. Finally, a series of examples are used to verify the derived displacement demand equation and proposed design strategy. In this study, the displacement mitigation mechanism yields an effective design method that is suitable for the inerter-based isolation system and has a clear physical basis. Through the proposed displacement mitigation–oriented optimal strategy, a target displacement demand for a structure can be satisfied directly, which also provides an optimized displacement performance for the isolation layer. The displacement mitigation mechanism and equation are practical for the simplification of the design procedure and help to reveal the advantageous features of the inerter-based isolation system.