Causal rate-independent damping device using a rotary inerter damper

The resistive force of linear viscous damping (LVD), which is commonly used as a damping model for structures, decreases proportionally with the frequency. Another linear damping model known as the rate-independent linear damping (RILD) model is used as a linear mathematical model for representing the damping characteristics of structures and materials that have a low frequency dependency. Because the resistive force of RILD is proportional to the displacement amplitude instead of the velocity, it is expected to directly and effectively control the seismic response displacement of low-frequency structures if implemented in a physical device. In this study, we propose the application of a causal approximation model of the RILD model—based on Biot’s model—that extends the order of dynamic stiffness of each branch to the second order with seismically isolated structures. A few branches of commercially available tuned viscous mass dampers with second-order dynamic stiffness are arranged in parallel in the proposed device. When the demand for isolator displacement mitigation is moderate, the proposed model simulates the performance of the RILD model well. The proposed system outperforms the LVD system even when the demand for isolator displacement mitigation becomes more severe.