Causal Realization of Rate-Independent Linear Damping for the Protection of Low-Frequency Structures

Abstract

The devastating low-frequency ground motions of the 2011 Great East Japan Earthquake produced large displacements in low-frequency structures previously thought to be safe, including base-isolated structures. Rate-independent linear damping (RILD) is a promising damping model for low-frequency structures because it provides direct control over displacement. Because the control force generated by RILD is proportional to displacement (advanced in phase by π/2 radians) and independent of frequency, it performs well under both low-frequency ground motions and more common higher-frequency ground motions (relative to the structure’s fundamental natural frequency). The phase advance makes RILD noncausal, which has hindered its practical applications. This paper proposes a causal filter-based method to approximate RILD that can be easily implemented in time-domain or frequency-domain analyses. The calculated force can be tracked in real-time (due to causality) through semiactive or active control methods. The approach is applied to a base-isolated structure with supplemental control provided by a magneto-rheological (MR) damper. Both numerical simulations and shake table tests are conducted to demonstrate the performance of the proposed causal approach. The results compare well to noncausal simulations in both the achieved forces and structural responses.