Semi-Active Approximation of Rate-Independent Linear Damping for the Seismic Protection of Low-Frequency Structures

Abstract eng:
Rate-independent linear damping, also known as linear hysteretic damping or complex-value stiffness, provides direct control over displacement, a desirable feature for low-frequency structures. The greatest benefit is realized when the frequency of the input is larger than the frequency of the structure, typical of low-frequency structures under earthquake excitations. In such scenarios, rate-independent linear damping provides comparable reduction in displacement and velocity as other damping types with greater acceleration reduction and at about half of the restoring force. In rate-independent linear damping, the restoring force is proportional to displacement but in phase with velocity, leading to its non-causality. Numerical investigations have illustrated the promise of rate-independent linear damping through non-causal time-domain and frequency-domain analyses. However, there are limited practical approaches to determine the rate-independent force through causal analysis. Causal determination of the force associated with rate-independent linear damping will facilitate the realization of this force through semi-active or active control methods. This study proposes a filter-based approach to approximate rate-independent linear damping. The filter is used to approximate the preceded displacement, which is by definition proportional to the desired force. A semi-active control algorithm is then used to track the desired force. The approach is demonstrated for a hybrid base-isolation system with a magnetorheological damper incorporated in isolation layer of a base-isolated structure. Both numerical and experimental tests are conducted to examine the performance of this method to achieve the ideal damping force. Results compare very well with non-causal numerical simulations, confirming both through simulation and experimentation the proposed approach to achieve the benefits of rate-independent linear damping in practical structures.

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