Unifying causal model of rate-independent linear damping for effectively reducing seismic response in low-frequency structures

Abstract

Rate-independent linear damping (RILD) demonstrates similar performance to that of linear viscous damping for the same loss factor when incorporated in a structure to control seismic response displacement. Nevertheless, the damping force generated by the RILD is relatively low in frequency ranges higher than the natural frequency of the primary structure. This leads to efficient displacement control with low damping force and floor response acceleration when RILD is integrated with low-frequency structures. However, the noncausality of RILD hinders its practical applications, and thus, causal models are widely studied to mimic the RILD behavior. This paper proposes a causal model of RILD using Maxwell elements whose damping force is generated according to the fractional-order derivative of displacement. The proposed model, further represented by a fractional-order damping function, is found to be a unifying model that includes existing causal RILD models from literature, thereby providing further insights to better understand the nature of RILD. Furthermore, several methods were examined to physically realize the proposed model.