When rate-independent linear damping (RILD) is incorporated into a base-isolated structure, it achieves a similar response displacement reduction eﬀect with signiﬁcantly lower ﬂoor response acceleration compared with linear viscous damping (LVD) with the same loss factor. To address the undesirable stiﬀness added to an isolation layer when we adopt a mechanical device compris- ing a few branches of a spring-dashpot link to realize RILD, this study proposes canceling the undesirable isolator stiﬀness by adding an inerter element and reducing the isolator stiﬀness. A heuristic optimization method was developed to design the proposed mechanical device to mimic the behavior of RILD. A parametric survey on the optimal designs of the device suggests that the three branches of the spring-dashpot link work best in terms of practicality and feasibility. Seismic control performance was assessed using a 10-story base-isolated building mounted on linear and nonlinear isolation systems. Analyses of linear systems revealed that the proposed device achieved lower inter-story drifts and approximately 40% reduction in ﬂoor response acceleration with a 4% increase in isolator displacement compared with the LVD when subjected to high-frequency ground motions. Analyses of the nonlinear systems showed that the displacement control performance of the proposed model was slightly compromised when subjected to ground motions dominated by low-frequency components, thereby identifying a further challenge in developing a causal RILD device for nonlinear structures. Keywords: rate-independent linear damping, Maxwell-Wiechert model, inerter, low-frequency structure, global optimization algorithm ∗Corresponding author 468-1, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8572, Japan Email addresses: wu.zhanzhan.p5@dc.tohoku.ac.jp (Zhanzhan Wu), wei.liu.b4@tohoku.ac.jp (Wei Liu), ikago@irides.tohoku.ac.jp (Kohju Ikago) Preprint submitted to Engineering Structures November 6, 2022 1. Introduction The 2011 Great East Japan Earthquake caused many low-frequency structures, such as base- isolated and high-rise buildings (previously considered safe), to suﬀer from excessive displacement and long-duration vibrations, causing interior and exterior damage [ 1]. Consequently, the pro- tection of low-frequency structures, including their nonstructural components, from low-frequency 5 ground motion induced by massive earthquakes is attracting increasing attention from engineers and researchers. Adopting conventional energy dissipators, such as viscous and hysteretic dampers(HDs), may be ineﬀective in mitigating excessive displacement in base-isolated structures. A viscous damper can generate insuﬃcient control force against low-frequency vibration, whereas the maximum resistive 10 force of an HD is constant, irrespective of the response displacement, thereby resulting in a decreased equivalent damping ratio for excessive displacement. Magnetorheological dampers can provide an adaptive control force [ 2] but may fail during strong earthquakes. Thus, there is a need for alternative approaches that use a passive system that does not require an external power source, is unconditionally stable, and is easy to maintain. Rate-independent linear damping (RILD), also 15 referred to as structural damping, complex-valued stiﬀness, and linear or ideal hysteretic damping [ 3, 4,5,6] is an attractive option that provides eﬀective damping performance when incorporated into base-isolated structures [ 7]. The idea of RILD was ﬁrst proposed to represent the damping properties of materials, such as metals and soils, whose energy loss per cycle is independent of the frequency over a wide frequency 20 range [ 8,9]. The resistive force of the RILD is in phase with the velocity, resulting in energy dissi- pation, whereas its amplitude is proportional to the response displacement, thus enabling the direct control of the total displacement [ 10]. Nonetheless, RILD is a physically unsound mathematical model that cannot be realized using a real-life device owing to its non-causality (i.e., it exhibits a response even when no excitation is applied), as discussed in