**4. Conclusions**

A novel inerter system for vibration control, which uses tension-only cables for translation-to-rotation conversion, was proposed in this paper. This device can be put into practical use with an inertia mass amplification element, enabling it to simultaneously achieve the displacement amplification effect. To study the performance of a CBIS on the seismic response mitigation of structures, the motion equations, both with and without flexibility of the cable, were derived and studied based on parametric analysis.

CBIS has the potential for seismic rapid retrofit of structures due to their easy installation and adaptive deployment. In this system, cables are used to convert translational deformation of the primary structure into the rotational motion of the fly wheels; thus, small actual mass can be amplified to large inertance by several hundred times. The proposed cable-bracing system can be adjusted for various frame configurations and design capacities. It can be installed in any direction and part of the structure as long as there exists relative deformation, not limited to horizontal vibration. This cable-bracing system uses simple connections with rapid and adjustable installation. It has the advantages of lower construction cost and easy replacement. The CBIS with a non-contacting damping mechanism shows excellent performance in the adjustable damping ratio by varying the air gap between the permanent magne<sup>t</sup> and the conductor.

The CBIS is an effective structural response mitigation device used to mitigate the response of structural systems under dynamic excitation. The peak and RMS responses of the SDOF structure were reduced after they were equipped with this system. To obtain a more rational parameter set for practical design, the demand-oriented multi-objective optimum design method is used to find the boundary of the feasible criterion space. Using the proposed method, the parameters of the CBIS can be effectively designed to satisfy the target vibration mitigation effects.

The vibration mitigation effect of an SDOF structure with the inerter system was analyzed in this paper. Future research will explore its application to multi-degree of freedom structures. Currently, a physical realization of the CBIS has been developed, and experimental verifications, including free vibration and shaking table tests, are underway.

**Author Contributions:** Conceptualization, L.X. and S.X.; methodology, X.B.; software, X.B., J.K.; validation, K.I.; formal analysis, L.X. and X.B.; data curation, J.K. and S.X.; writing—original draft preparation, X.B.; writing—review and editing, H.T.

**Funding:** This study was supported by the National Natural Science Foundation of China (Grant No. 51478356, No. 51778490), the Key Program for International S&T Cooperation Projects of China (Grant No. 2016YFE0127600), Open Research Fund Program of Guangdong Key Laboratory of Earthquake Engineering and Application Technology (Grant No. 2017B030314068), the Ministry of Science and Technology of China (Grant No. SLDRCE19-B-02), and the National Key R&D Program of China (Grant No. 2017YFC0703607).

**Conflicts of Interest:** The authors declare no conflict of interest.
