Connecting a flexible supporting element to an inerter arranged in parallel with a viscous element yields a tuned‐mass damper‐like system, designated as a tuned viscous mass damper (TVMD). The advantage of a TVMD is that it exploits the flexibility of the supporting member, which is usually considered to compromise the energy‐dissipating performance, and the inerter and soft spring form a supplemental oscillator to enhance the damping performance with resonance to the primary structure. The fixed‐point method for the optimal design of a single‐degree‐of‐freedom structure containing a TVMD is further expanded to a multidegree‐of‐freedom structure, in which a TVMD is arranged concentratedly. Furthermore, approximated closed‐form formulae for a concentratedly arranged TVMD are derived under the assumption that the primary structure is undamped, remains in an elastic range, and the target mode dominates the response of the structure. An analytical example illustrates that installing a TVMD spanning three stories in a concentrated manner based on the proposed design methods ensures the efficiency of the damping system, which demonstrates a damping effect similar to that of stiffness‐proportionally distributed TVMDs with less demand for inertance and total control force, thus resulting in a lower cost.

In this paper, cables are proposed to connect the inerter and main frame for translation-to-rotation conversion, i.e., the cable-bracing inerter system (CBIS), with a magnified mass and enhanced damping effect. This novel configuration has the benefits of deformation relaxation at the connecting joints, easy installation, and an adaptive layout for nonconsecutive-story deployment. Dynamic motion equations were established for a single degree-of-freedom (SDOF) model equipped with a CBIS. The influence of dimensionless parameters, such as inertance-mass ratio, stiffness ratio and additional damping ratio on vibration mitigation were studied in terms of displacement response and force output. A single objective and multiple objective optimal design method were developed for a CBIS-equipped structure based on a performance-oriented design framework. Finally, the mitigation effect was illustrated and verified by a numerical simulation in a time-domain. The results showed that a CBIS is an effective structural response mitigation device used to mitigate the response of structural systems under earthquake excitation. Using the proposed optimization method, CBIS parameters can be effectively designed to satisfy the target vibration control level.

Inerter-based vibration control systems have been developed rapidly in recent years. However, previous studies mainly focus on the development of new devices and parameter optimization strategies, while ignoring the improvements in the utilization efficiency of the inerter system that the bracing system and novel installation methods may bring. In this paper, a cross-layer installed cable-bracing inerter system (CICBIS) is proposed to improve the utilization efficiency of the inerter system, which can cross more layers and is suitable for shear-type multi-degree-of-freedom (MDOF) structures. A demand-based cable-bracing inerter system (CBIS) design method is developed. The mass enhancement and utilization efficiency improvement of the inerter system caused by the cross-layer installation are quantified through calculating the effective inerter-mass ratio of the CBIS-equipped MDOF structure. A 10-story benchmark structure is used to verify the control performance of the CICBIS and the design method. The analysis results show that the proposed design method can exert the cable-bracing system’s adjustability and the damping enhancement of the inerter system. The CICBIS can reduce the total apparent mass and damping coefficient requirements of the inerter systems without increasing the control force. It means that the proposed design method is effective, and the CICBIS has a high efficiency.