In this paper, the mechanical model of grotto–eave system with cable inerter viscous damper (CIVD) is established, and the vibration control equations are established. Firstly, the stochastic response is carried out, and the optimization design of design parameters of CIVD is carried out for the grotto–eave systems with different connection types. Finally, the vibration mitigation control performance of CIVD under different seismic inputs is analyzed. The research shows that in the optimal design of CIVD, the inerter–mass ratio and damping ratio should be reduced as much as possible to improve the feasibility of the application of CIVD in cultural relics protection engineering under the condition of meeting the target damping ratio. The demand-based optimal method can minimize the cost by enhancing damping element deformation in a small damping ratio, while ensuring that the value of displacement index of grotto–eave system can be reached. Hence, the deformation and damping force of CIVD will increase simultaneously due to the efficient tuning and damping amplification of CIVD. CIVD can enlarge the apparent mass through rotation and damping force through enhancement deformation. Hence, compared with other conventional dampers (such as viscous damper), optimal CIVD has lower damping ratio under the same demand index of grotto–eave system. It can be realized that the lightweight and high efficiency of the damper, and can be applied to the vibration mitigation and reinforcement of the grotto–eave system.
In this paper, parameter analyses of a tuned inerter damper (TID) are carried out based on the displacement mitigation ratio. The optimal design of TID based on the closed-form solution method is carried out and compared with the fixed-point method. Meanwhile, applicable conditions of two methods are discussed in wider range of values of objective function under different inherent damping ratios. Finally, seismic responses of SDOF system with TID are carried out, which verifies the feasibility of the closed-form solution optimization method. Compared with the fixed-point method, the inherent damping ratio of the original structure is considered in the closed-form solution method, and the optimal damping ratio of a TID is smaller than that of the fixed-point method under same displacement mitigation ratio. The parameters’ combination of a TID designed by the fixed-point method obtains a vibration mitigation effect with a larger damping ratio by cooperating with the deformation enhancement effect of the inerter, which may make the vibration mitigation effect of the TID lower than that of the VD in structures with large inherent damping ratios. However, the deformation enhancement effect on the damping element of the inerter can be fully used by using the closed-form solution method. Better applicability and robustness are shown in closed-form solution method. Under the same displacement mitigation ratio, the damping ratio of a TID obtained by using the closed-form solution method is about one tenth of that obtained by using the fixed-point method, which can realize the lightweight design of the TID.
In this paper, a mechanical model of a transformer–bushing with an inerter isolation system (IIS) is established. An IIS is composed of an inerter element, a damping element, and a spring element connected in parallel between the same two terminals. Vibration control equations and frequency response functions are also established. The influence of parameters on IIS, including inerter–mass ratio, damping ratio, and frequency ratio, was studied. In the extremum condition that represents the most efficient parameter set of inerter–mass ratio and damping ratio for relative displacement response ratio, an optimal design method was developed by exploiting a performance demand. Finally, the seismic response of the transformer–bushing with IIS was carried out to verify the isolation performance of IIS. The research shows that the equivalent mass coefficient and damping coefficient of IIS can be amplified by an inerter element and the inerter–mass ratio and damping ratio are reduced simultaneously under the conditions of meeting the performance demand after parameter optimization. Meanwhile, the parameter optimization design method proved to be effective for meeting the target demand of the relative displacement response of the bushing and tank, while base shear force and isolation displacement were reduced simultaneously. Based on the results from a response history analysis under ground motion records, IISs can significantly suppress the resonance response of a structure and the continuous vibration response in the stable state. The peak displacement can be reduced by 50% compared with a traditional isolation system.
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