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.

The "Meiyuanshi-stone", who has witnessed the prosperous of the Maritime Silk Road, has attracted the attention of scholars in China, Japan, and South Korea in recent years. Meiyuanshi-stone was prestige material for carving, figures or building elements of temples. Not only for authentical conservation of such stone monuments, the features of Meiyuanshi-stone provide the most direct physical information for confirming similar stone materials in China, Japan, and countries around the Maritime Silk Road. Aiming to define Mieyuanshi-stone, petrographic and geochemical investigations of rocks were carried out on samples collected from quarries and the Sumeru seat in the main hall of Baoguosi (Ningbo, Zhejiang, China). The integrated chemical data acquired by inductively coupled plasma-mass spectrometry (ICP-MS) and X-Ray Diffraction (XRD) analysis, along with petrographic data, allowed us to ascertain the compositions of raw materials. Through comparison of petrographic features, major and trace elements contents of Meiyuanshi-, Xiaoxishi-, and Dayinshi-stone, it has been concluded that Meiyuanshi-stone is massive (no internal stratification), thick structureless, well sorted, and fine-grained trachytic tuff. By comparing petrographic and chemical features, we were able to confirm that the Sumeru seat in Baoguosi is made of Meiyuanshi-stone.