## 2 Evaluation Strategy for MIMM at Electric Power Generator  
The electric power plant was developed using a 3-d.o.f. system including the MIMM. The original system model was consistent with those developed in previous studies [23,24]. However, the target system model is an extended version derived from the original by incorporating variable stiffness and damping coefficients in both the upper and lower sub-mounts, as illustrated in Figure 1. The electric power plant, mass block, and surrounding building were modeled as concentrated masses \(M_{p}\), \(M_{M}\), and \(M_{B}\), respectively. The connecting element between the electric power plant and the mass block was expressed by the upper sub-mount (spring \(K_{p}\), damper \(C_{p}\)), and the lower sub-mount was placed between the mass block and surrounding building by spring \(K_{p}\) and damper \(C_{p}\), respectively. The  
Figure 2: Main components of MIMM of electric power plant. variations in the connecting element were indicated by the symbol \(\Delta\); for example, \(K_{p}(\Delta)\) is the adjusted coefficient obtained by adding \(\Delta K_{p}\) to \(K_{p}\). A low stiffness value for \(K_{B}\) was chosen to prevent the building system dynamics from affecting the MIMM. In addition, self-excitation from the electric power plant was assigned at \(F_{p}\) and the basement input from the surrounding building was set for \(F_{B}\), respectively. The theoretical model of an electric power plant supported by the MIMM is illustrated in Figure 3.  
The theoretical model for the supported power generator in Figure 3 can be expressed as a linear formula because all connecting elements consist of linear connecting elements: the stiffness coefficient is proportional to the displacement and the damping coefficient is proportional to the velocity. Based on an earlier study [24], the governing equations are expressed as Equations (1)-(3). The displacements of the three concentrated masses \(M_{p}\), \(M_{M}\), and \(M_{B}\), were denoted by \(X_{p}\), \(X_{M}\), and \(X_{B}\), respectively. \[M_{p}\ddot{X}_{p}+C_{p}(\Delta)\dot{X}_{p}+K_{p}(\Delta)X_{p}=C_{p}(\Delta) \dot{X}_{M}+K_{p}(\Delta)X_{M}+F_{p}, \tag{1}\]  
\[ \begin{split} M_{M}\ddot{X}_{M}+\big{(}C_{p}(\Delta)& +C_{M}(\Delta)\big{)}\dot{X}_{M}+\big{(}K_{p}(\Delta)+K_{M}(\Delta) \big{)}X_{M}\\ &=C_{p}(\Delta)\dot{X}_{p}+K_{p}(\Delta)X_{p}+C_{M}(\Delta)\dot{ X}_{B}+K_{M}(\Delta)\dot{X}_{B},\end{split}  \tag{2}\]  
\[M_{B}\ddot{X}_{B}+C_{M}(\Delta)\dot{X}_{B}+(K_{M}(\Delta)+K_{B})X_{B}=C_{M}( \Delta)\dot{X}_{M}+K_{M}(\Delta)X_{M}+F_{B}. \tag{3}\]  
The original system model parameters listed in Table 1 were determined experimentally based on the required characteristics of the system. The mechanical properties of the upper sub-mount (spring \(K_{p}\), damper \(C_{p}\)) were measured using elastomer testing equipment (835 model/MTS systems, Eden Prairie, Minnesota, United States). The mechanical properties of the lower sub-mount (spring \(K_{M}\), damper \(C_{M}\)) were adjusted from the values of the upper sub-mount, and two masses (\(M_{p}\), \(M_{M}\)) were obtained using simple measurements. The mechanical properties (\(M_{B}\), \(K_{B}\)) of the surrounding buildings were selected as rigid bodies with low resonance frequencies in the frequency range 1-120 Hz. The experimental frequency response function between the target electric power plant and the mass block was used to update the constructed 3-d.o.f. model in Figure 3, and the detailed  
Figure 3: Equivalent electric power generator model supported by vibration isolators. selection of the system parameters is explained in an earlier study [23]. A summary of the current system model is listed in Table 1.  
The solution for the three displacement variables can be effectively obtained through Fourier transforms, therein the variable's' is substituted with '\(j\omega\)' in the Equations (1)-(3) originally formulated in the Laplace domain. Two performance indices developed in earlier studies [23,24] were reused.