## 5 Summary and Conclusions  
Many studies have reported the change of dynamic characteristics of built-up structures with an increase in internal energy. Previous studies used the Iwan model to investigate the change of dynamic characteristics by the slip phenomenon on the contact interface. In general, the Iwan model consists of four parameters \(\{\chi,K_{T},\)\(\mathrm{F_{S}},\) and \(\beta\}\), where \(\{\chi\) and \(K_{T}\}\) represent the change of dynamic characteristics in the micro-slip regime, and \(\{\mathrm{F_{S}}\) and \(\beta\}\) determine the characteristics at the border line of the micro- and macro-slip regimes. In this study, it is assumed that built-up structures vibrate only in the micro-slip regime. To estimate the two parameters that determine the dynamic characteristics in the micro-slip regime, modal analysis is done instead of quasi-static experiments, which were used in the previous studies. Further, modal equations for each mode of the built-up structures were derived. A technique to estimate two parameters using the derived modal equations was proposed.  
In this study, to estimate the variation of natural frequency and damping ratio according to the change in internal energy or external force, the slip phenomenon occurring at the built-up structure's interface was described using the Iwan model. Based on this model, the variation of natural frequency and damping ratio were estimated. The proposed method was developed and tested to estimate two out of the four parameters, which define the Iwan model. The study used modal analysis. In this process, the force variation occurring in the constitutive model during dynamic behavior was investigated. The numerical model for the full system was examined. In addition, the numerical model and modal analysis were combined to determine a method that could estimate the parameters using variations in the damping magnitude. This proposed method was verified through simulations. The characteristics of the results were examined. To verify the proposed method, 10 experiments were performed using a partially connected double beam structure with increasing external force. Two parameters of the Iwan model were estimated by applying the proposed method to the first seven experiments. The estimated parameters were then used to determine the dynamic characteristics for the remaining three experiments. We could, thus, confirm the reliability of the proposed method.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Order of Expt.** & **Measured (\%)** & **Estimated (\%)** & **Error (\%)** \\ \hline \(1^{\mathrm{st}}\) to \(2^{\mathrm{nd}}\) & \(6.072\times\mathrm{e}^{-4}\) & \(\ast\) & \(\ast\) \\ \(2^{\mathrm{nd}}\) to \(3^{\mathrm{rd}}\) & \(-4.385\times\mathrm{e}^{-4}\) & \(\ast\) & \(\ast\) \\ \(3^{\mathrm{rd}}\) to \(4^{\mathrm{th}}\) & \(2.457\times\mathrm{e}^{-4}\) & \(\ast\) & \(\ast\) \\ \(4^{\mathrm{th}}\) to \(5^{\mathrm{th}}\) & \(1.167\times\mathrm{e}^{-3}\) & \(\ast\) & \(\ast\) \\ \(5^{\mathrm{th}}\) to \(6^{\mathrm{th}}\) & \(2.118\times\mathrm{e}^{-3}\) & \(\ast\) & \(\ast\) \\ \(6^{\mathrm{th}}\) to \(7^{\mathrm{th}}\) & \(3.804\times\mathrm{e}^{-3}\) & \(\ast\) & \(\ast\) \\ \(7^{\mathrm{th}}\) to \(8^{\mathrm{th}}\) & \(4.122\times\mathrm{e}^{-3}\) & \(4.012\times\mathrm{e}^{-3}\) & \(-2.67\) \\ \(8^{\mathrm{th}}\) to \(9^{\mathrm{th}}\) & \(5.569\times\mathrm{e}^{-3}\) & \(5.329\times\mathrm{e}^{-3}\) & \(-4.30\) \\ \(9^{\mathrm{th}}\) to \(10^{\mathrm{th}}\) & \(9.583\times\mathrm{e}^{-3}\) & \(8.280\times\mathrm{e}^{-3}\) & \(-13.60\) \\ \hline \end{tabular}
\end{table}
Table 5: List of \(\Delta\zeta_{\mathrm{Jp}}\) between successive experiments.  
**Funding:** This work was supported by the Dong-A University research fund.  
**Conflicts of Interest:** The authors declare no conflict of interest.