## 4 Conclusions  
This study developed a numerical procedure for the coupled dynamic response analysis between two floats, connecting arms with hinge points, and a bottom-fixed elastic foundation structure under irregular wave conditions. The foundation structure was modeled using three-dimensional beam elements, and its natural frequencies and vibration modes were obtained through modal analysis. The equation of motion of the structure was decomposed into multiple SDOFs using a modal matrix to improve the calculation time. The motion of the floating body was analyzed using an augmented formulation, one of the multi-body dynamics techniques. The frequency-dependent hydrodynamic coefficients of the dual floating body were obtained using WAMIT, a hydrodynamic solver. The float was modeled with many quadrilateral elements, and the body-nonlinear Froude-Krylov based on linear wave theory and hydrostatic forces were calculated with respect to the instantaneous wetted body surface at every time step. The respective steps of the present hydrodynamics results were compared with the published results, and they showed good agreement.  
Using the developed time-domain program, the fully coupled dynamics of a dual-buoy Wavestar WECs connected to an elastic foundation structure were investigated for a typical irregular wave condition in a Korean nearshore region. First, after coupled dynamic analysis considering the influences of the WECs, the maximum values of the displacement and stress of the foundation structure were increased 10- and 2.2-fold, respectively. The RMS values of the stresses were also increased by approximately 20% by the influence of the WECs. The results underscore that this kind of fully coupled dynamic analysis is essential for a reliable estimation of the fatigue life of the system. The increased dynamic responses of the foundation structure directly affect the forces transmitted to the WECs, but they have little influence on the motion of the floats and the corresponding generated power outputs.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Float** & **Average** & **Maximum** & **RMS** & **Standard Deviation** \\ \hline \multirow{2}{*}{Coupled analysis} & Float 1 & 1.847 & 58.62 & 3.34 & 2.78 \\  & Float 2 & 2.206 & 74.98 & 4.14 & 3.50 \\ \hline \multirow{2}{*}{Fixed platform analysis} & Float 1 & 1.862 & 92.32 & 3.81 & 3.32 \\  & Float 2 & 2.169 & 74.53 & 4.10 & 3.48 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Statistics of the produced wave power (unit: kW).  
Figure 17: Time histories of produced wave power: (**a**) Float 1; (**b**) Float 2.  
Interestingly, the average power production of Float 2 (rear) was slightly larger than that of Float 1 (front) because of two-body hydrodynamic interactions and other coupled effects. Considering the coupled effects with platform elasticity, the power fluctuation (standard deviation) is reduced slightly, which benefits the electric system. Overall, the coupled dynamic analysis is essential to the reliable performance evaluation and design of such a system.  
Conceptualization, S.H. and W.K.; methodology, S.H. and W.K.; software, S.H. and W.K.; validation, S.H.; formal analysis, S.H. and W.K.; investigation, S.H. and W.K.; writing--original draft preparation, S.H.; writing--review and editing, S.H., M.-H.K. and W.K.; supervision, M.-H.K. and W.K.; project administration, W.K.; funding acquisition, W.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by INHA UNIVERSITY Research Grant.  
Not applicable.  
The authors declare no conflict of interest.