## 3 Numerical Examples
### Dynamic Coupled Analysis of Turbine and Support Structure-Pile-Soil Interaction  
In this example, the coupled analysis of a NREL 5 MW offshore wind turbine, jacket support structure and structure-pile-soil interaction was performed. The geometry and section properties of the jacket structure were mentioned in the above section. In this case, the pile head was connected with four cylindrical tubes of 55 m depth, 1.5 m diameter and 0.05 m thickness and penetrated the soil. The soil consisted of five layers with the property data given in Figure 13. The piled support structure was considered as the substructure and the soil behavior was predicted as nonlinear soil spring stiffness. The information of the soil stiffness was due to the P-Y, T-Z and Q-Z curve data specific offshore design standard. In addition, the second model of the piled support structure uses the super element concepts to reduce the matrix size and computation time. The basic concept is the condensation of three-dimensional soil stiffness to a single value. The natural frequency analysis of the piled support structure was carried out using the X-SEA program. This analysis was proposed to avoid a non-stationary load, which causes the system resonance when excitation due to the environmental load and natural frequencies being closer to the design chart. The model of the frequency analysis provides the six modes as illustrated in Figure 14. The scaling factor of 25 was used to amplify the jacket support structure shape in the X-SEA program. Figure 12: Comparison of displacement in the y-direction resulted from coupled and uncoupled analyses from the X-SEA program. Figure 13: The jacket support structure with the pile-soil-structure interaction (PSSI) model. In the first mode, the jacket support structure was oscillating globally in the x-direction. The mode shape was the movement of the whole structure with a natural frequency of 2.039 Hz as illustrated in Figure 14a. The second mode shapes were slightly different with a natural frequency of 2.135 Hz and oscillated globally in the opposite x-direction as illustrated in Figure 14b. In the third mode shape, which was the bending mode of the pile structure and without the effect of a whole structure with a natural frequency of 3.343 Hz as illustrated in Figure 14c. The fourth mode shape with a natural frequency of 3.386 Hz had a similar shape to the third mode was oscillating globally in the z-direction as illustrated in Figure 14d. Figure 14: The natural frequencies and mode shape of piled support structure (scaling factor = 25). The fifth mode shape was a torsional mode about the z-direction, where twisting occurred along the structure at the free to end boundary condition with a natural frequency of 4.571 Hz as illustrated in Figure 14e. Whereas the sixth mode shape with a natural frequency of 4.58 Hz was a combination mode due to twisting along the support structure and insignificance at the pile structure as shown in Figure 14f. By comparing the natural frequencies of the fixed support structure, it was obvious that those of the piled-support structure increased 1.351, 1.291, 1.497, 1.599, 1.670 and 1.667 times, respectively, as illustrated in Figure 15. The significant differences in natural frequencies were attributed to the self-weight and soil stiffness along the pile length. It could be concluded that a larger self-weight and soil stiffness leads to the increase in excitation but a decrease in the natural frequencies of the structure. Compared with the fixed support structure, the piled support structure produced a more flexible response with 3.83 times in terms of the maximum values as shown in Figures 16 and 17. The results of the pile using the superelement were identical to that of the piled support structure. Whereas, the resulted displacements in the y-direction had a similar trend as the x-direction but increased 3.13 times in terms of the peak values.