3.3.2. Tower

Similarly, the free vibrations of the tower are compared. The modes considered in the aeroelastic tool are the first and second fore-aft modes and the first side-side mode. Natural frequencies are shown in Table 2 and mode shapes are shown in Figures 8 and 9.


**Table 2.** Natural frequencies for the tower: single rotor configuration.

**Figure 8.** Tower fore-aft mode shapes: single rotor configuration.

**Figure 9.** Tower side-side mode shape: single rotor configuration.

Natural frequencies as well as mode shapes of the tower show agreemen<sup>t</sup> between the results of Modes compared to the reference.

With the aerodynamic steady state response and the structure dynamic response verified separately, the next step is validation of the aeroelastic tool, where both aerodynamics and the structure of the turbine are coupled.

## *3.4. Aeroelastic Analysis*

In this subsection, the coupling between the aerodynamic loads and the structural behavior is introduced. The aerodynamic loads affecting the blades cause deformation, and hence the relative velocities on the blade sections are changed. Inertial loads generated from the blade vibration also affect the structural behavior. The effects of blade vibrations are considered every time step in the simulation to catch the aeroelastic behavior for both the blades and the tower.

For validation of the results, a FAST simulation is made for the NREL 5MW wind turbine blades and tower, using the same simulation conditions as in the in-house tool. The blades are subject to a constant wind speed and are rotating at a constant angular speed. Simulation parameters are as follows:

