## 1 Test description

In this load case, we compare the eigenfrequencies of the model between aeroelastic software. The results are given in figure 6 in Jonkman et al. (2010f).

## 2 Model

The model is the Offhsore NREL 5-MW reference wind turbine, which corresponds to the offshore template in Ashes. For each comparison, the correpsponding mode shape is applied as initial conditions, as is done in Decay test : For each load case, at the beginning of the simulation
$$t=0$$
, all nodes are constrained to move at a given velocity and the constraint is then removed for
$$t>0$$
. The velocity applied at each node is scaled with the displacement of that node for a given mode shape, and normalized so that the maximum velocity is
$$1\text{ m}\cdot{s}^{-1}$$
.

Note: in this benchmark, we only compare the frequency of oscillation of the response (hub node displacement for tower modes, tip displacement for blade modes), and not the amplitude.

## 3 Benchmarks

In the following sections, the different mode shapes are illustrated.

## 4 Results

A time simulation with the aforementioned initial conditions is run for 10 seconds. The average oscillation period during these 10 seconds is then compared to the expected values.
The expected values for the eigenfrequencies corresponding to the modes deicted in the previous section can be found in Figure 6 of Jonkman et al. (2010f). In this benchmark, we compare the results produced bt Ashes to the median of all the results submitted by the participants. The test is considered passed if the results from Ashes are within one standard deviation of the median.

The table below sumarises the median and the standard deviation for each mode.

 Mode Median [Hz] Standard Deviation [Hz] First Tower Fore-Aft 0.2785 0.004854 First Tower Side-to-Side 0.2773 0.004582 First Blade Collective Flap 0.6955 0.01434 First Blade Asymmetric Flapwise Pitch 0.6643 0.01431 First Blade Asymmetric Flapwise Yaw 0.6288 0.02937 First Blade Asymmetric Edgewise Pitch 1.0769 0.01186 First Blade Asymmetric Edgewise Yaw 1.0870 0.01018 Second Tower Fore-Aft 2.414 0.1393 Second Tower Side-to-Side 2.3453 0.0536 Second Blade Collective Flap 1.959 0.05151 Second Blade Asymmetric Flapwise Pitch 1.8118 0.0531 Second Blade Asymmetric Flapwise Yaw 1.685 0.1517