## 1 Test description

In this test we compare the eigenfrequencies of an isolated IEA 15-MW blade given in Table 2.1 of Gaertner et al. (2020) to results obtained in Ashes in a time domain simulation.

## 2 Model

The IEA 15-MW blade can be found in the Blade database. The blade is fixed at its root, and its 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
$$1\text{ m}\cdot\text{s}^{-1}$$
. This ensures that the motion of the model will be purely harmonic, i.e. if the 1st mode shape is chosen to scale the velocities, only 1st mode motion will be observed in the simulation.

Neither Rayleigh nor numerical damping are applied, and gravity and aerodynamic loads are disabled, therefore no decay in the motion of the blade is expected. The frequency of oscillation of the tip of the blade in-plane and ou-of-plane is then observed and compared to the data in Table 2.1 of Gaertner et al. (2020)

Note: in this test we only compare the frequency of oscillation of the in-plane or out-of-plane tip displacement, and not its amplitude. The in-plane and out-of-plane displacement are coupled, and to our knowledge there is no benchmark available showing a decomposition of tip displacement into in-plane and out-of-plane.

## 3 Benchmarks

In the following sections, the different modeshapes are illustrated and the expected eigenfrequencies as listed in Gaertner et al. (2020) are given.

### 3.1 First flapwise mode

The expected eigenfrequency is
$$f_1 = 0.555 \text{ Hz}$$
. The mode shape is illustrated in the figure below:

### 3.2 First edgewise mode

The expected eigenfrequency is
$$f_2 =0.642\text{ Hz}$$
. The mode shape is illustrated in the figure below:

## 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 test is considered passed if the values form Ashes are within 5% of the values from the specification document.

The report for this test can be found on the following link: