I am working on some modelling of blade displacements under load. In computing the in-plane and out-of-plane mode shapes, I understand the flapwise and edgewise modes need to be transformed first. For simplicity, I am using the mode shape curve fits from the OpenFAST input file (currently from the 5MW turbine). My question is about how these mode shapes are oriented. Does the flapwise mode shape account for structural twist of the blade? In other words, if I want to transform the flapwise and edgewise modes into an “out-of-plane” mode shape, would I need to account for the twist angle in addition to blade pitch?

So for example, taking the 5MW distributed blade structural twist:

```
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.3080000000000
13.1810000000000
12.8480000000000
12.1920000000000
11.5610000000000
11.0720000000000
10.7920000000000
10.2320000000000
9.67200000000000
9.11000000000000
8.53400000000000
7.93200000000000
7.32100000000000
6.71100000000000
6.12200000000000
5.54600000000000
4.97100000000000
4.40100000000000
3.83400000000000
3.33200000000000
2.89000000000000
2.50300000000000
2.11600000000000
1.73000000000000
1.34200000000000
0.954000000000000
0.760000000000000
0.574000000000000
0.404000000000000
0.319000000000000
0.253000000000000
0.216000000000000
0.178000000000000
0.140000000000000
0.101000000000000
0.0620000000000000
0.0230000000000000
0
```

To transform the mode shape into an out-of-plane shape for 0 degrees of blade pitch, Matlab pseudo-code could look something like this:

```
for i = 1:length(bnodes)
OoP_mode(i) = Flap_mode * cos(twist_angle) + Edge_mode * sin(twist_angle)
end
```

Or are the flapwise and edgwise modes based on a fixed point, such that only the blade pitch is relevant?

Dear @Ian.Ammerman,

The flapwise and edgewise mode shapes used in ElastoDyn are mode shapes that follow the principle axes of bending (oriented by the local structural twist). So, I agree that you must take into account the local structural twist to find the out-of-plane and in-plane mode shapes (which are called “twisted shape functions” in the ElastoDyn theory documentation). However, I don’t agree with your equation because the mode shapes must be found by double integrating the curvature, where the curvature is defined about the principle axes of bending. A similar question was discussed in the following forum post: Coupled blade modes in FAST and the full equations implemented in ElastoDyn are documented in the ElastoDyn Theory Manual: 4.2.7. ElastoDyn Users Guide and Theory Manual — OpenFAST v3.5.3 documentation.

Best regards,

Dear @Jason.Jonkman ,

Thank you for the response. I have spent some time reviewing the linked post and documentation which was helpful but I still have a couple of questions.

Firstly, regarding the twisted shape functions; in the documentation they are defined as follows:

Noting the r’’ term, does that mean that the integral is taken with respect to the second derivative of the radial distance? From a practical frame, using something like trapz in Matlab to integrate, would I need to differentiate my radius vector before integrating these terms?

Secondy, my goal ultimately is to focus on just the flapwise bending mode for simplicity to start. I initially thought that the twisted mode shapes would be required for this, but perhaps not? I am taking a rotating frame of reference at the hub which rotates with the blade such that i-hat is directed down the blade and k-hat is directed into the rotor plane. During flapwise displacement, the blade will displace primarily in the k-hat direction, but due to twist should also displace some in the j-hat direction as well. Given this, to compute the displacement vector for a blade element r distance from the hub, does the flapwise mode shape indicate displacement in the local flapwise direction? Such that I could write my position vector in the rotating frame as follows:

Where Beta is the twist angle and qB is the generalized displacement corresponding to the blade flapwise mode. Is this a valid approach?

Best,

Ian

Dear @Ian.Ammerman,

Regarding r’’ and r’, these are not the first and second derivatives of r; rather, these are “dummy” variables (i.e., different names for the same variable) because the outermost integral is from 0 to r, so, the integral can’t make use of dr directly.

Regarding your second question, no, the flapwise deflection cannot be assumed to occur along the principle axis of bending. It is the flapwise curvature that takes place about the principle axis of bending, and the deflection is found be double integrating this curvature, i.e., as is done in the twisted shape functions.

Best regards,