# Mass matrix Theoretical calculations of Blade

Dear Jason,
I am trying to calculate Mass matrix of a rotor blade ultimately to find the bending and torsional modes. If I consider blade as Ellipse then the polar coordinates will be (x,r cos[phi], r sin [phi]). But my professor suggested me to consider it as an airfoil. Is it possible to take the polar coordinates for any regular normal airfoil? If so, Can you please tell me how.
The calculations are coded in c# and using the classes from SiWEC, the values are found using SiWEC programming.
Also, Please explain how can we take the angle of deflection(rotation) of the blade around X-axis due to aerodyn loads? (I mean sum of any angles or angle b/w chord and any other axis.)
Where can I get the data of blade which contains edgewise,flapwise and Torsional stiffness, Inertia, mass, twist, chord length and thickness along the length of the blade? Please suggest

Dear Kamineni,

I’m sorry, but I don’t really understand your question regarding polar coordinates or aerodynamic loads.

Regarding your question on blade structural and aerodynamic data, for which wind turbine are you asking for this data?

Best regards,

where R is the vector in reference configuration,
ui(R, t) = Φ(R)q(t) is displacement field vector,
Φ(R) is the assumption function.
we can derive corresponding approach functions ϕ_i (x),ϕ_j (x) and ϕ_t (x).

where rcos(phi) and rsin(phi) are the polar coordinates of the ellipse, and radius is given as

the above calculations will be appropriate if the ellipse is considered, but can we calculate radius from the centre of axis to point on the airfoil(not, in particular, any regular airfoil). if so can you please explain how?

Dear Jason,

I am unable to attach the 4th image so I am writing separately,

how the beta(rotation) is taken, it is shown in the figure but there is no particular explanation. can you explain in detail or provide any reference.

Sir, I need the data of any regular airfoil just for testing case, I cannot take random values because it needs to be realistic.

Hope I am clear, Thank you for answering patiently.

Dear Kamineni,

The approach implemented in the structural modules of FAST (ElastoDyn, BeamDyn, SubDyn) is different than the approach you are describing, and I’m not familiar enough with the details of the approach you are describing to comment.

Regarding airfoil properties, I guess you are asking about a detailed composite layup. There is some discussion about this for the NREL 5-MW baseline turbine in the following forum post: http://forums.nrel.gov/t/structural-design-of-the-wind-turbine-blade/271/1 (particularly Brian’s post dated Jul 08, 2013). You’ll also be able to find realistic examples of the composite layups for wind turbine blade airfoils in the archives of various sectional analysis tools e.g. VABS, BECAS, NuMAD/BPE, PreComp, etc.

Best regards,

Dear Jason,
Thanks for your suggestions and also discussion in “Definition of Parameters” helped a lot.
Thank you