# Full-System natural frequencies

Hello everyone.

I am comparing the full-system natural frequencies of NREL 5MW baseline wind turbine to my FAST linearization results. The natural frequencies are tabulated in the chapter 9 of “Definition of a 5-MW reference wind turbine for offshore system development”. However, the detailed condition in the linearization analysis is not explained. Could you let me know the exact condition when the natural frequencies are obtained?

1. Rotor speed.
2. Are the tower and blade assumed to cantilever beam when the mode shapes in the appendix are obtained. (I copied the mode shapes below)
3. All the coupled effects among tower, blade, drivetrain, and generator are considered in the linearization analysis? I want to know whether the all modes are “TRUE” in the primary file.

0.0622 BldFl1Sh(2) - Flap mode 1, coeff of x^2
1.7254 BldFl1Sh(3) - , coeff of x^3
-3.2452 BldFl1Sh(4) - , coeff of x^4
4.7131 BldFl1Sh(5) - , coeff of x^5
-2.2555 BldFl1Sh(6) - , coeff of x^6
-0.5809 BldFl2Sh(2) - Flap mode 2, coeff of x^2
1.2067 BldFl2Sh(3) - , coeff of x^3
-15.5349 BldFl2Sh(4) - , coeff of x^4
29.7347 BldFl2Sh(5) - , coeff of x^5
-13.8255 BldFl2Sh(6) - , coeff of x^6
0.3627 BldEdgSh(2) - Edge mode 1, coeff of x^2
2.5337 BldEdgSh(3) - , coeff of x^3
-3.5772 BldEdgSh(4) - , coeff of x^4
2.3760 BldEdgSh(5) - , coeff of x^5
-0.6952 BldEdgSh(6) - , coeff of x^6’

Tower Mode Shape
---------------------- TOWER FORE-AFT MODE SHAPES
0.7004 TwFAM1Sh(2) - Mode 1, coefficient of x^2 term
2.1963 TwFAM1Sh(3) - 0.4857Hz, coefficient of x^3 term
-5.6202 TwFAM1Sh(4) - , coefficient of x^4 term
6.2275 TwFAM1Sh(5) - , coefficient of x^5 term
-2.5040 TwFAM1Sh(6) - , coefficient of x^6 term
-70.5319 TwFAM2Sh(2) - Mode 2, coefficient of x^2 term
-63.7623 TwFAM2Sh(3) - 10.521 Hz , coefficient of x^3 term
289.7369 TwFAM2Sh(4) - , coefficient of x^4 term
-176.5134 TwFAM2Sh(5) - , coefficient of x^5 term
22.0706 TwFAM2Sh(6) - , coefficient of x^6 term
------------------------ TOWER SIDE-TO-SIDE MODE SHAPES --------------------------
1.3850 TwSSM1Sh(2) - Mode 1, coefficient of x^2 term
-1.7684 TwSSM1Sh(3) - 0.3383Hz , coefficient of x^3 term
3.0871 TwSSM1Sh(4) - , coefficient of x^4 term
-2.2395 TwSSM1Sh(5) - , coefficient of x^5 term
0.5357 TwSSM1Sh(6) - , coefficient of x^6 term
-121.2097 TwSSM2Sh(2) - Mode 2, coefficient of x^2 term
184.4151 TwSSM2Sh(3) - 2.0091Hz, coefficient of x^3 term
-224.9037 TwSSM2Sh(4) - , coefficient of x^4 term
298.5360 TwSSM2Sh(5) - , coefficient of x^5 term
-135.8377 TwSSM2Sh(6) - , coefficient of x^6 term

Daniel Kim.

Dear Daniel,

The natural frequencies presented in Table 9-1 of the NREL 5-MW specifications report (nrel.gov/docs/fy09osti/38060.pdf) were derived for a stationary rotor with a locked generator (RotSpeed = 0, GenDOF = False). Results for varying rotor speed and a free generator are presented in the following forum topic: http://forums.nrel.gov/t/campbell-diagram-for-5mw-turbine-rotor/900/1.

Yes, the blade and tower mode shapes specified within the structural model of FAST v7 and the ElastoDyn module of FAST v8 are specified in a cantilevered condition i.e. the slope (coefficient of x^1) and intercept (coefficient of x^0) are assumed to be zero.

Yes, the coupling between the blades, tower, and drivetrain are considered within a FAST linearization analysis (depending on which structural DOFs have been enabled).

Best regards,

Dear Dr. Jason Jonkman

Daniel Kim.

Dear Dr. Jason Jonkman

I have one more question.

When you obtain the full-system natural frequencies in in Table 9-1 of the NREL 5-MW specifications report through the linearization, is the damping matrix considered or only the mass and stiffness matrices are used?

Thank you.
Daniel Kim.

Dear Daniel,

Table 9-1 presents the natural frequencies (undamped).

Best regards,