The natural frequency of the NREL 5-MW turbine's tower

Wind & Water Structural Analysis
1

屏幕截图 2025-03-19 030554
屏幕截图 2025-03-19 0305541060×1066 55.4 KB


TR(1)=10     ;
TR(2)=17.76  ;
TR(3)=25.52  ;
TR(4)=33.28  ;
TR(5)=41.04  ;
TR(6)=48.8   ;
TR(7)=56.56  ;
TR(8)=64.32  ;
TR(9)=72.08  ;
TR(10)=79.84  ;
TR(11)=87.6   ;
    
TD(1)= 5.5908700e+03 ;     
TD(2)= 5.2324300e+03 ;     
TD(3)= 4.8857600e+03 ;     
TD(4)= 4.5508700e+03 ;     
TD(5)= 4.2277500e+03 ;     
TD(6)= 3.9164100e+03 ;     
TD(7)= 3.6168300e+03 ;     
TD(8)= 3.3290300e+03 ;     
TD(9)= 3.0530100e+03 ;     
TD(10)=2.7887500e+03 ;    
TD(11)=2.5362700e+03 ;    
                    
Tk(1)= 6.1434300e+11    ;
Tk(2)= 5.3482100e+11    ;
Tk(3)= 4.6326700e+11    ;
Tk(4)= 3.9913100e+11    ;
Tk(5)= 3.4188300e+11    ;
Tk(6)= 2.9101100e+11    ;
Tk(7)= 2.4602700e+11    ;
Tk(8)= 2.0645700e+11    ;
Tk(9)= 1.7185100e+11    ;
Tk(10)=1.4177600e+11   ;
Tk(11)=1.1582000e+11   ;
x_Tgang=(TR-10)/77.6;
faiT_r_out     =   -2.504*x_Tgang.^6  +6.2275*x_Tgang.^5  -5.6202*x_Tgang.^4     +2.1963*x_Tgang.^3     +0.7004*x_Tgang.^2;
faiT_r_in      =   0.5357*x_Tgang.^6  -2.2395*x_Tgang.^5  +3.0871*x_Tgang.^4     -1.7684*x_Tgang.^3     +1.385*x_Tgang.^2;
faiT_r_out_dot =(-2.504*6*x_Tgang.^5  +6.2275*5*x_Tgang.^4-5.6202*4*x_Tgang.^3   +2.1963*3*x_Tgang.^2   +0.7004*2*x_Tgang.^1)/77.6;
faiT_r_in_dot  =(0.5357*6*x_Tgang.^5  -2.2395*5*x_Tgang.^4+3.0871*4*x_Tgang.^3   -1.7684*3*x_Tgang.^2   +1.385*2*x_Tgang.^1)/77.6;
faiT_r_out_dot2=(-2.504*6*5*x_Tgang.^4+6.2275*5*4*x_Tgang.^3-5.6202*4*3*x_Tgang.^2+2.1963*3*2*x_Tgang.^1+0.7004*2)/(77.6^2);
faiT_r_in_dot2 =(0.5357*6*5*x_Tgang.^4-2.2395*5*4*x_Tgang.^3+3.0871*4*3*x_Tgang.^2-1.7684*3*2*x_Tgang.^1+1.385*2)/(77.6^2);

Mn_in= trapz(TR,TD.*(faiT_r_in.^2)) +240000+56780;
Mn_out=trapz(TR,TD.*(faiT_r_out.^2))+240000+56780;
Kn_out=trapz(TR,Tk.*(faiT_r_out_dot2.^2));
Kn_in=trapz(TR,Tk.*(faiT_r_in_dot2.^2));
(Kn_in/Mn_in)^0.5/2/pi
(Kn_out/Mn_out)^0.5/2/pi

I would be appreciated it if you could reply. Thank you :smiley:
Best regards
Yingxin

2

Dear @Yingxin.Lv,

I agree with your approach, but I see a few issues:

  • The land-based version of NREL 5-MW baseline wind turbine has a tower that should start at 0 rather than 10 m, so, h, should extend between 0 and 87.6 m.
  • The tower-top mass should include not only the nacelle and hub, but also the blades; i.e., the full rotor-nacelle-assembly (RNA).
  • Your equation misses the RNA center of mass, RNA inertias, and the impact of blade flexibility on the tower natural frequencies.

Best regards,

2 Likes
3

Dear Dr. Jonkman,
According to your guidance, the modifications have been effective. Thank you very much for your reply
Best regards,