Page 286 - Wind Energy Handbook

260 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

R
2 r*
M x (r*) = ∫m(r)Ω r[ y(r) - y(r*)].∆r
r
r* ∆r
Ω
2
M x m(r)Ω r.∆r
y(r)
y(r*)
r*
r

R
2
M y (r*) = ∫m(r)Ω r[x(r) - x(r*)].∆r
r*
∆r
M y 2
x(r*) x(r) m(r)Ω r.∆r
r*
r

Figure 5.24 Restoring Moments due to Centrifugal Force for In-plane and Out-of-plane
Blade Deflections

The Stodola method for deriving blade mode shapes and frequencies described
in the preceding section can be modified to take account of centrifugal effects. In the
case of out-of-plane modes, the procedure is:

(1) assume plausible trial mode shape;
(2) ‘Purify’ trial mode shape of any lower mode content;

2
(3) assume trial value for frequency, ø ;
j
(4) calculate bending moment distribution due to lateral inertia forces according to:
ð R

2
M Y:Lat (r ) ¼ m(r)ø ì(r)[r r ]dr (5:73)
j
r
(5) calculate bending moment distribution due to centrifugal forces according to:
ð R

2
M Y:CF (r ) ¼ m(r)Ù r[ì(r) ì(r )] dr (5:74)
r
(6) calculate combined bending moment distribution;