Dynamic Strength - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 121

by.A-A.and.the.volume.of.the.region.above.this.plane,.by.V,.while.ρ.is.des-
ignated.the.mass.density,.ω.the.angular.velocity,.r.is.the.radius.of.rotating.
blade,.and.the.components.of.the.force.acting.on.the.cross.section.A-A.are.
given.by:

. Fx.=.ρω 2 ⌠ v cosθ.r 2 x.dr.dθ.dx. (5.1)

. Fx.=.Fy.=.ρω 2 ⌠ v cosθ.r 2 x.dr.dθ.dx. .(5.2)

While.the.moments.about.the.x,.y,.z.axis.are:

. M x. =.ρ.ω 2 ⌠.r 2 .sinθ.dr.dθ.dx. (5.3)

. M y. =.ρ.ω 2 ⌠x.r 2 .cosθ.dr.dθ.dx. (5.4)

. M z. =.ρ.ω 2 ⌠x.r 2 .sinθ.dr.dθ.dx. (5.5)

Here:
θ.is.the.angle.of.the.rotating.blade.
Equation.(1.1).to.Equation.(1.5).can.be.solved.as:

. Fz.=.-.ρω 2 x.r 3 /3.cosθ. (5.6)

. Fx.=.Fy.=.ρω 2 x.r 3 /3.sinθ.. (5.7)

. M x R. =.-.ρ.ω 2 x.cosθ.r 3 /3. (5.8)

. M y R .=.-.ρ.ω 2 x 2 .cosθ.r 3 /6. (5.9)

. M z R .=.-.ρ.ω 2 x 2 .sinθ.r 3 /6. (5.10)

5.3 TheoreticalInvestigation

In. the. linear. performance,. relationship. between. the. acting. forces. and. the.
linear.deformation.in.the.matrix.forming.the.following.was.established:

Fz,Fy,Fx Q Q Q Q ε

ε ε X ε R εθ

M

R

Q Q Q Q

z X ε X xR X θ Z

. . (5.11)

M

R

Q Q Q Q

y R ε Rx R R θ R

M

R

Q Q Q Q

x θε θ x θ y θ θ