Dynamic Strength - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 128

A(Q 11. -.mΩ 2 ).=.(L.-.D.-.W.sin.θ).sinΩt.and.δΩA.=.(L.-.D.-.W.sin.θ).sinΩt.(5.39)

The.phase.angle.ϕ.relects.a.different.phase.between.the.applied.force.and.
the.resulting.vibration.and.is.determined.as:

δ Ω

. tan φ = . (5.40.)

2

Q 11 - m Ω

The.sine.and.cosine.function.can.be.eliminated:

. AδΩ.+.A(Q 11 -mΩ 2 ).=.(L.-.D.-.W.sin.θ). (5.41)

The.forcing.frequency.Ω.can.be.determined.if.tanϕ.=.1.as:

Ω=.(.Q 11 A.-.(L.-.D.-.W.sin.θ)./mA) 1/2 . .(5.42)

The. forcing. frequency. Ω. has. never. been. it. with. a. natural. frequency. f,.
which.avoids.parametric.resonance..Submitting.two.boundary.conditions:

Ωt.-.ϕ=.0;.or.Ωt.-.ϕ=.π/2.results.in:

δΩA.=.(L.-.D.-.W.sin.θ).sinΩt. (5.43)

. -mΩ 2 t 2 A.+.Q 11 A.=.(L.-.D.-.W.sin.θ).sinΩt

Thus,.the.magnitude.of.amplitude.changes.from.A 1m .to.A 2m :

( L - D - W sin )sin θ Ω t ; A ( L - D - W sin )sin θ Ω t

A

. = = . (5.44)

1m 2m

Ω 2 2 δ Ω − m t + Q

11

The.electrical.circuit.for.electronic.countermeasures.to.compensate.vibra-
tion.and.the.critical.damping.coeficient.δ.for.the.carbon-epoxy.composite.
of. the. blades. can. be. determined. as. the. relationship. between. the. potential.
energy,.W,.and.the.energy.lost.during.one.deformation.cycle,.dW.

dW
W

2 1

− v

. δ = = m ωλ = m f π λ . (5.45)

Here:
m.is.the.mass.of.a.helicopter;
ω.is.the.natural.circular.frequency,.ω.=.2π.f. 1-v .;
λ.is.the.coeficient.of.internal.friction;
f.is.the.frequency.of.the.cycle.of.variation.of.the.deformation;
v.is.the.exponent.and.is.dependent.on.the.frequency.f.