Dynamic Strength - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 126

-2Gxz - 2Gyz
x(x - 2) - k[y -

( )

M = λ

. . (5.28)

1

2

α ( 1 + y - ) β ( 1 + y ) + 2 αβ ]

5.4 VibrationAnalysis

The.longitudinal.motion.of.a.stable.helicopter.will.be.found.to.exhibit.two.
modes,.which.are.damped.oscillations..The.irst.mode.with.light.damping.
and. a. relatively. long. period. is. called. the. long-period . or. phugoid . mode.. The.
second.heavy.damped.mode.is.referred.to.simply.as.the. short-period .mode..
The.equation.for.forced.vibration.without.damping.is:

2

∂
∂

= (

)

m x + Q x L - D - W sin θ sin Ω . t

. (5.29)

11

2

Here:

Ω.is.a.forcing.frequency.acting.from.turbulence.movement;
t.is.a.time.of.a.wave.propagation;
m. is. the. mass. of. the. blade,. is. constant. all. the. time. and. doesn't. depend.
upon.movement.and.attitude.

We.assume.a.periodic.force.of.magnitude;.F.=.(L.-.D.-.W.sin.θ).sinΩt.
Here:
L.is.a.lift.force;
D.is.a.drag.wind.force;
W.is.a.weight.of.a.rotor.blade.

The.force.of.the.lift.is.actually.much.stronger.than.the.wind's.force.against.
the.front.side.of.the.blade,.which.is.called. drag ..In.the.case.of.free.vibration.
when.turbulence.movement.doesn't.exist:.(L-D-W.sin.θ).sinΩt.=.0,.which.has.
the.following.solution.as: 8

. x.=.C 1 sinϖt.+.C 2 cosϖt. (5.30)

and.where.circular.frequency.ϖ.=.(Q 11 /m) 1/2 .
Here,.Q 11 .is.the.stiffness.of.the.rotor.blade.and.can.be.determined.using.
previous.equations..C 1 .and.C 2 .are.arbitrary.constants.
We.assume.C 1 .=.A.cosϕ;.C 2 .=.A.sinϕ..Here,.A.is.an.amplitude.of.vibration.
and.ϕ.is.a.phase.angle.of.vibration..We.input.this.into.Equation.(5.30).and.the