1

20 points

Consider a single

having equation of motion as

21.02 mm

mass-spring-damper system

* + 2x + 100x = 10t² + fot N

where fo = 35 N/s. The response of the system at

t = 0.15 sis

6.87 mm

10.97 mm

16.76 mm

1.01 mm

#0/nThe figure below shows an equivalent single

degree of freedom (SDOF) model of a wind

turbine. The rotor and nacelle system mass is

M = 2500 kg and the mass per unit length of the

tower is m = 500 kg/m. Assume the tower as an

uniform beam, with length L = 60 m, moment of

inertia I = 0.8 m4, Young's modulus E = 200

GPa. Consider the wind turbine is subjected to a

wind gust, modelled as

f(t) =

Fo (1-) N 0≤t≤ħ₁

0

N t > ti

where Fo= 12 kN and t₁ = 0.18 s. Determine the

response of the system at t = 0.36 s. Assume

damping ratio of the system is = 0.1./nNacelle

Tower,

-5.59 mm

-0.62 mm

-1.24 mm

-3.73 mm

-2.49 mm

Rotor

Ke

ww

x(1)

Me

F(0)