Frequency (rad/s)

Sea State1 v=38.7m/s

0 200 400 600 800 1000

-200 0 200 400 600 800 1000 1200

Time (s)

Thurst (kN)

Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

Feathered Blade2seized Blade123seized

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

5x 10⁴

Frequency (rad/s) Thurst Spectrum [m2 /s/rad]

Feathered Blade2seized Blade123seized

0 0.5 1 1.5 2 0

1 2 3 4 5 6 7 8 9 10x 10⁴

Frequency (rad/s) S() [kN2 /s/rad]

Normal, blades feathered Fault type1, blade2seized Fault type3, all blades seized

-30 -20 -10 0 10 20 30 40 50

Wave Load Fy (kN)

SparL Bottom Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather blade2seized

0 200 400 600 800 1000 -50

-40 -30 -20 -10 0 10 20 30 40 50

Time (s)

Hydro Fy[kN]

SparL, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather flexible feather rigid

0 200 400 600 800 1000

-50 -40 -30 -20 -10 0 10 20 30 40 50

Time (s)

Wave Load Fy (kN)

Feather, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

mass drag

0 200 400 600 800 1000 -30

-20 -10 0 10 20 30

Time (s)

Wave Load Fy (kN)

Blade2seized, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

mass drag

0 0.5 1 1.5 2 2.5 3

0 200 400 600 800 1000 1200

Hydro Fm -y S()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

Feathered Blade2seized Blade123seized

0 0.5 1 1.5 2 2.5 3 0

200 400 600 800 1000 1200 1400

Frequency (rad/s) Hydro Fy()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather flexible feather rigid

0 200 400 600 800 1000

-300 -200 -100 0 100 200 300

Time (s)

W a ve L o ad F y (k N )

spar Top Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather blade2seized

0 0.5 1 1.5 2 2.5 3 0

500 1000 1500 2000 2500

Frequency (rad/s) H yd ro F m - y S (

)[ m

/s /r ad ]

SparU, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

Feathered Blade2seized Blade123seized

500 1000 1500 2000

Hydro Fy()[m2 /s/rad]

Feather, SparU, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather flexible feather rigid

0 0.5 1 1.5 2 2.5 3 0

50 100 150 200

Frequency (rad/s) Hydro Fy()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

blade2seized flexible blade2seized rigid

0 0.5 1 1.5 2 2.5 3

0 500 1000 1500 2000

Frequency (rad/s) Hydro Fy()[m2 /s/rad]

blade2seized, SparU, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

blade2seized flexible blade2seized rigid

0 0.5 1 1.5 2 2.5 3 0

500 1000 1500 2000

Frequency (rad/s) Hydro Fy()[m2 /s/rad]

rigid tower, SparU, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather rigid blade2seized rigid

50 100 150 200

Hydro Fy()[m2 /s/rad]

rigid tower, SparL, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather rigid blade2seized rigid

0 200 400 600 800 1000 -300

-200 -100 0 100 200 300

Time (s)

Hydro Fy[kN]

Feather, SparU, Azimuth 0, Wavedir=0 Hs=12m, Tp=14.2s, V=38.7m/s

feather flexible feather rigid

Wavedir=90

0 200 400 600 800 1000

-50 0 50 100 150 200 250 300 350 400 450

Time (s)

Thurst (kN)

Azimuth 0, Wavedir=90, Hs=12, Tp=14.2, V=38.7

Feathered Seized

200 400 600 800 0

100 200 300 400 500 600 700 800 900 1000

Time (s)

Thurst (kN)

Azimuth 0, Wavedir=90, Hs=12, Tp=14.2, V=38.7

Feathered Blade2seized Blade123seized

0 200 400 600 800 1000

Hydro Fx()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s Feathered

Blade2seized Blade123seized

0 0.5 1 1.5 2 2.5 3 0

50 100 150 200

Frequency (rad/s) Hydro Fx()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s

feather flexible feather rigid

0 0.5 1 1.5 2 2.5 3

0 1 2 3 4 5 6

x 10⁴

Frequency (rad/s) Thurst Spectrum()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=90, Hs=12, Tp=14.2, V=38.7

Feathered Blade2seized Blade123seized

0 0.5 1 1.5 2 2.5 3 0

20 40 60 80 100

Frequency (rad/s) H yd ro F y(  )[ m

/s /r ad ]

SparL, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s

Feathered Blade2seized Blade123seized

-20 -10 0 10 20 30 40

S p a rL B o tt o m H yd ro F y( kN )

Azimuth 0,Wavedir=90, Hs=12, Tp=14.2, V=38.7M/S

mass drag

0 200 400 600 800 1000 -20

-15 -10 -5 0 5 10 15 20

Time (s)

S p a rU B o tt o m H yd ro F y( kN )

Feather, Azimuth 0,Wavedir=90, Hs=12, Tp=14.2, V=38.7M/S

mass drag

0 200 400 600 800 1000

-40 -30 -20 -10 0 10 20 30

Time (s)

SparU Bottom Hydro Fy(kN)

Seized, Azimuth 0,Wavedir=90, Hs=12, Tp=14.2, V=38.7M/S

mass drag

0 0.5 1 1.5 2 2.5 3 0

10 20 30 40 50 60 70 80 90 100

X: 0.2071 Y: 55.93

Frequency (rad/s) H yd ro F y(

)[ m

/s /r ad ]

SparL, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s

Feathered Seized

Wp1=0.2, wp2=2.16

5 10 15 20 25 30

35 X: 0.1841

Y: 36.61

H yd ro F y(

)[ m

/s /r ad ]

SparU, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s

Feathered Seized

0 0.5 1 1.5 2 2.5 3 0

5 10 15 20 25 30 35 40

Frequency (rad/s) H yd ro F y(  )[ m

/s /r ad ]

SparU, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s

Feathered Blade2seized Blade123seized

When wind speed=38.7m/s and wave direction is 0deg, the seized case would have larger low- frequency thrust force but damped hydrodynamic force in –y direction compared with the feathered cases. When the wave direction is 90 deg, the wave loads of the seized cases are more peaked, leading to a larger tower bottom shear force resonance. It is the hydrodynamic force that contribute most to the Tower bottom shear Fy and excites the second peak of resonant shear force. That’s why the Fy of the seized case is more damped.

Hs=12, Tp=14.2, V=0

There is negligible difference between seized case and feathered case when there is no wind.

0 200 400 600 800 1000

-60 -40 -20 0 20 40 60

Time (s)

Hydro Fy(kN)

SparL wavedir=0, Hs=12, Tp=14.2, V=0M/S

feather seize

0 0.5 1 1.5 2 2.5 3 0

200 400 600 800 1000

1200 ^{X: 2.148}Y: 1311

Frequency (rad/s) Hydro mass Fy()[m2 /s/rad]

SparL, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=0

Feathered Seized

0 0.5 1 1.5 2 2.5 3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Frequency (rad/s) Hydro Fm -y S()[m2 /s/rad]

SparU, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=0

Feathered Seized

Comparison between windless and wind speed v=38.7m/s

0 0.5 1 1.5 2 2.5 3

0 20 40 60 80 100 120 140

Frequency (rad/s) Nacelle Surge S()[m2 /s/rad]

Feather, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2

v=0 v=38.7m/s

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5

Frequency (rad/s) S()[m2 /s/rad]

Nacelle Surge, Azimuth 0, Wavedir=0, Hs=3, Tp=10

v=0 v=8m/s

0 0.5 1 1.5 2 2.5 3 0

20 40 60 80 100 120 140

Frequency (rad/s) H yd ro F m - y S (

)[ m

/s /r ad ]

SparL Feather, Azimuth 0, Wavedir=0, Hs=3, Tp=10

v=0 v=8m/s

100 200 300 400 500 600

Hydro Fm -y S()[m2 /s/rad]

SparU Feather, Azimuth 0, Wavedir=0, Hs=3, Tp=10

v=0 v=8m/s

0 0.5 1 1.5 2 2.5 3 3.5 0

500 1000 1500 2000 2500

Frequency (rad/s) S [kN2 /s/rad]

SparU, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

Feathered, V=38.7m/s Blade No.2 seized, V=38.7m/s All blades seized, V=38.7m/s Feathered, v=0m/s

0 0.5 1 1.5 2 2.5 3

0 200 400 600 800 1000 1200

Frequency (rad/s) S [ kN

/s /r ad ]

SparL, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

Feathered, V=38.7m/s Blade No.2 seized, V=38.7m/s All blades seized, V=38.7m/s Feathered, v=0m/s

Flexible mode

Wave frequency excitation Pitch resonant excitation

2 2

1 1 1 1

( 1) 1 ( )

4 4 2

M M D

D D

dF   C  dza   C   dz     C Ddz u    u   

0 0.5 1 1.5 2 2.5 3

0 200 400 600 800 1000 1200

Frequency [rad/s]

S [ kN

/s /r ad ]

SparL, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

Feathered, V=38.7m/s

Blade No.2 seized, V=38.7m/s All blades seized, V=38.7m/s Feathered, v=0m/s

Wave frequency excitation Pitch excitation

Sum frequency excitation

0 0.5 1 1.5 2 2.5 3

0 100 200 300 400 500 600 700 800 900 1000

Frequency (rad/s) Hydro mass Fy()[m2 /s/rad]

Flexible tower, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

Feathered threSeized

0 0.5 1 1.5 2 2.5 3 0

20 40 60 80 100 120 140 160 180

Frequency (rad/s) Hydro mass Fy()[m2 /s/rad]

Rigid, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

Feathered Threeblades seized

100 200 300 400 500 600 700 800 900 1000

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Time (s) a cc (m

/s )

Flexible tower, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

feather 3 blades seized

100 200 300 400 500 600 700 800 900 1000 -0.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Time (s) acc(m2 /s)

Rigid, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

feather 3 blades seized

The platform motion acceleration difference between feathered case and seized case is very small then the tower is rigid.

-1 -0.5 0 0.5 1 1.5

vel(m/s)

Flexible tower, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

feather 3 blades seized

100 200 300 400 500 600 700 800 900 1000 -1.5

-1 -0.5 0 0.5 1 1.5

Time (s)

ve l( m /s )

Rigid, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

feather 3 blades seized

0 0.5 1 1.5 2 2.5 3

0 100 200 300 400 500 600 700 800

Frequency (rad/s) Hydro mass Fy()[m2 /s/rad]

Flexible tower, SparL bottom

Azimuth 0,Wavedir=90, Hs=12, Tp=14.2, V=37.8

Feathered Threeblades seized

100 200 300 400 500 600 700 800 900 1000 -0.25

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

Time (s) a cc (m

/s )

Flexible tower, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

feather 3 blades seized

-1 -0.5 0 0.5 1 1.5

ve l( m /s )

Flexible tower, SparL bottom

Azimuth 0,Wavedir=0, Hs=12, Tp=14.2, V=37.8

feather 3 blades seized

0 0.5 1 1.5 2 2.5 3 0

20 40 60 80 100 120 140 160 180

Frequency (rad/s) Hydro mass Fy()[m2 /s/rad]

Rigid tower, SparL bottom

Azimuth 0,Wavedir=90, Hs=12, Tp=14.2, V=37.8

Feathered Threeblades seized

100 200 300 400 500 600 700 800 900 1000

-50 -40 -30 -20 -10 0 10 20 30 40 50

Time [s]

S p a rL F ym [ kN ]

Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

feathered 3bladesseized

0 200 400 600 800 1000 -50

-40 -30 -20 -10 0 10 20 30 40 50

Time (s)

F y [k N ]

SparL, Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

normal bd2 bd123

-200 -100 0 100 200 300

F ym [ kN ]

Azimuth 0, Wavedir=0, Hs=12, Tp=14.2, V=38.7

SparL SparU

0 0.5 1 1.5 2 2.5 3 0

200 400 600 800 1000

Frequency (rad/s) H yd ro F x(

) [k N

/s /r ad ]

SparU, Azimuth 0, Wavedir=90 Hs=12m, Tp=14.2s, V=38.7m/s Feathered

Blade2seized Blade123seized