failure analysis of large-scale wind power structure under

Research ArticleFailure Analysis of Large-Scale Wind Power Structure underSimulated Typhoon

Zihua Zhang Junhua Li and Ping Zhuge

College of Civil Engineering and Environment Ningbo University Ningbo 315211 China

Correspondence should be addressed to Zihua Zhang zhangzihuanbueducn

Received 5 January 2014 Revised 18 June 2014 Accepted 23 June 2014 Published 14 July 2014

Academic Editor Gisele Mophou

Copyright copy 2014 Zihua Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Recently a number of wind power structures in tropical cyclone zones are damaged by typhoon In order to study the failuremechanics and failure modes of wind power structure subjected to typhoon the typhoon wind field in Dongtai wind farm issimulated based on the classical autoregressive (AR)model and a regional power-spectrum-density (PSD)model and the simulatedspectrum is verified to be in good agreement with the target spectrum An integrated finite element (FE) model of wind powerstructure composed of rotor nacelle tower pile cap andPHCpiles is establishedModal analysis reveals that pile stiffness decreasesthe structurersquos natural frequencies especially for high order frequencies Structural responses under the simulated typhoon arecalculated by dynamic analysis Results show that tower buckling is the most prone failure mode of the structure The horizontaldisplacement of the hub and the axial force of the most unfavorable piles are both under the limit This study provides a way to theantityphoon design of large-scale wind power structures

1 Introduction

With the increase of investment of clean energy from gov-ernments wind energy has grown enormously all over theworld in the past decade andwill stand to benefit from its roleas both a source of energy security and a key to solving theproblem of climate change in the future Compared with theyear 2011 wind powermarket grew bymore than 10 in 2012and the new global total installed wind power capacity at theend of 2012 was 2825GW representing cumulative marketgrowth of more than 19 [1] And China has already takenthe leadership position of cumulative wind power capacity in2011

It should be noted that more and more wind farms areestablished in tropical cyclone zones making the wind tur-bine and its support structure have to face the threat oftyphoon For instance typhoon Maemi struck the Miyako-jima Islandwith an average speed of 384ms and amaximumgust of 741ms on September 11 2003 All of the wind tur-bines on the island were extensively damaged Three of sixturbines collapsed and the others suffered from destructivedamage whose blade were broken or the nacelle coverdrooped Based on FEM simulation and wind response

analysis Ishihara et al [2] found that the overlargemaximumbending moment was the reason for the buckling and col-lapse of the tower In September 2003 typhoon Dujuanattacked the Honghaiwan wind farm of Guangdong andvarying degrees of damage were caused to thirteen wind tur-bines In August 2006 typhoon Saomai passed through theHedingshan wind farm of Zhejiang and led to collapse of fivewind turbines [3]

Although massive losses in coastal wind farms have beencaused by typhoon the failure mechanism and failure modesof wind power structures are not clear yet Generally modernwind turbines are designed mainly according to the interna-tional standard (IEC 61400-1) [4] that is based on EuropeanandNorth American conditions without the experience fromareas attacked by typhoon On the other hand designers andengineers usually pay more attention to the wind turbineincluding rotor nacelle and tower but the soil-structureinteraction (SSI) is always out of consideration The two rea-sons above result in the ultimate wind load and the structuralresponses are inevitably underestimated no need to mentionthat the characteristic of typhoon is essentially different fromthe normal wind Recently attention has been increasinglypaid to the typhoon-induced damage of wind turbines

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 486524 10 pageshttpdxdoiorg1011552014486524

2 Mathematical Problems in Engineering

Li et al [3] analyzed the data of typhoon Saomai when it waspassing through Hedingshan wind farm It was pointed outthat the violent wind drastic turbulence and sudden changeof wind direction were major factors of wind turbine failuresFrom the view of economics Clausen et al [5] estimated thatthe cost of wind turbine in tropical cyclone zones is 20ndash30more than that in normal areas Chou et al [6] examined thecauses of blade damage of five wind turbines in ChanghuaCoastal Industrial Park of Taiwan It was found that long-term effects such as blade fatigue could cause local crack dam-age and delamination and the actual blade damage occurredmainly on the back edge of the blade near the wing section

In offshore wind turbines the structural responses aredriven not only by wind but also by water wave Conse-quently the dynamic analysis of offshore wind turbines ismore complex than that of land-based ones Karimirad andMoan [7] employed an advanced blade element momentumtheory panel method and the Morison formula to study thedynamic structural and motion responses of a spar-typefloating offshore wind turbine caused by stochastic nonlinearwave and wind loads in harsh and operational environmentalconditions It is found that the wind turbulence affectspower production rather than the dynamic motion andstructural responses Based on the Arbitrary Lagrangian-Eulerian (ALE) method and FEM Zhang et al [8] simulateda wind-induced aqueduct-water coupling system installedwith isolated bearings It is found that the resonance can beeliminated under high-order-frequency excitation and mayhappen when the excitation frequency is close to the first-order water sloshing frequency Karimirad andMoan [9] pre-sented a stochastic dynamic response analysis of a tension legspar-type wind turbine subjected to wind and wave actionsTo study the power performance and structural integrity ofthe system negative damping rotor configuration and towershadow effects are discussed

This paper aims at analyzing the potential failuremodes ofwind power structure subjected to typhoon and is organizedas follows The location and wind condition of Dongtai windfarm is introduced in Section 2 In Section 3 the fluctuatingwind speed of typhoon is simulated and verified based on aregional PSDmode and theARmethod followed by a presen-tation of wind load calculation in the same part A FE modelof a 15MW wind turbine with pile foundation is establishedin Section 4 and structurersquos natural frequencies and wind-induced responses are calculated by elastic dynamic analysisThe failure modes of the wind power structure are concludedfinally

2 Farm Location and Wind Condition

Dongtai wind farm is located in Dongtai City Jiangsu Prov-ince southeastern China at 120∘541015840 east latitude and 32∘471015840north longitude as shown in Figure 1 Totally one hundredand thirty-four 15MW wind turbines are installed in a60 km2 site Wind resource in this area is rich in east andpoor in west forming a long and narrow wind speed surgingregion

AlthoughDongtai is not a typhoon landing site in generalit still has to face the threat of typhoon For example in 2009

Table 1 Tropical cyclone classification

Classification Average wind speed(ms) Wind scale

Tropical depression (TD) 108ndash171 6-7Tropical storm (TS) 172ndash244 8-9Severe tropical storm (STS) 245ndash326 10-11Typhoon (TY) 327ndash414 12-13Severe typhoon (STY) 415ndash509 14-15Super typhoon (SuperTY) ge510 ge16

Figure 1 Location of Dongtai wind farm

Dongtai wind farm

JapanSouth Korea

China

Figure 2 The track map of typhoon Morakot

typhoon Morakot passed through Dongtai with an averagewind speed of 33ms and moved into East China Sea asshown in Figure 2 In 2012 typhoonDamrey landed inXiang-shui of Jiangsu Province with an average wind speed of35ms and brushed past Dongtai as shown in Figure 3 Itshould be noted that according to the extreme wind speedmodel (EWM) [4] the extreme wind speed with a recurrenceperiod of 50 years of the wind farm is 2437ms which is farbelow the average wind speed of the two typhoonsmentionedabove

According to [10] tropical cyclones are classified as 6grades as shown in Table 1 It can be seen that the lowerlimit of typhoonrsquos average wind speed is 327ms which isemployed to simulate the fluctuatingwind speed in this paper

3 Typhoon Wind Load Simulation

31 PSD Model of Typhoon Natural wind consists of twocomponents that ismeanwind and fluctuatingwind and the

Mathematical Problems in Engineering 3

Dongtai wind farm

JapanSouth Korea

China

Figure 3 The track map of typhoon Damrey

latter represents turbulence and randomness Consequentlythe instantaneous velocity of wind can be described as

119880119911(119905) = 119880

119911+ 119906119911(119905) (1)

where 119880119911and 119906

119911(119905) are the mean wind velocity and the

fluctuating wind velocity at height 119911 and time 119905 respectively119880119911obeys the logarithmic law and can be described as [11]

119880119911= 119880ref

ln (1199111199110)

ln (119911ref1199110) (2)

where 119880ref is a reference wind velocity measured at thereference height 119911ref and 1199110 is the roughness length

According to the randomvibration theory the fluctuatingwind velocity can be regarded as a zero-mean Gaussianprocess and described by the power-spectrum-density (PSD)model in the frequency domain [12] A lot of empiricalspectrum models mostly for the longitudinal wind velocityhave been published such as von Karman spectrum [13]Davenport spectrum [14] and Simiu spectrum [15] Consid-ering the features of typhoon such as strong turbulence highwind speed and significant regional characteristics the PSDmodel of typhoon is essentially different from that of normalwind Shi et al [16] proposed an empirical spectrum thatdoes not change with altitude according to the observed datain Shanghai since 1956 and taking the characteristics of thetyphoon turbulence scale varying with altitude into accountConsidering that the distance betweenDongtai and Shanghaiis acceptable Shirsquos spectrum is employed here The model isdefined as

119878V (119899) =546119896V2

10

11990924

119899(1 + 151199092

)14

(3)

119909 =1200119899

V10

(4)

119899 =120596

2120587 (5)

where 119878V(119899) is the PSD of the fluctuating wind speed 119896 is theground roughness coefficient V

10is the average wind speed

at the height of 10m 119899 is the wind frequency and 119909 is theturbulence integral scale factor

32 Fluctuating Wind Speed Simulation Discrete modelsof wind speed based on Box-Jenkins methods are usedcommonly in time-series analysis These models includingautoregressive (AR) [17] moving average (MA) [18] autore-gressive moving average (ARMA) [19] and autoregressiveintegratedmoving average (ARIMA)models [20] are usuallytermed as linear filtering method and are able to reproducethe statistical properties of the fluctuating wind speed for aparticular site with an acceptable computational cost Theclassical AR model is employed to simulate the wind fieldof typhoon in this paper [21] To generate a family of 119872processes the following equations are used

u (119905) =119901

sum

119896=1

120595119896

u (119905 minus 119896Δ119905) + N (119905) (6)

u (119905) = [1199061 (119905) 119906119872 (119905)]119879

(7)

u (119905 minus 119896Δ119905) = [1199061 (119905 minus 119896Δ119905) 119906119872 (119905 minus 119896Δ119905)]119879

(8)

N (119905) = [1198731 (119905) 119873119872 (119905)]119879

(9)

where 119906119894(119905) and 119906119894(119905 minus 119896Δ119905) 119894 = 1 119872 are the fluctuatingwind speed at time 119905 and time (119905minus119896Δ119905) respectively and119873119894(119905)is made of normally distributed random numbers with zeromean and unit variance120595

119896

are119872times119872matrices 119896 = 1 119901and 119901 is regarded as the order of the model

The covariance between 119906119894

(119905) and 119906119894(119905 minus 119896Δ119905) can bedenoted as [22]

119877119894

119906

[119896Δ119905]

= 119864 [119906119894

(119905 minus 119896Δ119905)minus119864 [119906119894

(119905 minus 119896Δ119905)] 119906119894

(119905) minus 119864 [119906119894

(119905)]]

(10)

Considering that 119906119894(119905) and 119906119894(119905 minus 119896Δ119905) are stationarystochastic processes with zero mean (10) can be rewritten as

119877119894

119906

[119896Δ119905] = 119864 [119906119894

(119905 minus 119896Δ119905) 119906119894

(119905)] (11)


Postmultiplying (6) by u(119905 minus 119896Δ119905)119879 and applying mathe-matical expectation derive

R = R120595

R119901119872times119872

= [R119906(Δ119905) R

119906(119901Δ119905)]

119879

120595119901119872times119872

= [120595119879

1

120595119879

119901

]119879

R119901119872times119901119872

=

[[[[[[[

[

R119906(0) R

119906(Δ119905) sdot sdot sdot R

119906[(119901 minus 2) Δ119905] R

119906[(119901 minus 1) Δ119905]

R119906(Δ119905) R

119906(2Δ119905) sdot sdot sdot R

119906[(119901 minus 1) Δ119905] R

119906(0)

d

R119906[(119901 minus 2) Δ119905] R

119906[(119901 minus 1) Δ119905] sdot sdot sdot R

119906[(119901 minus 4) Δ119905] R

119906[(119901 minus 3) Δ119905]

R119906[(119901 minus 1) Δ119905] R

119906(0) sdot sdot sdot R

119906[(119901 minus 3) Δ119905] R

119906[(119901 minus 2) Δ119905]

]]]]]]]

]

R119906(119895Δ119905)119872times119872

=

[[[

[

11987711

119906

(119895Δ119905) sdot sdot sdot 1198771119872

119906

(119895Δ119905)

d

1198771198721

119906

(119895Δ119905) sdot sdot sdot 119877119872119872

119906

(119895Δ119905)

]]]

]

119895 = 1 119901

[120595119895

]119872times119872

=

[[[

[

12059511

119895

sdot sdot sdot 1205951119872

119895

d

1205951198721

119895

sdot sdot sdot 120595119872119872

119895

]]]

]

119895 = 1 119901

(12)

The cospectrum and the covariance function satisfy theWiener-Khintchine equation that is

119877119894119896

119906

(119895Δ119905) = int

infin

0

119878119894119896

119906

(119899) cos (2120587119895Δ119905) 119889119899

119894 119896 = 1 119872

(13)

where 119878119894119896119906

(119899) denotes the cross-spectral density function ofpoint 119894(119909

119894 119910119894 119911119894) and point 119896(119909

119896 119910119896 119911119896) and can be expressed

as

119878119894119896

119906

(119899) = radic119878119894119894

119906

(119899) 119878119896119896

119906

(119899)coh119894119896 (119899) (14)

where 119878119894119894119906

(119899) represents the PSD of point 119894 associated with theprocess 119906119894(119905) and has the form of (3) and coh119894119896(119899) representsthe coherence function of longitudinal fluctuations betweenpoint 119894 and point 119896

Considering that wind power structure is a typical slenderstructure a simplified expression of coh119894119896(119899) proposed byShiotani and Avai [23] is adopted here

coh119894119896 = exp(minus1003816100381610038161003816119911119894minus 119911119896

1003816100381610038161003816

119871119911

) (15)

and 119871119911is proposed to be 60 [24]

Postmultiplying (6) by u(119905) = [1199061(119905) 119906119872(119905)] derives

R119873= R119906(0) minus

119901

sum

119896=1

R119906(119896Δ119905) (16)

The vector N(119905) of random series having R119873

as theircross-correlation matrix can be obtained by the linear com-bination

N (119905) = Ln (119905) (17)

n (119905) = [1198991 (119905) 119899119872 (119905)]119879

(18)

where n(119905) is a set of119872 independent random processes withzeromean andunit variance andL is a lower triangularmatrixand can be calculated by a Cholesky factorization of R

119873and

R119873= LL119879 (19)

Substituting 120595 (obtained from (10)) and N(119905) (obtainedfrom (17)) into (6) u(119905) including 119872 series of fluctuatingwind speed is obtained

Based on the AR model the fluctuating wind speeds atthe height of 5m 15m 25m 35m 45m 55m and 65m inthe wind farm are simulated For simplicity the wind speedhistories at the height of 5m 35m and 65m are shown inFigures 4(a)ndash4(c) respectively The simulation parametersare defined as follows 119901 = 4 point number = 7 Δ119905 = 01 secand Δ120596 = 001Hz


33 Verification of the Simulated Wind Speed In order toverify the simulated wind speed history the PSD of the simu-lated wind is compared with that of the target spectrum (see(3)) in Figure 5 It can be seen that the simulated spectrumagrees well with the target spectrum in the frequency domainwhich implies that the simulated wind has a similar powerdistribution as the natural wind and can be used to calculatethe structural typhoon-induced response

34 Wind Load Calculation The wind rotor is a complexaerodynamic system that converts wind energy into mechan-ical power The blade element theory is commonly used tocalculate the wind load acting on the rotating rotor Consid-ering that the wind turbine should be shut down before thecoming typhoon the aerodynamic force acting on the rotorcan be estimated by

F119877(119905) = 119862

119863120588u2119879

(119905) 119860 (20)

where 119862119863is the equivalent drag efficient of the rotor and 11

is used here [25] 120588 is the air density u119879(119905) is the total wind

speed at the hub height and 119860 is the swept areaThe relationship between wind speed and wind pressure

under ambient conditions is described by the Bernoulliequation

w (119905) =120574

2119892u2119879

(119905) asympu2119879

(119905)

1630 (21)

wherew(119905) is the wind pressure 120574 is the unit weight of air and119892 is the gravitational acceleration

Assuming that the wind speed is parallel to the normaldirection of the rotor which is the most unfavorable condi-tion for the support structure the wind load acting on eachelement of tower can be calculated by the following expres-sion

F119890(119905) = 120583

119904119890119860119890w (119905) (22)

where 119860119890is the element area and 120583

119904119890is the shape coefficient

of the element

4 FE Analysis

41 Differential Equation of Motion In order to study thedynamic responses of the wind power structure subjected totyphoon load varying in time a transient dynamic analysisshould be conducted Based on theDrsquoAlemberts principle anddue to the discretization process of a continuous structurewith FEs the following equation of motion can be derived

Mu119873(119905) + Cu

119873(119905) + Ku

119873(119905) = f (119905) (23)

whereM C andK denote the structural mass damping andstiffnessmatrices respectively u

119873(119905) u119873(119905) andu

119873(119905) are the

vectors of nodal accelerations velocities and displacementsrespectively and f(119905) is the vector of applied forces

The Newmark integration method which is an implicittime integration algorithm is employed to solve (23)

0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)

(a) At the height of 5m

0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15W

ind

spee

d (m

sminus1)

(b) At the height of 35m

0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)

(c) At the height of 65m

Figure 4 Fluctuating wind speed histories at different heights

Frequency (Hz)

Simulated spectrumTarget spectrum

102

103

101

100

10minus1

10minus3

10minus2

10minus3 10minus2 10minus1 100 101

(m2middotsminus1)

S

Figure 5 Comparison between the target spectrum and the simu-lated spectrum


Table 2 Dimensions of the tower

Segment Lower diameter (m) Upper diameter (m) Height (m) Shell thickness (m)Lower Upper

Lower 40 36 176 0026 0022Middle 36 30 224 0022 0016Upper 32 30 224 0016 0018Anchor ring 40 40 06 006 006

Table 3 Material parameters

Part Elastic modulus (Nsdotmminus2) Density (kgsdotmminus3) Poisonrsquos ration Yield strength (MPa)Nacelle 21 times 1011 563 03 Rotor 21 times 1011 448 03 Tower 21 times 1011 7850 03 345Pile cap 325 times 1010 2500 0167

It should be pointed out that damping plays an importantrole in the dynamic response of the wind power structureAmbient vibration tests are always employed to estimatethe damping ratio because of its strong advantage of beingpractical and economical using the freely available ambientwind wave excitation Shirzadeh et al [26] measured thedamping ratio of a 3MW offshore wind turbine under ambi-ent vibration and the measured values are 105 and 127for respectively the first FA mode and the first SS modeSimilarly Ma et al [27] obtained the damping ratio of a15MW land-based wind turbine tower Considering that thewind turbine and support structure of the latter case is thesame as this study the measured damping ratio 175 is usedhere

42 Modal Analysis Algorithm A modal analysis is per-formed to calculate the natural frequencies of the wind powerstructure Omitting the damping matrix and force vector in(23) the free vibration equation of the wind power structurefor eigenvalue analysis is obtained

Mu119873(119905) + Ku

119873(119905) = 0 (24)

Assume the general form of the solution is

u119873(119905) = 120593 sin (120596119905 + 120601) (25)

Equation (24) becomes10038161003816100381610038161003816K minus 1205962M10038161003816100381610038161003816 = 0 (26)

The block Lanczos method is a very efficient and robustalgorithm to perform a modal analysis for large models thusit is employed on the platform of ANSYS [28]

43 FE Model As mentioned before 15MW wind turbinesare installed in Dongtai wind farm The tower is 6275m inheight (the hub height is 65m) and is fixed on the pile cap byan anchor ring The tower consists of 3 segments of cylinderwith dimensions shown in Table 2 The material parametersof the nacelle rotor tower and pile cap are listed in Table 3

There are thirty PHCpiles arranged under the pile cap Sixof themare along the inner circlewith a diameter of 41m andthe others are along the outer circle with a diameter of 168mas shown in Figure 6 Based on pile tests the horizontal stiff-ness and vertical stiffness of the pile are 119864

ℎ= 18times 10

7Nsdotmminus2and 119864V = 19 times 10

8Nsdotmminus2 respectivelyThe FE model of the wind power structure is shown in

Figure 7 Totally 14898 elements are used with the types listedin Table 4 Considering that the failure mechanism of blade isbeyond the scope of this study solid element is employed tosimulate the rotor with an equivalent mass

Table 5 compares the natural frequencies of the structurewith piles (case 1) and the structure fixed on a rigid founda-tion (case 2) It can be seen that the primary and secondaryfrequencies are around 041Hz in both cases which is closeto the predominant frequency of typhoon Consequently aresonance is easy to happen Furthermore the natural fre-quencies of wind power structure in case 2 are higher thanthat in case 1 especially for 6th to 10th orders frequency Itreveals that piles decrease the structural stiffness and shouldbe taken into account in the structural dynamic analysis

5 Failure Mode Analysis

51 Horizontal Displacement of the Hub As a typical slenderstructure wind power structure is sensitive to horizontaldisplacement Consequently the horizontal displacement ofthe hub (119880

ℎ) is usually regarded as a safety control index of

the wind power structure In Figure 8 it can be seen thatthe hub moves from minus0160m to 1125m and the maximumdisplacement is under the limit value of 13m which is 150of the hub height [29]

52 Stress of the Tower Under the wind load the verticalstress of the tower which is predominant is small at the topand large at the bottomAccordingly the shell thickness of thetower gradually increases from the top to the bottom How-ever the tower bottom is still prone to buckling Figures 9(a)and 9(b) show theVon-Mises equivalent stress histories of thelowest element in the windward side and the leeward side of


Table 4 Element types of structural components

Part Nacelle Rotor Tower Pile cap PHC pilesElement type Solid 45 Solid 45 Shell 63 Solid 45 Combine 14

W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N

Figure 6 Arrangement of piles

Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X

Figure 7 FE model of the wind power structure with piles


Table 5 Natural frequencies of wind power structures

Frequencyorder Case 1 119891

1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)

Figure 8 The horizontal displacement history of the hub

the tower respectively Obviously at quite a lot of time stepsthe stress of the lowest elements not only at the windwardside but also at the leeward side is over the steelrsquos yieldstrength As a result buckling originates from the tower bot-tom Considering that the maximum stress appears at time =11125 sec the corresponding equivalent stress distributionsare described in Figure 10 Due to the bending stress andthe stress concentration the stress reaches the maximum atthe junction of the lower segment and the anchor ring Theyield range looks spindle-likewith the height of 05m approx-imately

53 Stress of the Anchor Ring Owing to the large thickness ofthe anchor ring the equivalent stress decreases rapidly and isunder the steelrsquos yield strength at most time steps Assumingthe stress concentration is eliminated by engineering meansthe yield possibility of the anchor ring can be reduced effec-tively (Figure 11)

The maximum equivalent stress of the anchor ring alsoappears at time = 11125 sec and the stress distribution isdescribed in Figure 12 It is shown that the ring protrudes atthe windward side and indents at the leeward side and it canbe regarded as a typical buckling mode of the tower [2]

54 Axial Force of the Unfavorable Piles Each foundation pilebears different bending moment based on moment distribu-tion method Consequently the piles at the windward sideand the leeward side on the outer circle are the most unfa-vorable and their axial force histories are shown in Figure 13

0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)

(a) The element at the windward side

0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)

(b) The element at the leeward

Figure 9 Von-Mises equivalent stress history at the bottom oftower

Nodal solutionStep = 445Sub = 1Time = 11125SEQV (AVG)DMX = 035964SMNSMX + 09

0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09

(a) At the windward side


0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09

(b) At the leeward side

Figure 10 Von-Mises equivalent stress at the bottom of tower whiletime = 11125 sec


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)

(a) The element at the windward

0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


Figure 11 Von-Mises equivalent stress histories at the bottom of anchor ring

Nodal solutionStep = 445Sub = 1Time = 11125SEQV (AVG)DMX = 012506

SMX = 616E + 09

Wind direction

Windward side

X

YZ

Leeward side 0130E + 08

0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08

Figure 12 Von-Mises equivalent stress distribution of the anchor ring

0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)

(a) Pile at the windward side

1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)

(b) Pile at the leeward side

Figure 13 Axial force of the most unfavorable piles

Pile tests that provided the ultimate compress and tensilebearing capacity of single pile are 1250 kNand470 kN respec-tively and the ultimate tensile bearing capacity of the pilebody is 2500 kNThus the pile foundation has enough deignsafety margin in this case

6 Conclusion

Based on the classical AR model and a regional PSD modelthe wind field of typhoon in a coastal wind farm is simulatedand verified A FEmodel of the wind power structure includ-ing nacelle rotor tower pile cap and PHC piles is estab-lished Modal analysis shows that the natural frequencies ofthe wind power structure fixed on rigid foundation are higherthan that of the structure with piles which implies thatpiles decrease the structural stiffness and should be takeninto account in the structural dynamic analysis The primaryand secondary frequencies of the structure are close to thepredominant frequency of typhoon leading to a resonancebetween the structure and thewindDynamic analysis reveals


that tower buckling is the most prone failure mode of thewind power structure subjected to typhoon The stress con-centration at the junction of tower and anchor ring should beeliminated by welding seam with gradient thickness or boltswith enough strength Although all piles are verified to besafe in this case they still have to be checked especially theunfavorable piles under the conditions of typhoon

Conflict of Interests

The authors declare no possible conflict of interests

Acknowledgments

The supports of National Natural Science Foundation ofChina (Grant no 51308307) Zhejiang Provincial Natural Sci-ence Foundation of China (Grant no LQ13E080008) NingboNatural Science Foundation (Grant no 2014A610169) andZhejiang Provincial Research Project of Technology Appli-cation for Public Welfare (Grant no 2014C33009) are highlyappreciated

References

[1] GWEC ldquoGlobal wind reportmdashannual market update 2012rdquohttpwwwgwecnetwp-contentuploads201206Annualreport 2012 LowRespdf

[2] T Ishihara A Yamaguchi K Takahara T Mekaru and S Mat-suura ldquoAn analysis of damaged wind turbines by TyphoonMaemi in 2003rdquo inProceedings of the 6thAsia-PacificConferenceon Wind Engineering pp 1413ndash1428 Seoul Republic of Korea2005

[3] Z Q Li S J Chen H Ma and T Feng ldquoDesign defect of windturbine operating in typhoon activity zonerdquo Engineering FailureAnalysis vol 27 pp 165ndash172 2012

[4] IEC 61400-1 Ed3 ldquoInternational electro-technical commis-sionrdquo Wind turbines-Part 1 Design requirements 2005

[5] N E Clausen S Ott N J Tarp-Johansen et al ldquoDesign of windturbines in an area with tropical cyclonesrdquo in Proceedings of theEuropean Wind Energy Conference 2006

[6] J S Chou C K Chiu I KHuang andKNChi ldquoFailure analy-sis of wind turbine blade under critical wind loadsrdquo EngineeringFailure Analysis vol 27 pp 99ndash118 2013

[7] M Karimirad and T Moan ldquoWave and wind induced dynamicresponse of a spar-type offshorewind turbinerdquo Journal ofWater-way Port Coastal and Ocean Engineering vol 138 no 1 pp9ndash20 2011

[8] H Zhang H Sun L Liu and M Dong ldquoResonance mecha-nismofwind-induced isolated aqueductwater coupling systemrdquoEngineering Structures vol 57 pp 73ndash86 2013

[9] M Karimirad and TMoan ldquoStochastic dynamic response anal-ysis of a tension leg spar-type offshore wind turbinerdquo WindEnergy vol 16 no 6 pp 953ndash973 2013

[10] GBT 19201-2006 ldquoGrade of Tropical Cyclonesrdquo (Chinese)[11] H Tennekes ldquoThe logarithmic wind profilerdquo Journal of Atmo-

spheric Sciences vol 30 pp 234ndash238 1973[12] J B Roberts and P D Spanos Random Vibration and Statistical

Linearization John Wiley amp Sons Chichester UK 1990

[13] T vonKarman ldquoProgress in the statistical theory of turbulencerdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 34 no 11 pp 530ndash539 1948

[14] A G Davenport ldquoThe spectrum of horizontal gustiness nearthe ground in high windsrdquoQuarterly Journal of the Royal Mete-orological Society vol 87 no 372 pp 194ndash211 1961

[15] E Simiu ldquoWind spectra and dynamic alongwind responserdquoJournal of the Structural Division vol 100 no 9 pp 1897ndash19101974

[16] Y Shi W Lu and Y Zhong ldquoThe study of typhoon characteris-tics in the Shanghai regionrdquo in Proceedings of the 2nd NationalConference on Wind Effect 1988 (Chinese)

[17] P Ailliot VMonbet andM Prevosto ldquoAn autoregressivemodelwith time-varying coefficients for wind fieldsrdquo Environmetricsvol 17 no 2 pp 107ndash117 2006

[18] L V Hansen and T LThorarinsdottir ldquoA note on moving aver-age models for Gaussian random fieldsrdquo Statistics ProbabilityLetters vol 83 no 3 pp 850ndash855 2013

[19] H Zhang L Liu M Dong and H Sun ldquoAnalysis of wind-induced vibration of fluidstructure interaction system for iso-lated aqueduct bridgerdquo Engineering Structures vol 46 pp 28ndash37 2013

[20] R G Kavasseri and K Seetharaman ldquoDay-ahead wind speedforecasting using f-ARIMAmodelsrdquo Renewable Energy vol 34no 5 pp 1388ndash1393 2009

[21] A Iannuzzi and P Spinelli ldquoArtificial wind generation andstructural responserdquo Journal of Structural Engineering vol 113no 12 pp 2382ndash2398 1987

[22] Y Q Li and S L Dong ldquoRandom wind load simulation andcomputer program for large-span spatial structuresrdquo SpatialStructures vol 7 pp 3ndash12 2001 (Chinese)

[23] M Shiotani and H Avai ldquoLateral structures of gusts in highwindsrdquo in Proceedings of the International Conference on WindEffects on Buildings and Structures 1967

[24] X T Zhang ldquoThe spatial correlations and conversion factor ofwind -excited random vibration for towers and tall buildingsrdquoJournal of Tongji University vol 2 1982 (Chinese)

[25] Q Y Li Design of Small Wind Turbine Machinery IndustryPress Beijing China 1986 (Chinese)

[26] R Shirzadeh C DevriendtM A Bidakhvidi and P GuillaumeldquoExperimental and computational damping estimation of anoffshore wind turbine on a monopole foundationrdquo Journal ofWind Engineering and Industrial Aerodynamics vol 120 pp 96ndash106 2013

[27] R LMa Y QMa H Q Liu and J L Chen ldquoAmbient vibrationtest and numerical simulation for modes of wind turbine tow-ersrdquo Journal of Vibration and Shock vol 30 no 5 pp 152ndash1552011 (Chinese)

[28] ANSYS Userrsquos Manual Structural Analysis Guide ANSYS Inc1998

[29] GB50135-2006 ldquoCode for design of high-rising structuresrdquo(Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Li et al [3] analyzed the data of typhoon Saomai when it waspassing through Hedingshan wind farm It was pointed outthat the violent wind drastic turbulence and sudden changeof wind direction were major factors of wind turbine failuresFrom the view of economics Clausen et al [5] estimated thatthe cost of wind turbine in tropical cyclone zones is 20ndash30more than that in normal areas Chou et al [6] examined thecauses of blade damage of five wind turbines in ChanghuaCoastal Industrial Park of Taiwan It was found that long-term effects such as blade fatigue could cause local crack dam-age and delamination and the actual blade damage occurredmainly on the back edge of the blade near the wing section

In offshore wind turbines the structural responses aredriven not only by wind but also by water wave Conse-quently the dynamic analysis of offshore wind turbines ismore complex than that of land-based ones Karimirad andMoan [7] employed an advanced blade element momentumtheory panel method and the Morison formula to study thedynamic structural and motion responses of a spar-typefloating offshore wind turbine caused by stochastic nonlinearwave and wind loads in harsh and operational environmentalconditions It is found that the wind turbulence affectspower production rather than the dynamic motion andstructural responses Based on the Arbitrary Lagrangian-Eulerian (ALE) method and FEM Zhang et al [8] simulateda wind-induced aqueduct-water coupling system installedwith isolated bearings It is found that the resonance can beeliminated under high-order-frequency excitation and mayhappen when the excitation frequency is close to the first-order water sloshing frequency Karimirad andMoan [9] pre-sented a stochastic dynamic response analysis of a tension legspar-type wind turbine subjected to wind and wave actionsTo study the power performance and structural integrity ofthe system negative damping rotor configuration and towershadow effects are discussed

This paper aims at analyzing the potential failuremodes ofwind power structure subjected to typhoon and is organizedas follows The location and wind condition of Dongtai windfarm is introduced in Section 2 In Section 3 the fluctuatingwind speed of typhoon is simulated and verified based on aregional PSDmode and theARmethod followed by a presen-tation of wind load calculation in the same part A FE modelof a 15MW wind turbine with pile foundation is establishedin Section 4 and structurersquos natural frequencies and wind-induced responses are calculated by elastic dynamic analysisThe failure modes of the wind power structure are concludedfinally

2 Farm Location and Wind Condition

Dongtai wind farm is located in Dongtai City Jiangsu Prov-ince southeastern China at 120∘541015840 east latitude and 32∘471015840north longitude as shown in Figure 1 Totally one hundredand thirty-four 15MW wind turbines are installed in a60 km2 site Wind resource in this area is rich in east andpoor in west forming a long and narrow wind speed surgingregion

AlthoughDongtai is not a typhoon landing site in generalit still has to face the threat of typhoon For example in 2009

Table 1 Tropical cyclone classification

Classification Average wind speed(ms) Wind scale

Tropical depression (TD) 108ndash171 6-7Tropical storm (TS) 172ndash244 8-9Severe tropical storm (STS) 245ndash326 10-11Typhoon (TY) 327ndash414 12-13Severe typhoon (STY) 415ndash509 14-15Super typhoon (SuperTY) ge510 ge16

Figure 1 Location of Dongtai wind farm

Dongtai wind farm

JapanSouth Korea

China

Figure 2 The track map of typhoon Morakot

typhoon Morakot passed through Dongtai with an averagewind speed of 33ms and moved into East China Sea asshown in Figure 2 In 2012 typhoonDamrey landed inXiang-shui of Jiangsu Province with an average wind speed of35ms and brushed past Dongtai as shown in Figure 3 Itshould be noted that according to the extreme wind speedmodel (EWM) [4] the extreme wind speed with a recurrenceperiod of 50 years of the wind farm is 2437ms which is farbelow the average wind speed of the two typhoonsmentionedabove

According to [10] tropical cyclones are classified as 6grades as shown in Table 1 It can be seen that the lowerlimit of typhoonrsquos average wind speed is 327ms which isemployed to simulate the fluctuatingwind speed in this paper

3 Typhoon Wind Load Simulation

31 PSD Model of Typhoon Natural wind consists of twocomponents that ismeanwind and fluctuatingwind and the


Dongtai wind farm

JapanSouth Korea

China



119880119911(119905) = 119880

119911+ 119906119911(119905) (1)

where 119880119911and 119906



119880119911= 119880ref

ln (1199111199110)

ln (119911ref1199110) (2)



119878V (119899) =546119896V2

10

11990924

119899(1 + 151199092

)14

(3)

119909 =1200119899

V10

(4)

119899 =120596

2120587 (5)





u (119905) =119901

sum

119896=1

120595119896

u (119905 minus 119896Δ119905) + N (119905) (6)

u (119905) = [1199061 (119905) 119906119872 (119905)]119879

(7)


(8)

N (119905) = [1198731 (119905) 119873119872 (119905)]119879

(9)


119896




119877119894

119906

[119896Δ119905]

= 119864 [119906119894

(119905 minus 119896Δ119905)minus119864 [119906119894

(119905 minus 119896Δ119905)] 119906119894

(119905) minus 119864 [119906119894

(119905)]]

(10)


119877119894

119906

[119896Δ119905] = 119864 [119906119894

(119905 minus 119896Δ119905) 119906119894

(119905)] (11)



R = R120595

R119901119872times119872

= [R119906(Δ119905) R

119906(119901Δ119905)]

119879

120595119901119872times119872

= [120595119879

1

120595119879

119901

]119879

R119901119872times119901119872

=

[[[[[[[

[

R119906(0) R


119906[(119901 minus 2) Δ119905] R

119906[(119901 minus 1) Δ119905]

R119906(Δ119905) R


119906[(119901 minus 1) Δ119905] R

119906(0)

d

R119906[(119901 minus 2) Δ119905] R


119906[(119901 minus 4) Δ119905] R

119906[(119901 minus 3) Δ119905]

R119906[(119901 minus 1) Δ119905] R


119906[(119901 minus 3) Δ119905] R

119906[(119901 minus 2) Δ119905]

]]]]]]]

]

R119906(119895Δ119905)119872times119872

=

[[[

[

11987711

119906

(119895Δ119905) sdot sdot sdot 1198771119872

119906

(119895Δ119905)

d

1198771198721

119906

(119895Δ119905) sdot sdot sdot 119877119872119872

119906

(119895Δ119905)

]]]

]

119895 = 1 119901

[120595119895

]119872times119872

=

[[[

[

12059511

119895


119895

d

1205951198721

119895

sdot sdot sdot 120595119872119872

119895

]]]

]

119895 = 1 119901

(12)


119877119894119896

119906

(119895Δ119905) = int

infin

0

119878119894119896

119906

(119899) cos (2120587119895Δ119905) 119889119899

119894 119896 = 1 119872

(13)

where 119878119894119896119906


119894 119910119894 119911119894) and point 119896(119909


as

119878119894119896

119906

(119899) = radic119878119894119894

119906

(119899) 119878119896119896

119906

(119899)coh119894119896 (119899) (14)

where 119878119894119894119906




1003816100381610038161003816

119871119911

) (15)



R119873= R119906(0) minus

119901

sum

119896=1

R119906(119896Δ119905) (16)



N (119905) = Ln (119905) (17)

n (119905) = [1198991 (119905) 119899119872 (119905)]119879

(18)


119873and

R119873= LL119879 (19)






F119877(119905) = 119862

119863120588u2119879

(119905) 119860 (20)





w (119905) =120574

2119892u2119879

(119905) asympu2119879

(119905)

1630 (21)



F119890(119905) = 120583

119904119890119860119890w (119905) (22)



of the element

4 FE Analysis


Mu119873(119905) + Cu

119873(119905) + Ku

119873(119905) = f (119905) (23)


119873(119905) u119873(119905) andu

119873(119905) are the



0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15W

ind

spee

d (m

sminus1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)



Frequency (Hz)


102

103

101

100

10minus1

10minus3

10minus2


(m2middotsminus1)

S










Mu119873(119905) + Ku

119873(119905) = 0 (24)


u119873(119905) = 120593 sin (120596119905 + 120601) (25)





ℎ= 18times 10













W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N


Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X





1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Dongtai wind farm

JapanSouth Korea

China



119880119911(119905) = 119880

119911+ 119906119911(119905) (1)

where 119880119911and 119906



119880119911= 119880ref

ln (1199111199110)

ln (119911ref1199110) (2)



119878V (119899) =546119896V2

10

11990924

119899(1 + 151199092

)14

(3)

119909 =1200119899

V10

(4)

119899 =120596

2120587 (5)





u (119905) =119901

sum

119896=1

120595119896

u (119905 minus 119896Δ119905) + N (119905) (6)

u (119905) = [1199061 (119905) 119906119872 (119905)]119879

(7)


(8)

N (119905) = [1198731 (119905) 119873119872 (119905)]119879

(9)


119896




119877119894

119906

[119896Δ119905]

= 119864 [119906119894

(119905 minus 119896Δ119905)minus119864 [119906119894

(119905 minus 119896Δ119905)] 119906119894

(119905) minus 119864 [119906119894

(119905)]]

(10)


119877119894

119906

[119896Δ119905] = 119864 [119906119894

(119905 minus 119896Δ119905) 119906119894

(119905)] (11)



R = R120595

R119901119872times119872

= [R119906(Δ119905) R

119906(119901Δ119905)]

119879

120595119901119872times119872

= [120595119879

1

120595119879

119901

]119879

R119901119872times119901119872

=

[[[[[[[

[

R119906(0) R


119906[(119901 minus 2) Δ119905] R

119906[(119901 minus 1) Δ119905]

R119906(Δ119905) R


119906[(119901 minus 1) Δ119905] R

119906(0)

d

R119906[(119901 minus 2) Δ119905] R


119906[(119901 minus 4) Δ119905] R

119906[(119901 minus 3) Δ119905]

R119906[(119901 minus 1) Δ119905] R


119906[(119901 minus 3) Δ119905] R

119906[(119901 minus 2) Δ119905]

]]]]]]]

]

R119906(119895Δ119905)119872times119872

=

[[[

[

11987711

119906

(119895Δ119905) sdot sdot sdot 1198771119872

119906

(119895Δ119905)

d

1198771198721

119906

(119895Δ119905) sdot sdot sdot 119877119872119872

119906

(119895Δ119905)

]]]

]

119895 = 1 119901

[120595119895

]119872times119872

=

[[[

[

12059511

119895


119895

d

1205951198721

119895

sdot sdot sdot 120595119872119872

119895

]]]

]

119895 = 1 119901

(12)


119877119894119896

119906

(119895Δ119905) = int

infin

0

119878119894119896

119906

(119899) cos (2120587119895Δ119905) 119889119899

119894 119896 = 1 119872

(13)

where 119878119894119896119906


119894 119910119894 119911119894) and point 119896(119909


as

119878119894119896

119906

(119899) = radic119878119894119894

119906

(119899) 119878119896119896

119906

(119899)coh119894119896 (119899) (14)

where 119878119894119894119906




1003816100381610038161003816

119871119911

) (15)



R119873= R119906(0) minus

119901

sum

119896=1

R119906(119896Δ119905) (16)



N (119905) = Ln (119905) (17)

n (119905) = [1198991 (119905) 119899119872 (119905)]119879

(18)


119873and

R119873= LL119879 (19)






F119877(119905) = 119862

119863120588u2119879

(119905) 119860 (20)





w (119905) =120574

2119892u2119879

(119905) asympu2119879

(119905)

1630 (21)



F119890(119905) = 120583

119904119890119860119890w (119905) (22)



of the element

4 FE Analysis


Mu119873(119905) + Cu

119873(119905) + Ku

119873(119905) = f (119905) (23)


119873(119905) u119873(119905) andu

119873(119905) are the



0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15W

ind

spee

d (m

sminus1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)



Frequency (Hz)


102

103

101

100

10minus1

10minus3

10minus2


(m2middotsminus1)

S










Mu119873(119905) + Ku

119873(119905) = 0 (24)


u119873(119905) = 120593 sin (120596119905 + 120601) (25)





ℎ= 18times 10













W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N


Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X





1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











R = R120595

R119901119872times119872

= [R119906(Δ119905) R

119906(119901Δ119905)]

119879

120595119901119872times119872

= [120595119879

1

120595119879

119901

]119879

R119901119872times119901119872

=

[[[[[[[

[

R119906(0) R


119906[(119901 minus 2) Δ119905] R

119906[(119901 minus 1) Δ119905]

R119906(Δ119905) R


119906[(119901 minus 1) Δ119905] R

119906(0)

d

R119906[(119901 minus 2) Δ119905] R


119906[(119901 minus 4) Δ119905] R

119906[(119901 minus 3) Δ119905]

R119906[(119901 minus 1) Δ119905] R


119906[(119901 minus 3) Δ119905] R

119906[(119901 minus 2) Δ119905]

]]]]]]]

]

R119906(119895Δ119905)119872times119872

=

[[[

[

11987711

119906

(119895Δ119905) sdot sdot sdot 1198771119872

119906

(119895Δ119905)

d

1198771198721

119906

(119895Δ119905) sdot sdot sdot 119877119872119872

119906

(119895Δ119905)

]]]

]

119895 = 1 119901

[120595119895

]119872times119872

=

[[[

[

12059511

119895


119895

d

1205951198721

119895

sdot sdot sdot 120595119872119872

119895

]]]

]

119895 = 1 119901

(12)


119877119894119896

119906

(119895Δ119905) = int

infin

0

119878119894119896

119906

(119899) cos (2120587119895Δ119905) 119889119899

119894 119896 = 1 119872

(13)

where 119878119894119896119906


119894 119910119894 119911119894) and point 119896(119909


as

119878119894119896

119906

(119899) = radic119878119894119894

119906

(119899) 119878119896119896

119906

(119899)coh119894119896 (119899) (14)

where 119878119894119894119906




1003816100381610038161003816

119871119911

) (15)



R119873= R119906(0) minus

119901

sum

119896=1

R119906(119896Δ119905) (16)



N (119905) = Ln (119905) (17)

n (119905) = [1198991 (119905) 119899119872 (119905)]119879

(18)


119873and

R119873= LL119879 (19)






F119877(119905) = 119862

119863120588u2119879

(119905) 119860 (20)





w (119905) =120574

2119892u2119879

(119905) asympu2119879

(119905)

1630 (21)



F119890(119905) = 120583

119904119890119860119890w (119905) (22)



of the element

4 FE Analysis


Mu119873(119905) + Cu

119873(119905) + Ku

119873(119905) = f (119905) (23)


119873(119905) u119873(119905) andu

119873(119905) are the



0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15W

ind

spee

d (m

sminus1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)



Frequency (Hz)


102

103

101

100

10minus1

10minus3

10minus2


(m2middotsminus1)

S










Mu119873(119905) + Ku

119873(119905) = 0 (24)


u119873(119905) = 120593 sin (120596119905 + 120601) (25)





ℎ= 18times 10













W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N


Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X





1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












F119877(119905) = 119862

119863120588u2119879

(119905) 119860 (20)





w (119905) =120574

2119892u2119879

(119905) asympu2119879

(119905)

1630 (21)



F119890(119905) = 120583

119904119890119860119890w (119905) (22)



of the element

4 FE Analysis


Mu119873(119905) + Cu

119873(119905) + Ku

119873(119905) = f (119905) (23)


119873(119905) u119873(119905) andu

119873(119905) are the



0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15W

ind

spee

d (m

sminus1)


0 20 40 60 80 100 120 140 160 180 200

0

5

10

15

Time (s)

minus5

minus10

minus15

Win

d sp

eed

(msminus

1)



Frequency (Hz)


102

103

101

100

10minus1

10minus3

10minus2


(m2middotsminus1)

S










Mu119873(119905) + Ku

119873(119905) = 0 (24)


u119873(119905) = 120593 sin (120596119905 + 120601) (25)





ℎ= 18times 10













W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N


Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X





1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















Mu119873(119905) + Ku

119873(119905) = 0 (24)


u119873(119905) = 120593 sin (120596119905 + 120601) (25)





ℎ= 18times 10













W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N


Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X





1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












W-1 W-2 W-3W-4

W-5

W-6

W-

W-7

8

W-9

W-10

W-11

W-12W-13W-14

W-15

W-16

W-17

W-18

W-19

W-20

W-21

W-22W-23

W-24

N-1

N-2N-3

N-4

N-5 N-612060141

00

18000

6 times PHC600

24 times PHC600

12060116800

N


Wind direction

Rotor

Nacelle

Tower

Anchor ring

Pile cap

Piles

X





1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1

(Hz) Case 2 1198912

(Hz) (1198912

minus 1198911

)1198911

1 04093 04139 1122 04150 04198 1163 16073 16251 1114 21899 22304 1855 24607 25216 2476 34773 47378 36257 35011 49219 40588 46193 58408 26449 47378 58443 233510 49218 61542 2504

002040608

112

0 50 100 150 200

Time (s)

minus02

Uh

(m)






0100200300400500600

0 50 100 150 200Equi

vale

nt st

ress

(MPa

)

Time (s)


0100200300400500600

0 50 100 150 200

Equi

vale

nt st

ress

(MPa

)

Time (s)




0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09



0

= 582E0+ 07= 770E0

0770E + 07

0715E + 08

0135E + 09

0199E + 09

0263E + 09

0327E + 09

0391E + 09

0455E + 09

0518E + 09

0582E + 09




0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)


0100200300400500600

0 50 100 150 200Time (s)

Equi

vale

nt st

ress

(Mpa

)




SMX = 616E + 09

Wind direction

Windward side

X

YZ


0800E + 08

0147E + 09

0214E + 09

0281E + 09

0348E + 09

0415E + 09

0482E + 09

0549E + 09

0616E + 09

0

0SMN = 0130E+ 08


0100200300400500

500 100 150 200Time (s)

minus100minus200

Fy

(kN

)


1000

800

600

400

200

0500 100 150 200

Time (s)

Fy

(kN

)




6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









failure analysis of large-scale wind power structure under

Documents