Analysis of a Wind Turbine Blade

7/22/2019 Analysis of a Wind Turbine Blade

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UNIVERSIDAD DE CONCEPCINFACULTADA DE INGENIERA AGRCOLA

NATURAL FRECUENCIES ANALYSIS OF A WIND TURBINE BLADE

RODRIGO FUENTES CCERES

CHILLAN CHILE

2009

TESIS PRESENTADA A LA ESCUELA DEGRADUADOS DE LA UNIVERSIDAD DECONCEPCION, PARA OPTAR AL GRADO DEMAGISTER EN INGENIERA AGRCOLA,MENCIN MECANIZACIN Y ENERGA.


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Aprobado por:

Gabriel Merino Coria

Licenciado en Fsica, Ph. D.Profesor Asociado Profesor Gua

Cristian Rodrguez GodoyIngeniero Civil Mecnico, DoctorProfesor Asistente Profesor Asesor Externo

Emilio Dufeu DelarzeIngeniero Civil Mecnico, DoctorProfesor Asociado Profesor Asesor Externo

Octavio Lagos RoaIngeniero Civil Agrcola, Ph. D.Profesor Asistente Director de Programa

Eduardo Holzapfel HocesIngeniero Agrnomo, Ph. D.Profesor Titular Decano


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INDEX

Page

Summary..................................................................................................

Resumen..................................................................................................

Introduction..............................................................................................

Finite Elements Model......................................................................

Experimental Modal Test..............................

Results............................................................................

Conclusions........................................................................

References...............................................................................................

Figures and Tables..................................................................................

1

3

5

8

9

11

13

14

16


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Keywords:Wind Turbine, FEM, Natural Frecuencies.

ABSTRACT

This paper studies the influence of the rotor angular speed on the natural

vibration frequencies of the blades for a low power wind turbine, due to the

stiffness effect produced by the centrifuge force. The wind turbine under

study corresponds to a 1 kW wind turbine, which consists of three blades of

compound material of fiber glass with epoxy resin, and whose range of

angular speed in operation fluctuates from 0 to 600 rpm.

The research has considered a finite elements model (FEM) of the blades

calculate their natural frequencies at several operational rotating speed, and

an experimental modal test for validating the numerical model at zero rotating

speed. For the FEM development, SAMCEF software was used, using

volume elements for the discretization of the blade. The impact test done on

the turbine blade was carried out reproducing the clampling condition of the

blade on the turbines rotor in the laboratory, using a Bruel & Kjaer, 8206

Model impact hammer, and a data collector-analysis system PXI, National

Instruments, 4472B Card was used to experimentally obtain the natural

vibration frequencies of the blade at a zero rotating speed.

Researches related to the natural frequencies about wind turbine blades have

considered a beam model to simulate the blades on the wind turbine. This


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research has focused on high power turbines. Results presented about the

stiffness effect of the blades on large turbines due to rotation speed, show a

non-significative stiffness effect, which means that the natural frequencies do

not significantly change in operation, regarding its resting position.

By using the FEM model developed in this study, graphs of the first, second

and third natural vibration frequencies of the blades in flapwise mode were

obtained, versus the turbines rotating speed where the blades stiffness

effect appears, due of the centrifugal force. Results indicate that the first

natural frequency, in flapwise bending, varies from 4 to 20 Hz, in a range of

speeds from 0 to 600 rpm, that is, an increase of five times the value of

natural frequency of the resting blade, regarding its value in operation at 600

rpm.


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ANALISIS DE LAS FRECUENCIAS NATURALES DE VIBRAR DE LAS

ASPAS DE UNA TURBINA EOLICA

Palabras ndice adicionales: Fotovoltaico, bombeo PV, bombeo de acopledirecto, monitoreo.

RESUMEN

En este trabajo se ha estudiado el grado de incidencia que produce la

velocidad de rotacin del rotor sobre las frecuencias naturales de vibrar delas aspas, en un aerogenerador de baja potencia, debido al efecto de

rigidizacin que produce la fuerza centrfuga. El modelo bajo estudio,

corresponde a una turbina de 1 kW de potencia, que consta de tres aspas de

material compuesto de fibra de vidrio con resina epxica y cuyo rango de

velocidad de rotacin, en operacin, flucta entre 0 y 600 rpm.

La investigacin ha contemplado la generacin de un modelo numrico en

elementos finitos de las aspas, para calcular sus frecuencias naturales de

vibrar a distintas velocidades angulares de operacin, previo un ensayo

modal experimental para validar el modelo numrico, a velocidad de rotacin

cero. Para el desarrollo del modelo numrico, se utiliza el programa

SAMCEF, para modelacin por elementos finitos, utilizando elementos devolumen para la discretizacin del aspa. El ensayo de impacto realizado al

aspa de la turbina, se ejecuta replicando en banco de pruebas, la condicin

mecnica de empotramiento del aspa montada sobre el rotor de la turbina y

se utiliza un martillo de impacto Bruel & Kjaer, Modelo 8206 y un sistema de


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Adquisicin de datos PXI, National Instruments, Tarjeta 4472B para obtener

en forma experimental las frecuencias naturales de vibrar del aspa, a

velocidad de rotacin cero.

Investigaciones relacionadas a frecuencias naturales sobre aspas de

turbinas, han considerado un modelo de viga para simular las aspas en la

turbina, aunque los trabajos desarrollados se centran en turbinas de grandes

potencias. Resultados presentados sobre el efecto rigidizador de las aspas

en grandes turbinas, debido a la velocidad de rotacin, muestran un no gran

efecto rigidizador, esto significa que las frecuencias naturales no varan

significativamente, en operacin, con respecto a su condicin de reposo.

Al utilizar el modelo de elementos finitos desarrollado en este estudio, se

obtienen grficos de las tres primeras frecuencias naturales de vibrar de las

aspas, en modo flapwise, versus la velocidad de rotacin del rotor de la

turbina, en los cuales se aprecia el efecto de rigidizamiento de las aspas,

producto de la fuerza centrfuga. Se puede apreciar que la primera frecuencia

natural, en flexin flapwise, vara desde 4 Hz hasta 20 Hz, en un rango de

velocidades desde 0 rpm hasta 600 rpm, esto es, un aumento de cinco veces

el valor de la frecuencia natural del aspa en reposo, con respecto a su valor

en operacin a 600 rpm.

.


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INTRODUCTION

Due to the Chilean growing energy demand, which increases with the

countrys economic development, in addition to the exponential increase in

prices of the oil, to obtain electric energy from non-conventional renewable

sources is becoming more and more important. Wind power is a good

alternative source of non-contaminating renewable energy. Its low power

demand is growing, due to the increase of generation costs based on diesel

in isolated areas. The big barriers for using wind power have been the high

costs of the turbines and the lack of general knowledge in terms of the

selection, installation, performance and maintenance of the equipment.

Based on this fact, the objective of this study is to contribute with

indispensable knowledge for the development of this type of technology at a

national level.

Wind turbines can be classified as small and large, related to their power.

According to [12], we refer to small turbines as those with power less than 10

kW. Those with greater power are considered large wind turbines. According

to [9], currently, the majority of the machines that are installed present

nominal powers between 0.6 and 5 MW.

The objective of small wind turbines is to supply electric energy to residents,

farms, or small rural groups, isolated from the electric supply network. The

power of these machines usually varies between 0.1 and 10 kW [14]. These

wind turbines are much more simple than those used for large scale


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generation. In terms of its operating conditions, low power wind turbines have

operation speeds that can reach 1100 rpm, according to [14], and its blades

length between 1 and 4.5 m, compared with high power turbines, in which the

rotating speed does not exceed 60 rpm, according to [11] and [13], and

whose blades measure length between 10 and 55 m. These operational

characteristics produce a greater rigidity effect of the blades in the small

turbines, due to the angular velocity. In the large turbines, a greater rigidity

effect of the blades occurs due to their mass and radius.

In general, researches done about wind turbines related to the natural

vibration frequencies focuses on high power turbines, because of the

prioritary economic interest on the electric energy conversion. Tests done on

high power turbines blades show a minimal blades rigidity effect due to the

centrifugal force (see Figure 2).

In [4], the vibration response of a turbine tower and blades assembling under

the action of the stationary wind force was studied. In this case, the blades

are modeled as beams fitted to a rotating mass and only consider the

bending of one of its axis.

Studies done about beams fitted to a rotating mass, as in [1] and [2], where

the equations of motion of the beam are represented, considered as a Euler

Bernoulli beam, under large rotation displacements (rigid body motion) and

with small elastic deformations, like in [5], considering three variables:

bending in the most flexible direction (flapwise), bending in the most rigid


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direction (edgewise) and the lengthening of the beam (stretching). This way,

three partial differential equations about the beam motion are obtained.

In [2], these equations of motion are solved by the finite elements method and

an analysis of the dimensionless natural vibration frequencies versus the

beams dimensionless rotation speed was done on the three previously

mentioned variables. As they are dimensionless, these results are applied to

beams of any size.

In [3], the blade is modeled considering its complete geometry, but only for

zero angular speed, for which the influence of the centrifugal force due to

rotational speed on the behavior of the blades natural vibration frequency

was not considered. In this case, a mathematical model is presented

regarding a high power turbine blade (19 m in length) mounted on a rigid

mass (See Figure 1). The equations of motion describe small rotations of the

mass (hub), small flapwise and edgewise bending, and considers the warp

movement of the blade (warping). The mathematical model is solved as a

eigenvalues problem and then compared with an experimental modal

analysis, with excellent results.

As previously mentioned, the stiffness increase that is result of the rotating

speed of blades on large size turbines is not considerable. According to [11],

it is worth asking what the influence of the rotating speed of the blades on

small size turbines is, since the rotation speed are greater, considering its

geometry and the material parameters it is made of.


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The principal objective of this study is to investigate the degree of influence of

the rotors rotating speed on the natural vibration frequencies of the blades,

due to the stiffness increase that the centrifugal force produces on a low

power wind turbine (1 kW). For this purpose, a numerical model of the

turbines blade will be generated, with the SAMCEF software, for modeling

by the finite elements method. In addition, the natural frequencies of the

turbines resting blade will be determined through an experimental modal test.

Then, the numerical model at rotation speed zero will be validated, comparing

it with the natural frequencies experimentally obtained, to then determine

through the numerical model, the natural frequencies of the wind turbines

blade for different operation angular speeds.

FINITE ELEMENTS MODEL (FEM)

The modal dynamical analysis, through the finite elements method, was done

with the SAMCEF program. In this study the blade is discretized using volume

elements, pentahedrons and hexahedrons of first order [6], using a total of

4646 nodes of 3 degrees of freedom, and 2600 elements, with a total of 200

pentahedron elements (7.7%) and 2400 hexahedrons (92.3%). The model

was made considering the blade clamped in one of its extremes, as shown in

Figure 4, and replicating the real profile of the blade, as observed in Figures 3

and 5. The blade is built of fiber glass with epoxy resin, for which, according

to [10] and [8], an elasticity module (Young) of 38600 MPa and a Poissons

model of 0.26 were considered. On the other hand, the measured density is


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1.9 X 10-9 ton/mm3. This data was used in the simplified construction of the

model, where the non-linear elastic orthotropic properties that compound

materials generally present were not considered, but the isotropic properties

with behavior within a linear elastic range of the materials were, as was

estimated in [3], achieving good results.

With the model in question, the modal study of the blade was carried out, at a

rotating speed zero, where the natural vibration frequencies were obtained,

which were then compared with those obtained in the experimental modal

test in Table 1.

Next, the results obtained from the numeric model are presented, in terms of

the three first flapwise bending modes (regarding the Y axis) of the blades

vibration. The first vibration mode has a natural frequency of 4.4 Hz and

posseses a node on the extreme of the blades clamping, see Figure 6. The

second vibration mode has a frequency of 27.7 Hz and posseses two nodes,

as observed in Figure 7. The third vibration mode is observed in Figure 8,

which has a frequency of 77.4 Hz, with its corresponding three nodes.

EXPERIMENTAL MODAL TEST

In the impact test, a Bruel & Kjaer, 8206 Model impact hammer, a Bruel &

Kjaer, 4513-001 model accelerometer sensor and a PXI, National

Instruments, card 4472B data adquisition card were used, as well as

LabView software.


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The blade was clamped to a base in the laboratory, as obserevd in Figure 9,

to simulate its behavior when mounted on the turbines rotor. The modal

impact test consisted of hitting the blade, which is measured with the impact

hammer, and then the vibratory amplitude of the blades vibration is measured

by the accelerometer. This signal is captured by the data acquisition card,

and with the LabView software, the frequencies answer function of the

vibration was calculated, where the natural vibration frequencies of the blade

were obtained [7].

In Figure 10, that answer in the time of the amplitude of the blades vibratory

acceleration is observed, due to the impact given in its free extremity. The

accelerometer was installed in the clamped side of the blade. The impact

given and the blades response of the free - damped vibration can be seen in

the waveform, which decreases in amplitude as time passes. In Figure 11,

the spectrum in frequencies of the acceleration amplitude of the vibration is

observed, in a range of frequencies from 0 to 800 Hz. The several

frequencies of which the vibratory wave is composed of can be seen, among

which the blades natural vibration frequencies are found.

The following natural vibration frequencies were obtained by this impact test,

which are compared with those obtained by the numerical model by finite

elements, in Table 1.

Comparing the blades natural frequencies obtained through the experimental

test with those obtained through the numerical model (on SAMCEF), in Table

1, a minimum difference can be seen (less than 8%), in the results of both


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methods regarding the three first natural frequencies. The dispersion of the

values of high frequencies could be caused by a lack of refinement of the

mesh (4646 nodes), and by the using elements of first order. However, this

does not detriment the study objectives, as they require analyzing the

dynamic behavior of the blades for a range of the turbines operational speed,

for which, the high frequencies are very outside the range. Therefore, it is not

necessary to make any adjustments to the numerical model.

With this, the numerical model is validated at zero angular speed and will be

used to simulate the behavior of the blades natural frequencies for the

turbines several operational speeds, and study its stiffness effect on the

blade and the influence on the behavior of its natural frequencies under

operational conditions.

RESULTS OF NATURAL VIBRATION FREQUENCIES OF THE BLADES

VERSUS ROTATING SPEED

The range of rotating speed in normal operation of the turbine is from 0 to 600

rpm. The modal analysis was simulated for rotating speeds of 10, 20, 30, 40,

50 and 60 rad/s, that is, between 95 and 668 rpm. With this data, a graph was

created with the behavior of the three first natural vibration frequencies for

flapwise mode, versus the rotating speed in rpm (see Figure 12). In this first

graph, it can be seen that the behavior of the second and third modes natural

frequency are out of the range of turbines frecuencies, 1X, 2X and 3X.


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For better observation about if there is at some time a resonant zone of one

of the two first natural vibration frequencies, in flapwise bending, a graph

was made of these two first natural frequencies (in Hz) versus the rotating

speed of the turbine (in Hz) in its range of operational speed. It can be

observed that the rotating frequency 1X, is out of the range of the second

natural vibration frequency. In terms of the first natural vibration frecuency,

which at a zero rotating speed is of 4.92 Hz, it can be observed that as the

rotating speed increases, it generates an increase of the value of the natural

frequency, due to the stiffness effect, unable the 1X to reach this first natural

frequency, for which there are no problems of resonance.

In terms of the blades frequency, it means 3X, there is a problem around the

2 Hz (120 rpm) of rotation, as the 3X = 6 Hz coincide with the first natural

frequency, for which there is a posible problem of structural resonance at this

speed (see Figure 13). It must be considered that this condition is given for

the blades frequency, when passing in front of the tower tube, for which the

excitation force should be transmitted from the tower to the turbines rotor and

then to the blades, therefore it is not a direct excitation, which is not very

significative.


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CONCLUSIONS

The experimented by [3] is proven in this paper; by developing a modal

dynamical model of the blades, the non-linear elastic orthotropic condition of

the compound materials can be approximated by a simplified linear elastic

isotropic model, with good results, at a zero rotating speed.

Under the conditions of the simplifed model previously indicated, it is possible

to simulate the behavior of the blades of a wind turbine with the method of

finite elements, acheiving a very good approximation by comparing the

obtained natural vibration frequencies with the finite elements model (FEM),

versus those obtained through an experimental modal test, at a zero

rotational speed.

In this paper, it can be appreciated that the stiffness effect of the blades due

to rotating speed, for small sized turbines, is considerably significative.

Graphs are presented of the blades three first natural vibration frequencies,

in flapwise mode, versus the turbines rotors rotating speed, in which it can

be seen that the first natural flapwise frequency varies from 4 Hz to 20 Hz, in

a range of speed from 0 to 600 rpm, that is, an increase of up five times the

blades natural frequency while resting, versus its operational value at 600

rpm. Therefore, for the design of low power turbine blades, where rotational

speed is high, it is not sufficient to only calculate the natural frequencies with

an impact test of the resting blade, rather it also requires a study of their

dynamical behavior, to avoid resonances and prolong its lifespan.


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REFERENCES.

[1] H. H. Yoo, R. R. Ryan and R. A. Scott 1995, Journal of Sound and

Vibration 181, 261 278. DYNAMICS of FLEXIBLE BEAMS UNDERGOING

OVERALL MOTIONS.

[2] J. Chung and H. H. Yoo 2002, Journal of Sound and Vibration 249, 147

164. DYNAMICS ANALYSIS of a ROTATING CANTILEVER BEAM by

USING the FINITE ELEMENT METHOD.

[3] A. Baumgart 2002, Journal of Sound and Vibration 251, 1 12. A

MATHEMATICAL MODEL FOR WIND TURBINE BLADES.

[4] P.J. Murtagh, B. Basu, B.M. Broderick 2005, Engineering Structures 27,

1209 1219. ALONG WIND RESPONSE OF A WIND TURBINE TOWER

WITH BLADE COUPLING SUBJECTED TO ROTATIONALLY SAMPLED

WIND LOADING.

[5] J. C. Simo 1985, Computer Methods in Applied Mechanics and

Engineering 49, 55 70. A FINITE STRAIN BEAM FORMULATION. THE

THREE DIMENSIONAL DYNAMIC PROBLEM. PART I.

[6] T. Chandrupatla, A. Belegundu 1999, INTRUDUCCION AL ESTUDIO DEL

ELEMENTO FINITO EN INGENIERIA. Prentice Hall.

[7] Peter Avitabile 2001, Sound and Vibration 35, 20 31. EXPERIMENTAL

MODAL ANALYSIS. A SIMPLE NON MATHEMATICAL PRESENTATION.

[8] C.Kong, J. Bang, Y. Sugiyama 2005, Energy 30, 2101 2114.

STRUCTURAL INVESTIGATION OF COMPOSITE WIND TURBINE BLADE

CONSIDERING VARIOUS LOAD CASES AND FATIGUE LIFE.


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[9] J. W. Larsen 2005, Tesis for the degree of Doctor of Philosophy.

Department of Civil Engineering, Faculty of Engineering and Science, Aalborg

University. NONLINEAR DYNAMICS OF WIND TURBINE WINGS.

[10] R. F. Gibson 1994: PRINCIPLE OF COMPOSITE MATERIALS

MECHANICS. Mc Graw-Hill Ed. p. 1.

[11] R. Gasch, J.Twele 2002, WIND POWER PLANTS. Fundamentals,

Design, Construction and Operation.

[12] J.F. Sanz 2001. GUIA DE LAS ENERGIAS RENOVABLES APLICADAS

A LAS PYMES.

[13] J. Wiley and Sons Ltda. 2001, WIND ENERGY HANDBOOK.

[14] M. Sagrillo 2002, APPLES AND ORANGES CATALOGUE


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Figure 1. Motion Sequence of the Blade in its Second Flapwise Mode. Three

times in the same figure are shown.


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Figure 2. Graph of the Primary Natural Vibration Frequencies versus Rotation

Velocity of the Blade of a Turbine. Turbine Test DEBRA (DLR) [15].


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Figure 3. Profile of the Bergey XL1 turbine blade, of 1 kW. Its clamped

condition to the rotor of the turbine can be seen.


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Figure 4. Model of turbine blade done on SAMCEF. The fitted condition of the

model is marked the red oval.


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Figure 5. Profile of the Bergey XL1 turbine blade, model done on SAMCEF.


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FIGURE 6. First vibration mode of the blade in flapwise bending.

nodo


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FIGURE 7. Second vibration mode of the blade in flapwise bending.

nodo 1

nodo 2


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FIGURE 8. Third vibration mode of the blade in flapwise bending.

nodo 1

nodo 2

nodo 3


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Figure 9. Impact test with the blade bolted to its base, such as the turbines

rotor.


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Figure 10. Response of the vibratory acceleration amplitude (g) in time, of theturbines blade, when is hit with the hammer.


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Figure 11. Response in frequencies (from 0 to 800 Hz) of the vibratory

acceleration amplitude (g), of the turbines blade, when is hit with the

hammer.


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0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800

velocidad de rotacin, rpm.

fnatural,Hz.

fn 1er modo flapwise

fn 2o modo flapwise

fn 3er modo flapwise

1X

2X

3X

Figure 12. Graph of the three primary natural vibratuon frequencies, in

flapwise mode versus rotation velocity in rpm of the turbines blade.


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0

5

10

15

20

25

30

35

40

45

0,00 2,00 4,00 6,00 8,00 10,00 12,00

velocidad de rotacin, Hz.

fnatural,Hz. fn 1er modo flapwise

fn 2o modo flapwise

1X

2X

3X

Figure 13. Graph of the two primary natural vibration frequencies,

inflapwisemode, versus rotating speed, in Hz, of the turbines blade


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Modal Impact Test

FRF

Numeric Model

FEM Deviation

Flapwise

Bending Mode Frequency (Hz) Frequency (Hz)

Percentage

%

1 4.2 4.4 4.8

2 26.2 27.7 5.7

3 72.0 77.4 7.5

4 138.4 151.1 9.2

5 214.6 248.4 15.8

6 315.6 368.6 16.8

7 402.4 510.6 26.9

Table 1. Comparison of the natural frequencies of the first seven modes of

flapwise bending, obtained with the numerical model FEM and the modal test

FRF.

Documents

Analysis of a Wind Turbine Blade