This paper presents selected results and aspects of the multidisciplinary and interdisciplinary research oriented for the experimental and numerical study of the structural dynamics of a bendtwist coupled full scale section of a wind turbine blade structure. The main goal of the conducted research is to validate finite element model of the modified wind turbine blade section mounted in the flexible support structure accordingly to the experimental results. Bendtwist coupling was implemented by adding angled unidirectional layers on the suction and pressure side of the blade. Dynamic test and simulations were performed on a section of a full scale wind turbine blade provided by Vestas Wind Systems A/S. The numerical results are compared to the experimental measurements and the discrepancies are assessed by natural frequency difference and modal assurance criterion. Based on sensitivity analysis, set of model parameters was selected for the model updating process. Design of experiment and response surface method was implemented to find values of model parameters yielding results closest to the experimental. The updated finite element model is producing results more consistent with the measurement outcomes.
Wind turbine blades must be designed to resist the extreme load cases and fatigue loads from normal operation. Sudden wind gusts are often too quick for the active pitch control system to react and may shorten the fatigue life substantially. This problem may be overcome by an aeroelastic tailoring of the blades. Particular implementation of the anisotropic composite material can introduce the bendtwist coupling in the blade [
The object of investigation is an 8meter long section cut from a 23meter wind turbine blade. Blade section is mounted in the two root clamps (Figure
Experimental setup showing the wind turbine blade section mounted on the test rig with the coordinate system.
The blade is a hollow structure with two shells. The two shells form the suction and pressure side of the blade. To join the two shells together the structural web is incorporated. Investigated blade designed by Vestas has a load carrying box girder. The original blade section was modified with four layers of UD1200, which were laminated on the pressure and suction side of the blade with the fibers angle of 25° to create a measurable flapwise bendtwist coupling. The additional layers were laminated as indicated in [
Basic information about geometry and material properties used for modeling of supporting structure.
Geometry [mm]  Pipes  CShapes  IShapes  Plywood 

Inner radius 170 Outer radius 160  Standard UPN 200  Two bolted standard UPN 200  Thickness 180  

200  200  200  13.2 
Density [kg/m^{3}]  7890  7890  7890  736 
Poisson’s Ratio  0.3  0.3  0.3  0.01 
The modified blade section was investigated by means of experimental modal analysis. Particular focus was on the influence of the support structure in the correlation analysis between numerical and experimental modal models [
Blade section was excited with two electrodynamic shakers attached at the tip end in the flapwise and edgewise directions. Frequency response functions were measured and stored within 0 and 120 Hz frequency range.
For adequate identification of the blade dynamic displacement, accelerations of the vibrations were measured in 130 points. Thirteen equidistant measurement crosssections were defined along the spanwise direction (
Model quality assessment was an integrated part of the investigation. Except time invariance another condition must be observed to satisfy of modal analysis assumptions: linearity, Maxwell’s reciprocity principle, and observability. Possible sources of nonlinearities within investigated structure are material properties, geometrical properties, and the existence of bond connections verification of a superposition rule is one of the methods of detecting nonlinearities. Linearity check was done for the level of driving voltage ranging from 0.5 (V) to 2 (V) with a step of 0.5 (V). Results are presented in Figure
Linearity check for one of the points on the blade. Voltage values = 0.5 V, 1 V, 1, 5 V, and 2 V.
The reciprocity check is based on Maxwell’s principle, which states that the FRFs obtained by applying the force on point 1 and measuring the response in 2 and vice versa should be the same. The results for the two checks performed confirmed applicability of the reciprocity rule.
During the processing of the data, some significant noise was observed in the acquired FRFs in the low frequency region. The driving point coherence functions show a small drop in this region, meaning a nonideal excitation (Figure
Coherence functions for the two driving points. It is used as measure of the FRF quality. Ideally it should take value equal to 1.
The modal parameter identification technique was not able to clearly stabilize modes in this region, possibly resulting in some local errors in the mode shapes below 7 Hz. The estimation provided natural frequencies, mode shapes, and corresponding damping ratios in the frequency bandwidth 0–60 Hz. First five out of 12 identified mode shapes are provided in Figure
Estimated experimental mode shapes of the modified blade section and support structure.
1st bend flap,
1st bend edge,
2nd bend flap,
2nd bend edge,
1st torsion,
Bendtorsion,
AutoMAC matrices for experimental modal models with sensors only on the modified blade section (a), support structure (b), and blade section with support structure (c).
AutoMac blade only
AutoMac support only
AutoMac complete structure
Low valued offdiagonal terms for the blade only model ensure linear independence of estimated modal vectors. The correlation between offdiagonal terms is increased when including the supporting structure in the analysis. This is due to the fact that the clamping is not perfectly rigid and the support has its own dynamic behavior which influences the measured response of the blade.
In Figure
The numerical model adopts MSC.Patran/Nastran blade FE model (Figure
FE model of the blade section clamped to the support structure. Yellow bulbs denote test and FE geometry correlation node mapping.
The boundary conditions which were adequately representing support structure in static analysis [
As it can be seen in Figure
The additional FE model consists of beam elements (CBEAM in Nastran notation), shell elements representing plywood (QUAD8), elastic springs representing mountings between beam elements (CELAS1), rigid bars connecting plywood and I shape clamp beams (RBE2 and), and additional rigid bars with ends at position corresponding to the position of measuring points from test setup (RBAR). Rigid connection between plywood and I shapes is justified because of the large difference in E modules of both materials. Representation of FEtotest matching with rigid bars does not introduce additional stiffness to the system and is acceptable as long as global mode shapes of support are of interest only. After preparation of support FE model, both additional and the original FE models were merged. Nodes at the interface between blade and supporting structure, that is, between plywood and outer surface of the blade, have restrained rotational DOFs. Such an approach was taken because in the real structure interface between profilecut plywood and the blade is realized on approximately 200 mm of width, while in the numerical model only single row of nodes is used.
Based on the estimated experimental modal model and modified blade FEM analysis models the correlation analysis can be applied. The FE model should yield natural frequencies values and mode shapes conforming to the measured. Modal assurance criterion is used as the originalmodified blade simulation and also testsimulation correlation metrics.
The global coordinate system used to define the test model differs from that used for the FE model. In order to make the models match it is necessary to apply geometric correlation by translation and rotation of the test model (Figure
The blade section model was solved to compute mode shapes in the 0–60 Hz frequency bandwidth. Calculations were carried out at the CI TASK, Academic Computer Center in Gdańsk on a 50Tflop cluster. Modal assurance criterion was calculated for the corresponding modes in order to associate the closest numerical and experimental mode shapes The procedure accounted for both natural frequency value and the mode shape consistency (Table
Initial consistency of the modal model parameters.
Initial WT blade  

TEST  FE  
Freq. 1  Freq. 2  MAC value  Freq. 2−Freq. 1 (Hz)  Freq. 2−Freq. 1 (% of Freq. 1) 



































The following modes were investigated: 1st and 2nd flapwise bending, 1st and 2nd edgewise bending, and 1st torsional (Figure
MAC matrix for test and FE simulation modal vectors of modified blade without support structure.
The consistency of the results can be recognized as satisfactory; however the present differences need to be further investigated. Observing the values of the MAC criterion between test and simulation modes (Figure
Satisfactory conformity of the static tests and simulations results has proven the validity of the FE model of modified blade section. Structural dynamics analysis revealed the unsatisfactorily large difference in between tests and simulations. The main reason for these differences is associated to the influence of the flexibility of the support structure. It is complex structure constructed with numerous pipes clamping rings, screwed I beams, and plywood. Part of the structure is constrained to the next structure. For the improvement of the FE model the threestep routine was realized. In the first step sensitivity analysis of the model was computed in order to determine model parameters which are most influential on the investigated modes. In the second step the design of experiment (DOE) procedure to produce statistical data tabulating inputoutput relationships. In the third step the response surface model (RSM) is calculated to determine how model parameters influences on the natural frequencies. Study of responses obtained from particular values of the model parameters allows to update the FE model of support structure.
Parameters of the original blade section model were assumed to be constant and were not a subject of updating analysis. 56 parameters characterizing the support structure and additional composite unidirectional layers model were defined as a design variable for the preliminary sensitivity analysis. They comprised material properties such as elasticity modulus, shear modulus and density of the additional composite unidirectional layers, plywood clamps, the rubber pads, the steel pipes, and the bushings. This study was realized to:
identify parameters (inputs) which have no impact on the mode frequencies of interest (outputs);
identify inputs that cause significant change in the outputs.
Outcome of the frequency sensitivity analysis is presented in Figure
Updated parameters as variables in the model and their initial values.
Name  Initial 

I Bush K1 

Steel pipes 

Steel 

MAT9_7_G13 

MAT9_7_G14 

MAT9_7_G24 

MAT9_7_G34 

MAT9_8_G56 

Frequency sensitivity matrix graphically presenting normalized magnitude of the impact of selected design variables (inputs) on the modes frequencies of interest (outputs).
Frequency sensitivity analysis provided information about most influential material properties of the supporting structure and additional composite layers. There are several uncertainties related to unknown properties of support structure construction components (Figure
Mountings of supporting structure modeled with steel pipes, steel, and bushing properties.
Computation of the FE model of the system under investigation takes large number of hours for a single run. Therefore applying optimization analysis which would require large number of runs is not a best available method of model updating. In the system with numerous variable inputs (factors) which affect the outputs (responses) the design of experiment procedure can be used to gather data. The result data is used to develop an approximate model (such as response surface method) linking outputs and inputs. Experimental design which was used is full factorial. It required computation of 2^{k} combinations where
Analysis of DOE data was performed to identify inputs (factors) which introduce significant change in output (response). For this purpose numerous scatter plots were drawn and analyzed. Example of 3D scatter plot is shown in Figure
Example of 3D scatter plot of two inputs (factors) impact on the output (response) 7th mode frequency.
Next to the scatter plot the histogram plots were drawn to present the distribution of the computed responses. It is possible to identify the center, spread, and outliers. Example of the histogram plot for the 9th mode frequency is presented in Figure
Histogram plot of 9th mode frequency distribution.
Histogram of 9th mode frequency shows the results distribution is almost symmetric with most of the results located in the proximity of nominal value. Data is not skewed nor contains outliers and the distribution is moderate tailed—the number of runs is dying off out in the tails of the histogram.
Based on design of experiment, response surface method was computed using polynomial model of several factors, including terms for quadratic crossproducts displayed in Figure
Quadratic response surface models 3D perspective plot for the same input variables and (a) 4th mode, (b) 5th mode, and (c) 7th mode frequency.
The RSM methodology allows for further processing of the DOE results. 3D graphs are plotted based on the available design variables contributions. The inherent trend of the factorresponse multidimensional relationship was computed for selected inputs applying Taylor polynomial. Statistical model allows to approximate data and correctly predicts the response without lengthy and costly simulation runs.
Based on the analysis of the RSM model the values of the FE model parameters (factors/inputs) were selected (Table
Updated parameters and their final values.
Name  Final 

I Bush K1 

Steel pipes 

Steel 

MAT9_7_G13 

MAT9_7_G14 

MAT9_7_G24 

MAT9_7_G34 

MAT9_8_G56 

As a result a correlation analysis of updated and validated FE model shows significant improvement in comparison to the results from original FE model (Figure
MAC matrix, test versus updated FE model of the blade with flexible support.
Comparison of frequency value differences of initial (Table
Final consistency of the modal model parameters.
Final WT blade (versus initial)  

TEST  FE  
Freq. 1  Freq. 2  MAC value  Freq. 2−Freq. 1 (Hz)  Freq. 2−Freq. 1 (% of Freq. 1) 

4.4  0.634 ( 
−0.1 ( 
−2.2 ( 

10.2  0.942 ( 
1.73 ( 
20.6 ( 

17.8  0.962 ( 
−1.41 ( 
−7.3 ( 

26  0.722 ( 
−7.3 ( 
−21.9 ( 

38.8  0.602 ( 
−2.11 ( 
−5.2 ( 

42.1  0.538 ( 
−1.72 ( 
−3.9 ( 

50.3  0.802 ( 
−7.03 ( 
−12.3 ( 
This paper presents some results and aspects of the multidisciplinary and interdisciplinary research oriented for the numerical study in updating of the finite element model of a wind turbine blade section using experimental modal analysis results.
Experimental test data examples were shown and used for two purposes: firstly to evaluate the influence of the flexible support structure onto measurement results of the bendtwist coupled blade section and secondly to use the test results for FE models updating. The common observation from displayed investigations is that the blade section model accuracy strongly depends on the boundary conditions represented in the model. Simple approaches based on constraining degrees of freedom led to discrepancies in between experimental and numerical results. Presented research introduced complex parametric model of the flexible support structure which led to more realistic structural behavior of the objectsupport system. In detail the plywood plates and steel profiles were included and contact elements were applied to model the contact between the clamps and the blade section. As expected that the more sophisticated support structure FE representation has improved the consistency in between test and simulations. Design of experiment with response surface model study allowed successful updating of the FE model confirmed by modal assurance criterion. The comparison of experimental and numerical models clearly shows the influence of support structure flexibility.
The authors declare that there is no conflict of interests regarding the publication of this paper.
Vestas Wind Systems A/S has provided and modified the blade sections presented in this study. The work is partly supported by the Danish Energy Authority through the 2007 Energy Research Programme (EFP 2007). The supported EFPProject is titled “Anisotropic beam model for analysis and design of passive controlled wind turbine blades” and has journal no. 330330075. The support is gratefully acknowledged and highly appreciated. Authors would like to acknowledge the assistance of Mr. Philipp Haselbach. Research presented in Section