seismic response of wind turbines due to earthquake and wind...

ABSTRACT: A study of the structural dynamic response of wind turbines is presented. Two different wind turbines were utilized: a 65-kW wind turbine, which has previously been subject to shake table testing at University of California, San Diego (UCSD) and a 5-MW reference wind turbine produced by National Renewable Energy Laboratory. The 65-kW wind turbine was utilized in order to compare its earthquake response in SAP2000 to the results obtained from full-scale shake table tests at UCSD, and served as a validation for numerical modelling of the 5-MW wind turbine. For the 5-MW model, surrounding soil was included in the model in order to account for the soil-structure interaction, and it was excited by the horizontal and vertical components of the 1985 Nahanni, Canada earthquake. These records are modified and scaled in order to match the response spectra from Eurocode 8. Wind-induced load was applied in a simplified manner in order to gain insight into the significance of earthquake loading on a design based on wind loads. It is shown that the vertical excitation from an earthquake can produce severe vertical accelerations in upper parts of a wind turbine. This motivates more research on buckling in the steel tower (when combined with wind), disturbance to the fine-tuned machinery in the nacelle, and design of the connection between nacelle and turbine tower. Secondly, a comparison between statically applied wind and horizontal earthquake excitation concluded that soil-structure interaction can be of the uppermost importance in regards to the displacement along the wind turbine. Results showed that earthquake is not expected to govern the design for small to moderate earthquakes in stiff soils. However, for softer soils, the displacement and base moment demand from earthquake could very well match the response from wind-induced forces.

KEY WORDS: Wind turbines; Earthquake; Dynamic response; Soil-structure interaction; Time series; Wind energy; FEM

1 INTRODUCTION

Focus on renewable and clean energy over the past decade has increased the motivation for wind energy using wind turbines. Some of the countries at the forefront of wind power developments, such as China, India and the U.S. are considered highly seismic active.

Some research has been conducted in the field of wind turbines and seismic response, and a number of guidelines have already been developed, such as Risø [1], GL [2] and IEC [3]. In addition, with the growth of offshore wind industry, there exist some specific standards for these [4–6].

Recognizing the fact that a wind farm is a collection of large, expensive, and homogeneous structures important to the infrastructure, it becomes imperative that the probability of total shut-down should be minimized. Some guidelines recommend designing the wind turbines (or at least some of its components) as high safety class [1, 4, 7].

Wind turbines are more-or-less considered confidential, and their design information is not revealed by the manufacturers. As a consequence, National Renewable Energy Laboratory (herein NREL) developed a numerical 5-MW reference wind turbine [8]. This turbine was developed by using any publicly available information on the structural, operational and other aspects of wind turbines that existed at the time.

1.1 Previous Research

University of California, San Diego (herein UCSD) has conducted extensive work on several wind turbines with focus on seismic response and other dynamic properties:

A study was made on the seismic response of a 65-kW wind turbine at the Large High Performance Outdoor Shake Table (LHPOST) at UCSD from 2004 [9, 10]. In addition, a more extensive study of the same 65-kW turbine was conducted at the same location that included parked and operating states, and different levels of shaking and denser instrumentation in 2010 [11, 12].

Prowell et al. [13] modified the code FAST (an open-source software capable of modelling turbine dynamics [14]) to enable base shaking in addition to other loads.

A number of research from various institutions has been conducted based on NREL. Some of the work from UCSD on this matter includes estimating the seismic load demand for a wind turbine in time domain, using FAST [15], and checking the soil-structure interaction (SSI) effects using OpenSees [16].

Based on numerical simulations, Prowell [17] concluded that soil-structure interaction was an important issue, especially for large machines. Prowell et al. [16] stated that it was important to conduct further SSI research as an integral component of seismic response studies.

Zhao and Maißer [18] conducted numerical simulations on the SSI effects on the dynamic characteristics of wind turbine towers using linear springs. They concluded that SSI effects is particularly important in the response of wind turbine structures on relatively flexible soil.

A study on the role of damping of an offshore wind turbine [19] concluded that, in general, significant research is needed

Seismic Response of Wind Turbines due to Earthquake and Wind Loading

Remi André Kjørlaug1, Amir M. Kaynia2,3, Ahmed Elgamal4 1Norconsult AS, Vestfjordgaten 4, 1338 Sandvika, Norway

2Department of Structural Engineering, Norwegian University of Science & Technology, Richard Birkelands vei 1a, 7491 Trondheim, Norway

3Norwegian Geotechnical Institute, P.O. Box 3930 Ullevaal Stadion, 0806 Oslo, Norway 4Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0085,

USA email: [email protected], [email protected], [email protected]

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4

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for the determination of dynamic properties of offshore wind turbine structures.

While a limited research has been conducted on the horizontal seismic response of wind turbines, it appears that very little attention has been given to the vertical response of wind turbines due to seismic loads. Ritschel et al. [20] briefly reported a high response in vertical direction due to earthquake excitation.

2 MODEL VALIDATION

The 65-kW and 5-MW wind turbines analysed here are HAWTs (Horizontal Axis Wind Turbine) and use active yaw. The 65-kW wind turbine is a Danish wind turbine, produced by Nordtank [17]. The 5-MW turbine is developed as a reference turbine, and exists only on paper.

The software SAP2000 was used for the numerical analyses in this study. For this purpose, a validation of the results was carried out. A model of the 65-kW wind turbine was created based on its geometry, mass and materials, and its natural frequencies were compared to the existing results. Some data for the wind turbine is presented in Table 1.

Table 1. 65-kW wind turbine data [10].

Property Values Rated power 65-kW Rated wind speed 11.9 m/s Operational RPM 45-55 RPM Rotor diameter 16 m Tower height 21.9 m Tower wall thickness 5.314 mm Rotor hub height 22.6 m Tower mass 6400 kg Nacelle mass 2400 kg Rotor mass (with hub) 1900 kg

The tower was modelled as a cylindrical steel shell (discretized angularly into 16 shells); the nacelle was modelled using solid elements of a user-defined material with the correct mass and size. The blades were modelled as cylindrical sections of fibreglass reinforced polyester material defined through a user-defined material. In order to match the given data and natural periods of the turbine, the mass density and stiffness parameters had to be slightly modified. The turbine was assumed fixed to its base. A summary of the different components are given in Table 2.

Table 2. Components of 65-kW model.

Component Material Mass density Youngs' Mod. [kg/m3] [MPa]Tower Steel, S275 9 891 200 000Nacelle User-defined 1 529 210 000Rotor Steel, S275 1 101 210 000Blades Polyester 1 101 10 000

2.1 Natural Frequencies

The natural frequencies computed by SAP2000 are presented and compared with existing results [9, 11] in Table 3. The model exhibits a good match with previous work.

2.2 Static Wind-Induced Load

Because SAP2000 is not a software for aerodynamic analysis, the wind was applied as an equivalent thrust-force working on the rotor with a load value depending on the wind speed. There is no available information for the 65-kW wind turbine

thrust-force as a function of wind speed; therefore scaling has been applied from the documentation of the NREL 5-MW wind turbine. According to Manwell et al. [21], the relation in Equation (1) can be applied to scale the thrust force:

(1)

where Tn is the thrust-force for wind turbine n and Rn is its rotor radius. The meteorological data from the extended shake table test [12] reports different wind speeds. For this validation analysis, the averaged wind speed of 3.5 m/s was used. Thus, a static horizontal thrust force of 2.8 kN was applied at the nacelle in the fore-aft direction.

Table 3. Natural frequencies of 65-kW wind turbine, compared to previous work. (S-S: side-side, F-A: fore-aft)

2004 [9] 2010 [11] This study [28] fn ShakeTable Model ShakeTable Model # Type f[Hz] Type f[Hz] Type f[Hz] Type f[Hz]

1 S-S 1.70 S-S 1.68 F-A 1.70 F-A 1.66

2 Comb 11.7-12.3 F-A 1.68 S-S 1.71 S-S 1.68

3 … … Tors. 9.20 … Tors. 9.16

4 S-S 10.8 F-A 11.9 F-A 11.9

5 F-A 10.9 S-S 12.4 S-S 11.9

2.3 Earthquake Record & Analysis Procedure

The acceleration time series selected for the test program was the East-West component of the Landers earthquake with Moment Magnitude 7.3 [22]. The time history has PGA = 0.154g.

Modal damping ratios were taken as the modal damping ratios for the parked 65-kW wind turbine, obtained from LHPOST at UCSD [17], and are listed in Table 4.

Table 4. Modal damping ratios.

Mode # Type ξ 1st 1st Fore-aft 1.0 % 2nd 1st Side-side 1.1 % 3rd 1st Torsional 3.5 % 4th 2nd Fore-aft 1.5 % 5th 2nd Side-side 2.2 %

… … …

nth … 3.5 %

2.4 Seismic Response of 65-kW Wind Turbine

In order to compare the numerical model implemented in SAP2000 to the shake table test in Prowell et al. [9], response along the height of the 65-kW wind turbine was collected in terms of acceleration.

Figure 1 presents the results from SAP2000, while Figure 2 exhibits the results reported in [9]. The decay of motion at the free-vibration phase in Figure 1 indicates damping as assigned in the modelling, and damping as documented in [9], and the model implemented in SAP2000 exhibits very satisfactory results.

The responses obtained in this study matched the results from previous research very well. Thus, the confidence and experience from this section was necessary in the rest of the research.

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

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Figure 1. Time series response from SAP2000, this study [28].

Figure 2. Results from shake table testing of 65-kW wind turbine [9].

3 NREL 5-MW WIND TURBINE

Following the verification of the software, the idea to develop a model of a larger and more modern wind turbine was pursued.

NREL created a 5-MW reference wind turbine [8]. This model serves as a baseline for research and development in the field of wind turbines. Some of the data for the turbine is presented in Table 5. The tower diameter decreases linearly towards the top, along with the tower wall thickness. The same modelling techniques used for the 65-kW turbine presented in Section 2 were utilized.

Table 5. 5-MW wind turbine data [8].

Property Values Rated power 5-MW Rated wind speed 11.4 m/s Operational RPM 12.1 RPM Rotor diameter 126 m Tower height 87 m Lower section diameter 6 m Top section diameter 3.87 m Hub diameter 3 m Tower wall thickness 27 - 19 mm Rotor hub height 90 m Tower mass 347 460 kg Nacelle mass 240 000 kg Rotor mass (with hub) 110 000 kg Total wind turbine mass 697 460 kg

Even though it is not described in [8], stiffening rings were added within the turbine tower, at approximately every 3 m along the tower height in order to prevent buckling of the tower. This agrees with previous work [23, 24]. The stiffener rings are made of the same material as the tower. Material parameters are summarized in Table 6. Overall, the mass of the different components and the mass of the entire turbine is correct.

Figure 3 shows the numerical model of the 5-MW wind turbine developed in SAP2000, and displays the points of interest and the coordinate system.

Table 6. Component data of 5-MW model.

Component Material Mass density Young's Mod. [kg/m3] [MPa]Tower Steel, S275 10 500 210 000Nacelle User-defined 1 578 210 000Rotor Steel, S275 152 9051 210 000Blades Polyester 158 10 0001The high mass density is due to rotor modelled as a finite number of beams.

Figure 3. Model of the 5-MW wind turbine.

3.1 Modelling Soil

Previous research has shown that tall and slender structures can be prone to significant soil-structure interaction effects, especially for soil with Vs ≤ 750 m/s [25].

In order to include the effect of SSI in this study, a body of the soil was included in the model down to 30 m depth and a width of 80 m in the direction of uni-axial horizontal shaking. In total, the modelled soil consists of 5328 solid eight-noded solid elements with lengths of 2.5 m [26].

The direct solution method was applied meaning that the entire soil-foundation-structure system was modelled and analysed in a single step [27].

3.2 Validating Soil Response

In order to verify the modelling of the soil, a comparison to analytical response of a uniform soil layer with hysteretic damping on rigid rock was performed. The amplification from bedrock motion to free surface motion is given by [27]:

| |⁄ ⁄

(2)


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where H is the thickness of soil layer, V is the shear wave velocity of the soil and ξ is the hysteretic damping ratio. The amplification function for the modelled soil was obtained through a steady-state analysis at a number of frequencies, and was shown to give good agreement with Equation (2). The validation process is documented in Kjørlaug [28].

Special boundary conditions were imposed in order to represent the boundaries realistically. For horizontal shaking, the vertical sides normal to the direction of shaking were restrained against displacements in the Z-dir. Furthermore, the nodes with the same Y&Z coordinates were constrained to move together in the direction of shaking; that is:

# , , # , , (3)

This will ensure that the horizontal layers of the soil will move as shear-beams [27]. For the vertical shaking, all the vertical boundaries were restrained against horizontal displacement.

3.3 Monopile Foundation

As foundation for the wind turbine a hollow monopile was assumed and modelled to a depth of 25 m, with the same material, diameter and wall thickness as the lower part of the turbine tower. This type of monopile foundation (shown in Figure 4) is one of the normal foundation types [29, 30].

Figure 4. Model of monopile foundation in SAP2000.

3.4 Dynamic Properties and Responses & SSI

The natural frequencies obtained from the model shown in Figure 3, are presented and compared with the data from [8] in Table 7. Some difference was observed for the 2nd order fore-aft and side-side natural frequencies.

Table 7. Natural frequencies of 5-MW wind turbine, compared to guideline work (S-S: side-side, F-A: fore-aft).

NREL [8] This study [28]

fn #

Type FAST ADAMS fn #

Type SAP2000 Mass PF

[Hz] [Hz] [Hz] [%]

1 F-A 0.324 0.320 1 S-S 0.294 Us-s 68%

2 S-S 0.312 0.316 2 F-A 0.295 Uf-a 69%

3 Tors. 0.621 0.609 3 Tors. 0.647 Rz 91% …

(Blades)

…

…

... (Blades)

…

…

12 F-A 2.900 2.859 10 F-A 2.434 Uf-a 13%

13 S-S 2.936 2.941 11 S-S 2.534 Us-s 12%

…

…

…

21 Vert. 9.646 Uz 77%

The mode shapes for natural frequencies 1, 2, 10 and 11 are shown in Figure 5, and the first mode shape in the vertical direction (frequency number 21 in Table 7) is shown in Figure 5e. The blades have been removed for clearly illustrating the mode shapes of the tower in Figure 5c-e.

In order to examine the sensitivity of the results to the soil stiffness, the shear wave velocity was varied from 100 m/s to 1000 m/s. Figure 6 presents results for the first fore-aft mode shape as a function of Vs. The dotted line represents the corresponding natural frequency from a fixed-base condition.

Figure 5. First global mode shapes.

Figure 6. 1st fore-aft natural frequency as function of Vs.

A more extensive investigation of the SSI-effects is presented in Kjørlaug [28].

Note on Radiation Damping: With the type of model utilized in this research, it is not possible to capture the radiation damping correctly [31, 32]. Therefore, an alternative approach was investigated in order to investigate the level of radiation damping expected in reality.

To develop an insight into the effect of radiation damping in the vertical direction, the expression for a foundation using a rigid circular plate (e.g. [31]) was used as follows:

1.79 (4)

where Kv is the vertical stiffness of the soil, ρ is the mass density of the soil and r is the radius of the rigid circular plate which is taken as the radius of the pile.

Table 8 presents the resulting total damping coefficient in the vertical direction which was computed through a unit ramp load applied in the vertical direction, and logarithmic decrement for three different soils (Vs = 800-600 m/s) in the free-vibration phase. The applied modal damping ratio, without radiation damping, is presented later in Table 9. Comparing Table 8 to Table 9 shows that between 0.5-1.1% damping is lost by excluding radiation damping. This investigation is further elaborated in Kjørlaug [28].

Table 8. Investigation of total vertical damping; applied modal damping and approximated radiation damping.

Soil Spring-stiffness Damping-coefficient Calc. damping Vs [m/s] Kv [kN/m] Crad [kN/(m/s)] ξtot [%]800 5.13·107 9.42·104 2.35 700 4.04·107 8.36·104 2.49 600 3.09·107 7.31·104 2.72


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4 ANALYSIS PROCEDURE

Structural softwares like SAP2000 are not able to handle the significant aero-elastic damping in both directions for an operating turbine [33]. This justifies analysing the model uni-axial, i.e. only one direction in each analysis, and using modal analysis to approach damping more correctly. The modal analysis was performed using Load Dependent Ritz vectors (LDR) [26, 31] with modal participation factors up to 99%.

4.1 Earthquake Record

Time series from the 1985 Nahanni earthquake, with a moment magnitude of 6.76 [22] was selected. The time series was modified and scaled in order to match the response spectrum for ground type A in Eurocode 8 [7] with a PGA = 0.05g in the horizontal direction and 0.03g in the vertical direction. The modified time series for the horizontal and vertical components of the Nahanni earthquake are plotted in Figure 7, while Figure 8 presents Pseudo-acceleration response spectra together with the corresponding EC8 Spectra.

Figure 7. Time series in horizontal & vertical directions for Nahanni earthquake.

Figure 8. Response spectra in horizontal & vertical directions for Nahanni earthquake.

4.2 Static Wind-Induced Load

The wind-induced force was applied as a horizontal force at the rotor. Numerical data for the equivalent thrust force to apply for given wind conditions are provided in [8]. The wind induced thrust force was applied as a static load of 800 kN at the nacelle in the fore-aft direction.

4.3 Modal Damping Ratios

Not much direct recommendations for damping are provided in the current guidelines. Only IEC [3] suggest a damping value of 1% in the first natural mode. The modal damping ratios given in Table 9 were used to simulate an operating turbine based on previous research on wind turbines in the megawatt-scale:

For a 900-kW wind turbine, Prowell [17] reported a mean damping of 4.7-5.9% from in-situ observations operating at 22 RPM. The shear wave velocity at the site was estimated to increase from 300 m/s at the surface, to 650 m/s at 10 m depth.

Damgaard et al. [19] studied an offshore wind turbine. The rated power is not provided in [19]; however, based on tower height, it seems to be around 2-3 MW. This turbine has a monopile foundation, and an oscillation damper installed just below the nacelle. The study concluded a damping of 2.25% in the first mode. The soil conditions vary from loose sand to very stiff clay in the top 10 m below seabed.

Bazeos et al. [24] used a viscous damping of 0.5% in the finite element models of a 450-kW wind turbine. Ishihara and Sarwar [34] also utilized the same level of damping for turbines of size 400-kW and 2-MW, and showed underestimations in seismic response from response spectrum methods from codes, due to the assumptions of high damping in the codes (1-5%).

Table 9. Assigned modal damping ratios.

Mode # Type ξ 1st Fore-aft 4.0 % 1st Side-side 3.0 % 2nd Fore-aft 2.0 % 2nd Side-side 1.3 % 1st Vertical 1.7 % … … …

nth … 2.0 %

The overall modal damping ratio of 2.0% assigned to all other modes is equal to the overall damping applied in [16] for the 5-MW wind turbine including SSI. The vertical natural frequency is based on results from Damgaard et al. [19] and Damgaard et al. [35]. Referring to the investigation of total damping (including radiation damping) presented in Table 8, the applied modal damping ratio in the first vertical mode shape (1.7%) lacks approx 0.5-1.1% damping due to radiation.

5 ANALYSIS RESULTS

Vertical Acceleration in Turbine Tower: Even though the time series of the vertical component from the Nahanni earthquake has a rather low PGA, the amplification of the responses was of interest.

Table 10 presents the computed peak vertical accelerations along the turbine height, together with the amplification factor at the nacelle for different soil conditions. All the models displayed severe amplification of the input acceleration.

Table 10. Summary of acceleration in vertical direction.

Vs PGA (EQ) Base Jnt. Lower Jnt. Upper Jnt. Nacelle Ampl.

[m/s] [g] [g] [g] [g] [g] [-]

1000

0.028

0.066 0.083 0.126 0.220 8

800 0.063 0.128 0.246 0.383 14

700 0.092 0.277 0.508 0.790 28

600 0.142 0.298 0.461 0.644 23

500 0.130 0.204 0.284 0.373 13

300 0.093 0.101 0.114 0.126 5

Figure 9 plots the time histories of the computed vertical accelerations along the tower height for the model with Vs = 700 m/s which displays the most severe response. Figure 10 shows the transfer functions for the same model.


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Figure 9. Vertical time serie response, Vs = 700 m/s.

Figure 10. Vertical transform function, Vs = 700 m/s

The nacelle clearly experiences very high amplifications of the input motion. A closer look on Figure 10 shows large amplifications at the natural frequencies of the wind turbine (Nacelle vs. Bedrock), and it seems that there are two natural frequencies coinciding around 9-10 Hz. The two frequencies correspond to the soil layer and the tower.

Figure 11 shows responses for Vs = 1000 and 300 m/s, plotted together in order to show the difference of the response for a range of different soils. The amplification of input acceleration is clearly exhibited in both the plots:

Figure 11. Vertical acceleration for Vs = 1000 & 300 m/s.

The analysis was purely linear elastic. Therefore, one could simple scale the results for higher accelerations. For example, for the original Nahanni earthquake with PGA = 0.122g one would expect a peak vertical acceleration of 0.56g for a soil with Vs = 300 m/s. This is a very large acceleration that could

cause damage or disorder in the nacelle. Table 11 further present the scaled response models with varying soil conditions:

Table 11. Scaled vertical accelerations for nacelle from actual vertical acceleration of earthquake.

Vs PGA Nacelle Acc. [m/s] [g] [g] 1000

0.122

0.967 800 1.680 700 3.471 600 2.828 500 1.639 300 0.555

Vertical Forces in Turbine Tower: The corresponding

vertical forces in connections between nacelle-to-tower, and tower-to-base were investigated. For these purpose, the original vertical component of the Nahanni earthquake with PGA = 0.122g is used.

Figure 12 displays the vertical forces in the shell with the most extreme response in the tower at the nacelle and at the base, for Vs = 700 m/s and 300 m/s. The trend is very similar to Figure 9 and Figure 11. These high vertical forces may be governing the design, especially when combined with other loads acting on the turbine tower.

Figure 12. Vertical forces for Vs = 700 & 300 m/s, PGA = 0.122g.

Response due to Wind vs. Earthquake: A simple comparison of the effect of horizontal earthquake excitation and statically applied wind is presented in the following. Both the displacement along the turbine (relative to its base) and the base moment demand were studied. The objective has been to determine if the response from the earthquake would become equal, or greater than the response from the wind as the PGA varies in the range 0.05g to 0.85g.

Displacement: The largest displacement in the tower under static wind occurs at the nacelle. Due to the large period of wind turbine towers, the nacelle does not experience any large displacement under horizontal earthquake excitation. This is confirmed by the results in Figure 13:

Figure 13. Nacelle displacement by earthquake & wind.


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On the contrary, displacement caused by earthquake in both the upper and lower joints, proved to be more dominant. The displacement from static wind is much less in these locations as indicated in Figures 14 and 15. It is evident that earthquake excitation can reach the same level of response as the static wind. This observation leads to the conclusion that earthquake will mainly excite response in the higher modes (see Kjørlaug [28] for more details).

Figure 14. Effect of earthquake & wind in upper joint disp.

Figure 15. Effect of earthquake & wind in lower joint disp.

Base Moment Demand: The base moment demand is a key component in the design of wind turbine structure and its foundation. The comparison of the base moments are presented in Figure 16. The earthquake can match the response from the static wind, and exceeds the wind response for the softer soils.

Figure 16. Effect of earthquake & wind in base moment.

6 CONCLUSION

Vertical Acceleration and Forces in Turbine Tower: Severe accelerations and forces in the upper part of the turbine tower were presented. The importance of vertical acceleration near the nacelle also becomes evident when remembering the fine-tuned equipment in the nacelle, and the large mass from the nacelle, rotor and blades combined.

The extreme importance of SSI effects was observed, as some soils produced much higher responses than other soils. Careful considerations must be taken when the natural frequencies of the structure itself and the soil coincide. However, the reader must take note of the precarious weakness within the combined model of soil and wind turbine as it does not correctly take into account radiation damping.

Static Wind vs. Earthquake: In contrast to the conclusions drawn above, soil-structure interaction did not seem to have as

much effect on the wind-induced loads alone. However, it proved important when assessing the level of effect an earthquake can have on a wind turbine, compared to a statically applied wind. For the bottom joint (base), the earthquake may be design driving factors when considering base moment demand, connection to foundation, and buckling of the lower parts of the tower, especially for weaker soils.

In addition to the results presented above, the utilization of software like SAP2000 was thoroughly validated in modelling wind turbines, with comparison to research involving an actual wind turbine at University of California, San Diego.

ACKNOWLEDGMENTS

The authors wish to thank Mr. Øystein Flakk at EDR&Medeso for providing a SAP2000 license for the analysis reported here. This paper is widely based on the first authors’ master thesis, with Dr. Amir M. Kaynia as academic supervisor [28].

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