A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Modal Dynamics of Large Wind 

Turbines with Different Support 

Structures 

G. Bir and J. Jonkman 

National Renewable Energy Laboratory 

Presented at the ASME 27th International Conference on Offshore 

Mechanics and Arctic Engineering (OMAE2008) 

Estoril, Portugal 

June 15–20, 2008 

Conference Paper 

NREL/CP-500-43045 

July 2008 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
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MODAL DYNAMICS OF LARGE WIND TURBINES WITH DIFFERENT SUPPORT 

STRUCTURES*

Gunjit Bir Jason Jonkman 

National Renewable Energy Laboratory 

1617 Cole Blvd, Golden, Colorado, USA 

 *

 Employees of the Midwest Research Institute under Contract No. DE-AC36-99GO10337 with the U.S. Dept. of Energy have authored 

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Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow 

others to do so, for the United States Government purposes. 

ABSTRACT 

This paper presents modal dynamics of floating-platformsupported and monopile-supported offshore turbines, which are 

gaining attention for their ability to capture the immense wind 

resources available over coastal waters. Minimal dynamic loads 

and the absence of instability are imperative to the success of 

these turbines. Modal dynamics determine both loads and 

instabilities to a large extent, and therefore must always be 

analyzed. Also, to model the turbine, several aeroelastic 

computer codes require modes of the major components, e.g., 

the rotor blades and the rotor-nacelle support structure. To 

compute such modes, we used a recently developed finiteelement code called BModes. The code provides coupled 

modes either for the rotating blades or for the support structure. 

A coupled mode implies presence of coupled flexural, axial, and 

torsion motions in a natural mode of vibration. In this paper, we 

use BModes to provide modes only for flexible towers, which 

carry head mass (rotor-nacelle subassembly modeled as a rigid 

body) and are mounted atop either a floating platform or a soilsupported monopile. The code accounts for the effects of 

hydrodynamic inertia, hydrostatic restoring, and mooring lines 

stiffness on the floating platform. It also accounts for the 

distributed hydrodynamic mass on the submerged part of the 

tower and for the elastic foundation surrounding the monopile. 

Results are obtained for three turbine configurations: land-based 

turbine, floating-platform-supported turbine, and monopilesupported turbine. Three foundation models are used for the 

monopile configuration. Results show that the hydrodynamic 

and elastic-foundation effects strongly influence the turbine 

modal dynamics. 

1. INTRODUCTION 

Offshore wind turbines are gaining attention for their 

ability to capture the immense wind resources available over 

coastal waters. Monopile-supported turbines appear economical 

for shallow water; floating-platform-supported turbines may 

become so for deep water. Minimal dynamic loads and the 

absence of instability are imperative to the success of these 

turbines. The modal dynamics of a turbine determine both its 

loads and instabilities to a large extent. During the preliminary 

turbine design stages, designers examine modal characteristics 

to ensure that anticipated operational conditions will preclude 

resonances. During the refined design and analysis stages, 

analysts use modal dynamics to gain insight into dynamic 

couplings that determine loads, stability, and controls. Also, to 

model the wind turbine, several aeroelastic computer codes, 

e.g., FAST [1], require mode shapes of major turbine 

components, e.g., the rotor blades and the support structure. 

The fidelity of such mode shapes determines the fidelity of 

results obtained from these codes. 

We had developed a finite-element code, called BModes 

(Beam Modal Analysis Code) [2], to determine high-fidelity 

modes of turbine blades, rotating or non-rotating, and landbased towers. Realizing the emerging interest in offshore 

turbines, we recently extended the code to also handle towers 

supported either on floating platforms or on monopile 

foundations. The code allows computation of coupled modes 

for both the blade and the tower support structure. A coupled 

mode implies presence of coupled flexural, axial, and torsion 

motions in a natural mode of vibration. Obtaining coupled 

modes accurately, particularly for a rotating blade, is one of the 

most challenging tasks in the dynamics field, and only a few 

codes address the issue. BModes uses a sophisticated finiteelement approach in conjunction with analytical linearization 

and a special finite-element assembly that accurately captures 

Coriolis and centrifugal effects. The code relies on a 15-degree 

of freedom element with three internal and two boundary nodes. 

A salient feature of BModes is its potential to handle a complex 

range of boundary conditions. 

The objective of this paper is to analyze modal 

characteristics of three wind turbine configurations: a landsupported turbine, a turbine mounted on top of a floating 

 1 
platform, and a turbine supported on a monopile foundation. 

Common to the three configurations is the baseline NREL 

5-MW turbine [3], which is the rotor-nacelle part of the turbine 

mounted atop the support structure. Section 2 summarizes the 

baseline 5-MW turbine properties. We use BModes to 

determine modal characteristics of the three configurations, 

which differ only in the way the baseline turbine is supported. 

Figure 1 shows the land-based configuration along with 

three offshore configurations, which have been considered as 

economical for different water depths [4]. For the land-based 

configuration, the support structure is simply a tower 

cantilevered to the ground. For the shallow-water configuration, 

the support structure is a tower mounted atop a monopile dug 

into the seabed. For the transitional-depth configuration, the 

support structure is a tower attached to a space frame, which 

can be a tripod (shown), a quadpod, or a lattice structure. For 

the deep-water configuration, the support structure is a tower 

mounted atop a floating platform, which is anchored to the 

seabed via tension cables (shown) or mooring lines. For the 

floating-platform-supported configuration, several concepts 

have been suggested in the literature. Of these concepts, three 

appear most promising: the Spar-Buoy concept, the Tension Leg 

Platform (TLP) concept, and the Barge concept. These differ in 

terms of the mechanism used to attain static stability. Refs 5-11 

discuss modeling and engineering issues associated with these 

concepts. 

Land-Based Shallow Water Transitional Depth Deepwater 

Floating 

Figure 1. Floating wind turbine concepts. 

BModes can handle all configurations except the 

transitional-depth configuration, which uses a space frame 

support structure. Using BModes, we analyze three 

configurations in this paper: a land-based turbine, a floatingplatform-supported turbine, and a monopile-supported turbine. 

For the floating platform, we consider only the barge concept. 

Section 3 summarizes properties of this floating-platform 

configuration. Section 4 describes the monopile-supported 

configuration and the three models used to model this 

configuration. 

Section 5 describes the modal analysis approach. In 

particular, it describes how we use BModes to develop a finite 

element model of a specific turbine configuration and obtain its 

modal characteristics. Section 6 discusses the modal results 

obtained for the three turbine configurations. For the floatingplatform turbine, we study how the hydrodynamic-added mass 

and restoring alter the turbine modes. For the monopilesupported configuration, we compare modes resulting from the 

three models commonly used to model the monopile 

foundation. Section 7 summarizes conclusions and future work. 

2. BASELINE TURBINE DESCRIPTION 

The baseline turbine consists of an upwind, three-bladed, 

126-meter diameter rotor mounted upwind on top of an 87.6-

meter tower. Jonkman et al [3] established this concept so as to 

best match a few existing 5-MW designs. Salient turbine 

properties are summarized in Table 1; other properties can be 

found in the cited reference. 

Table 1. Summary of Baseline Wind Turbine Properties. 

Rating 5 MW 

Rotor Orientation Upwind 

Rotor Diameter 126 m 

Hub Height 90 m 

Rotor Mass 110,000 kg 

Nacelle Mass 240,000 kg 

Tower Head c.m. offset in upwind 

direction 

0.41 m 

Tower Head c.m. vertical offset from 

tower top 

1.97 m 

Tower Head moment of inertia about 

rotor-parallel axis through c.m. 

4.37X107 kg-m2

Tower Head moment of inertia about 

lateral axis through c.m. 

2.35X107 kg-m2

Tower Head moment of inertia about 

vertical axis through c.m. 

2.54X107 kg-m2

Ref 3 provides the distributed mass, inertia, and stiffness 

properties of the tower. This NREL offshore 5-MW baseline 

wind turbine has been used to establish the reference 

specifications for a number of research projects supported by 

the U.S. Department of Energy’s Wind Energy Technologies 

Program. In addition, the integrated European Union UpWind 

research program and the International Energy Agency Wind 

Annex XXIII Offshore Code Comparison Collaborative have 

adopted the NREL offshore 5-MW baseline wind turbine as 

their reference model. 

3. FLOATING PLATFORM SUPPORT 

In the floating-platform configuration, the 5-MW turbine 

described in the earlier subsection is mounted on top of a 

floating barge. We use a preliminary barge design developed by 

the Department of Naval Architecture and Marine Engineering 

at the Universities of Glasgow and Strathclyde under a contract 

with ITI Energy. The barge concept was chosen by ITI Energy 

because of its simplicity in design, fabrication, and installation. 

Not only is the barge designed to support a 5-MW baseline 

 2 
wind turbine, it also provides for an OWC (oscillating water 

column) wave power device, which is installed within a square 

moon pool located at the center of the barge and within the base 

of the wind turbine tower. We do not model the OWC assuming 

that its effect on turbine modal dynamics is negligible. The 

barge has a square section (40 x 40 m) and is ballasted with sea 

water. To prevent it from drifting, the platform is moored by a 

system of eight catenary lines, two of which emanate from each 

corner of the bottom of the barge, so that they are 45° apart at 

the corner. Table 2 lists salient features of the barge and 

mooring system. The concept is documented in greater detail in 

Ref 12. 

Table 2. Summary of the ITI Energy Barge Properties.

Size (W×L×H) 40 m × 40 m × 10 m

Moon Pool (W×L×H) 10 m × 10 m × 10 m

Draft, Freeboard 4 m, 6 m

Water Displacement 6,000 m3

Mass, Including Ballast 5,452,000 kg

Center of Mass (c.m.) below Mean 

Sea Level (MSL) 

0.282 m

Roll Inertia about CM 726,900,000 kg·m2

Pitch Inertia about CM 726,900,000 kg·m2

Yaw Inertia about CM 1,453,900,000 kg·m2

Anchor (Water) Depth 150 m

Separation Between Opposing 

Anchors 

773.8 m

Unstretched Line Length 473.3 m

Neutral Line Length Resting on 

Seabed 

250 m

Line Diameter 0.0809 m

Line Mass Density 130.4 kg/m

Line Extensional Stiffness 589,000,000 N

Figure 2 is a schematic of the floating-platform 

configuration analyzed in this paper. 

4. MONOPILE-FOUNDATION SUPPORT 

In the monopile-supported configuration, the turbine is 

installed on a monopile dug into the seabed (see leftmost 

schematic in Figure 3). The monopile foundation was designed 

by SWE (the Endowed Chair of Wind Energy at the University 

of Stuttgart in Germany) for the OC3 project [13-14]. As the 

figure shows, the flexible tower length is 143.6 m (comprising 

87.6-m baseline-tower length, 20-m submerged tower length, 

and 36-m soil-supported tower length). 

h=87.6 m 

MSL 

Barge 

Figure 2. Floating-platform-supported turbine. 

Mud Line 

MSL 

87.6 m 

20 m 

36 m 

Monopile Support 

distributed 

added mass 

distributed 

stiffness 

H = 

143.6 m 

17.5 m 

Equivalent CoupledSpring Model (ECS) Equivalent Fixity 

Model (EF) 

Distributed Spring 

Model (DS) 

Figure 3. Monopile foundation and equivalent models. 

The soil in reality behaves as a nonlinear elastic-plastic 

spring. However, most aeroelastic codes use a simpler 

representation. SWE derived three models to represent the 

monopile foundation (Figure 3): the distributed springs (DS) 

model, the coupled springs (CS) model, and the apparent fixity 

length (AF) model. In this paper, we designate the AF and CS 

models to be EF (equivalent fixity) and ECS (equivalent 

coupled springs) models, respectively. 

The DS model idealizes the monopile with flexible 

foundation as a free-free beam with lateral (Winkler-type) 

springs distributed along the subsoil portion of the monopile. 

The beam uses the real properties of the monopile both above 

and below the mudline—including the real penetration depth. 

The subsoil spring stiffness constants are depth-dependent and 

 3 
are calculated using linearization of the lateral soil force versus 

lateral monopile displacement (p-y) data. 

The EF model idealizes the monopile with flexible 

foundation as a cantilever beam whose properties are different 

above and below the mudline. The beam above the mudline has 

the real properties (i.e., diameter, thickness, and material) of the 

monopile. The beam below the mudline (17.5-m long tower 

part) has effective properties and a fictive length (i.e., the 

distance from the mudline to the cantilevered base) that are 

tuned so as to ensure that the overall response of the monopile 

above the mudline is the same as the response of the higher 

fidelity p-y model. The response can only be identical under a 

particular set of conditions, however, because the AF model is 

of lower fidelity. In the Offshore Code Comparison (OC3) 

project, the properties of the fictive beam were tuned such that 

the mudline displacement and rotation for both models would 

be the same when loaded by a mudline shear force and bending 

moment that are representative of the loading that exists when 

the offshore wind turbine is operating under normal conditions. 

The ECS model idealizes the foundation compliance as a 

set of translational and rotational DOF (degrees of freedom) 

with coupled springs (i.e., a stiffness matrix) positioned at the 

mudline. Above the mudline, the monopile is modeled as a 

beam with the real properties of the monopile. The mudline 

spring stiffness constants were derived to give the same 

response as the EF model under the same loading conditions. 

5. MODAL ANALYSIS APPROACH 

To determine modal characteristics of each turbine 

configuration, we first develop its finite element model and 

obtain the associated global mass and stiffness matrices. Next, 

we perform eigenanalysis to obtain frequencies and mode 

shapes. We use BModes [2] for modeling a specific turbine 

configuration and for computing its modes. A brief description 

of BModes follows. 

BModes provides dynamically-coupled modes for a beam. 

The beam can be a rotating or non-rotating rotor blade or a 

tower, and it can have arbitrary distribution of structural 

properties and geometry along its length. Both the blade and the 

tower can have end attachments. An end attachment is assumed 

to be a rigid body with mass, six moments of inertia, and a mass 

centroid that may be offset from the blade or tower axis. An 

example of an end attachment for a blade is the aerodynamic tip 

brake. For a tower, the end attachment can be a nacelle-rotor 

subassembly attached to the tower top. In addition to the tip 

inertia, the tower can also have tension-wire supports. 

Recently, we extended BModes to model floating-platform 

and elastic foundation in conjunction with a mono-tower. The 

floating platform may be subjected to hydrodynamic-added 

mass, hydrostatic restoring, and mooring lines stiffness. These 

added mass and stiffnesses are generally distinct from physical 

inertias and springs and are expressed as 6X6 matrices 

associated with the six DOF (three translational and three 

rotational). For a monopile support, the soil effect is modeled 

as a distributed linear stiffness along the soil-buried part of the 

tower. Also, hydrodynamic-added mass may be specified along 

the submerged part of the tower (i.e., the part of the tower 

between the mean sea level (MSL) and the mudline). 

As mentioned earlier, BModes provides coupled modes. A 

coupled mode implies presence of coupled flexural, axial, and 

torsion motions in a natural mode of vibration. Knowledge of 

coupled modes is crucial to several applications. Examples are: 

accurate modeling of major flexible components for modalbased aeroelastic codes such as FAST [1], validation of flexible 

component models using experimental data, modal-based 

fatigue analysis, and interpretation of aeroelastic-stability 

behavior of turbines. 

Accurately obtaining rotating-blade or tower coupled 

modes is a challenging task, and only a few codes address the 

issue. BModes is perhaps the most accurate among these 

because it uses a finite-element approach in conjunction with 

analytical linearization and a special finite-element assembly 

that accurately captures Coriolis and centrifugal effects. Its 

finite-element approach, built on its predecessor UMARC [15], 

is based on a 15-degree-of-freedom element with three internal 

and two boundary nodes. The 15 DOF comprise 3 DOF for 

torsion deflection and 4 DOF each for axial, flap, and lag 

deflections (Figure 4). In the figure, u, v, w, and φ represent the 

axial, tower fore-aft, tower side-side, and twist DOF, 

respectively. 

1

1

1

1

1

1

u

v

v

w

w

φ

⎫

⎪

⎪

′ ⎪⎪

⎬

⎪

′⎪

⎪

⎪⎭

4

2

2

2

2

3

u

v

v

w

w

φ

⎧

⎪

⎪

⎪⎪ ′ ⎨

⎪

⎪ ′ ⎪

⎪⎩

2 u 3 u φ2

Distributed stiffness 

Distributed hydrodynamic mass 

Figure 4. The 15-DOF finite element. 

We recently upgraded the finite element to account for 

distributed stiffness and added mass, which may arise for 

platform- and monopile-supported towers. The added 

distributed hydrodynamic mass affects only the lateral 

displacements (v, v’, w, w’) and not the torsion and axial 

motions. The distributed stiffness, like the distributed added 

mass, may vary along the element length and also may be 

different in the two lateral directions (normal to the element 

axis). 

The BModes finite element approach allows for arbitrary 

variation of structural properties along each element of the 

beam. The structural properties are specified in terms of the 

tower fore-aft (F-A) bending stiffness, side-side (S-S) bending 

stiffness, axial stiffness; mass; section moments of inertia; and 

chordwise offsets of section shear center, tension center, and 

center-of-mass along the tower. The tower head (nacelle-rotor 

 4 
subsystem) and the tower base attachment (e.g., floating barge) 

are idealized as rigid bar elements. 

A full discussion of the BModes theory basis is outside the 

scope of this paper. However, we provide an outline of the 

technical approach (Figure 5). First, we idealize the tower as an 

Euler-Bernoulli beam that undergoes F-A bending, S-S bending, 

elastic twist, and axial deflection. Next, we formulate energy 

expressions and use Hamilton’s principle to derive coupled 

integro-partial differential equations (PDEs) governing the 

dynamics of elastic beam attached to rigid end inertias. 

Figure 5. Technical approach: computation of tower 

coupled modes. 

These PDEs are nonlinear and include spatial integral 

terms, which represent Coriolis and centrifugal effects. We use 

finite element analysis (FEA), the basis of modern structural 

analysis, to discretize the spatial (axial) variables in the PDEs. 

This FEA is compatible with Hamilton’s principle. The beam is 

divided into a number of elements each with 15 DOF: 

Continuity of displacement and slope for F-A and S-S 

deflections and continuity of displacement for elastic twist and 

axial deflections are maintained between elements. The elastic 

twist is represented by a quasi-coordinate (non-Euler); this 

eliminates axial integral terms that otherwise would appear in 

orientation matrices for an elastic beam. Finite elements 

assembly, specialized for integro-partial differential equations, 

followed by application of appropriate boundary conditions, 

yields nonlinear ordinary differential equations (ODEs) in nodal 

coordinates. Analytical linearization (distinct from finitedifferencing) yields inertia and stiffness matrices. We then 

perform an eigenanalysis to obtain the desired coupled modes 

and frequencies. 

6. RESULTS 

Before performing modal analyses on the platformsupported and monopile-supported wind turbines, we needed to 

verify BModes. The earlier version of BModes had been 

extensively verified using both analytical results and code-tocode comparison with the Rotorcraft Comprehensive Analysis 

System (RCAS) code developed by NASA [16]. Recent 

extensions to BModes necessitated further verification. We first 

used analytical models (e.g., uniform and tapered beams with 

end masses). Excellent agreement was obtained with all models. 

For a more realistic verification, we built several tower models 

using BModes and MSC.ADAMS (ADAMS). Results from 

select models will be presented where appropriate in the 

following subsections. 

6.1. LAND-BASED TURBINE 

Using BModes, we modeled the land-based tower as a 

beam cantilevered to the ground and computed its natural 

frequencies and mode shapes. Table 3 lists the modal 

frequencies of the tower (with and without the rotor-nacelle 

head mass) and also compares these with frequencies obtained 

from the ADAMS models. We used 50 finite elements in 

BModes and 99 tower parts in ADAMS. The head mass is 

idealized as a rigid mass and inertia in both BModes and 

ADAMS. 

Beam Structural

Idealization

Nonlinear

Coupled PDEs

Spatial Discretization

using FEA

ODEs in Time

Analytical

Linearization

Coupled Mode Shapes

& Frequencies

Eigenanalysis

Hamilton’s Principle

Beam Structural

Idealization

Nonlinear

Coupled PDEs

Spatial Discretization

using FEA

ODEs in Time

Analytical

Linearization

Coupled Mode Shapes

& Frequencies

Eigenanalysis

Hamilton’s Principle

The modal frequencies are shown with four decimal points 

to aid verification. All frequencies, except very high ones, show 

good agreement. Also, for the tower without head mass, note 

that BModes predicts i

th F-A and ith S-A modal frequencies to 

be identical as should be the case. Similar results from ADAMS 

differ, though by a very small margin. We believe BModescomputed results, particularly for higher modes, are more 

accurate, because it uses a consistent-mass approach, whereas 

ADAMS effectively uses a lumped mass approach, which is 

somewhat less accurate, to model the flexible tower. Note that 

the head mass substantially lowers all the modal frequencies. 

As mentioned earlier, the head mass (rotor-nacelle subsystem) is 

considered rigid. Flexibility of the rotor would somewhat alter 

the system frequencies and mode shapes; the torsion 

frequencies, in particular, would be much higher. 

Figures 6 and 7 show the BModes-computed mode shapes 

for the land-based tower without and with the head mass (such 

modes are quantitatively difficult to extract from ADAMS, and 

this in fact motivated development of BModes). All mode 

shapes presented in this paper are mass-normalized. We do not 

normalize modes for unity tip deflection, as is typically done, 

for a reason we will explain shortly. 

Without the head mass (figure 6), the tower fore-aft (F-A) 

and side-to-side (S-S) modes are identical as expected of an axisymmetric tower. 

The presence of the tower head mass introduces coupling 

between the side-to-side and torsion motions (Figure 7b). The 

fore-aft modes, however, remain uncoupled (Figure 7a). Also 

note that the head mass substantially alters the mode shapes. 

The rotary inertia of the head mass results in 2nd fore-aft and 2nd

side-to-side mode shapes with near-zero deflections at the tower 

tip. An attempt to normalize such modes for unit tip deflections 

may lead to error-prone mode shapes. In fact, if the tip 

deflection were exactly zero (very possible in reality), it would 

be impossible to normalize modes for unity deflections. That is 

why BModes uses mass-normalization. 

 5 
Table 3. Modal Frequencies of Land-Based Tower with 

and without Head Mass. 

Mode 

ber ype 

 Wi

Num

Mode 

T

Without Head Mass th Head Mass 

Frequency (Hz) Frequency(Hz) 

BModes B D iff ADAMS Diff Modes A AMS D

1 SS 1st 0.8913 0.8904 0.001 0 0.3 01 .3291 188 0. 0

2 FA 1st 0.8913 0.8904 0.001 0 0.3 01 .3324 218 0. 1

3 2ndSS 4.3743 4.3437 0.031 1 1.8 00 .8805 820 0. 2

4 FA 2nd 4.3743 4.3435 0.031 2 2.2 00 .2432 391 0. 4

5 SS 3rd 11.3911 11.1856 0.205 4 4.7 07 .6526 244 0. 2

6 FA 3rd 11.3911 11.1843 0.207 4 5.1 19 .9865 833 0. 7

7 1st io Tors n 11.9656 11.4448 0.521 1 1.4 00 .4703 763 0. 6

8 xial 1st A 16.5217 16.5222 0.001 8 7.9 19 .1311 375 0. 4

9 SS 4th 21.8655 21.1146 0.751 1 1. 4 1.3142 1 2678 0.0 6

10 FA 4th 21.8655 21.1093 0.756 1 1. 1 1.4591 1 4719 0.0 3

11 2nd Torsion 27.7783 26.1221 1.656 1 7 1 7.9632 1 .9535 0.0 0

12 SS 5th 35.8273 33.8392 1.988 2 1 7 1.7054 2 .3291 0.3 6

13 FA 5th 35.8273 33.8236 2.004 2 1 2 1.7625 2 .4419 0.3 1

14 2nd Axial 43.4596 42.1715 1.288 3 0 9 0.2109 3 .1182 0.0 3

15 3rd Torsion 44.8623 43.4578 1.405 3 4 9 5.3975 3 .5078 0.8 0

16 SS 6th 53.2770 48.9445 4.332 3 4 5 5.6336 3 .5830 1.0 1

17 FA 6th 53.2770 48.9071 4.370 3 5 9 5.6636 3 .3740 0.2 0

18 4th Torsion 62.2312 58.6564 3.575 5 0 2 2.9449 5 .5171 2.4 8

19 3rd Axial 71.4741 65.8776 5.596 5 2 8 3.0811 5 .8981 0.1 3

20 7th SS 74.2155 65.9541 8.261 5 0 9 3.0673 5 .5720 2.4 5

0

0.2

0.4

0.6

0.8

1

-0.04 0 0.04 0.08 0.12

Modal displacement

Tower section height / h

1st S-S and 1st F-A

2nd S-S and 2nd F-A

3rd S-S and 3rd F-A

1st Twist

h=87.6 m

Undeformed tower

position

Figure 6. Modes of land-based tower without head mass. 

0

0.2

0.4

0.6

0.8

1

-0.06 -0.02 0.02 0.06 0.1

Modal displacement

Tower section height / h

1st F-A

 2nd F-A

3rd F-A

h=87.6 m

Figure 7a. Fore-aft modes of land-based tower with head mass. 

0

0.2

0.4

0.6

0.8

1

-0.1 0 0.1 0.2 0.3

Modal displacement

Tower section height / h

1st S-S

2nd S-S

3rd S-S

1st S-S (twist part)

2nd S-S (twist part)

3rd S-S (twist part)

1st Twist

1st Twist (S-S part)

Figure 7b. Coupled side-to-side and twist modes for the landbased turbine. 

 6 
6.2. FLOATING-PLATFORM-SUPPORTED TURBINE 

Using BModes, we model the floating-platform-supported 

turbine as a beam with all the six DOF (three translational and 

three rotational) unconstrained at both ends. The tower-top end 

of the beam carries head mass and the tower-base end carries 

the platform modeled as a rigid body. To account for the 

hydrodynamic and hydrostatic effects on the platform, 6x6 

inertia (added mass) and 6x6 restoring (stiffness) matrices, 

obtained from WAMIT [17], are input to BModes. The added 

mass values were chosen to be the values in the added mass 

matrix at the infinite-frequency limit of the frequencydependent solution to the wave-radiation problem. A 6x6 

matrix accounting for the mooring system stiffness is also 

included within BModes. This matrix was found by 

numerically linearizing the nonlinear mooring system module 

developed within FAST [1]. Because the particular 

configuration we select has no sea-submerged tower part, we do 

not include any distributed added mass (hydrodynamic) effect. 

Table 4 lists modal frequencies for three platform models: 

platform inertia only (platform physical inertia, but no added 

mass or stiffness), platform with all effects except the 

hydrodynamic added mass, and the full platform model. 

In Table 4, the surge mode is the fore-aft motion of the 

platform. Sway is the side-to-side motion, heave is the up-down 

motion, yaw is the rotational motion about the tower axis, roll is 

the rotational motion about the platform longitudinal axis, and 

pitch is the rotational motion about the platform lateral axis. In 

the absence of any added mass and spring forces on the 

platform (platform-inertia-only model), the turbine behaves as a 

free-free flexible beam with two end inertias. Consequently, we 

observe six zero-frequency rigid-body modes. Note that the 

added hydrodynamic mass lowers all frequencies somewhat. 

The heave mode is lowered substantially (from 0.2576 Hz to 

0.1283 Hz). The last column in the table lists ADAMScomputed frequencies for the full platform model. All 

frequencies agree well, except the heave frequency (identified 

in blue in the table). This result is because the ADAMS 

linearized model admits only a physical mass and inertia, 

whereas BModes permits the use of both physical and added 

masses. To account for the additional (hydrodynamic added) 

mass and inertia in the ADAMS model, we augmented the 

physical mass and inertia and altered the c.m. location of the 

barge. This could not be done perfectly because the actual 

hydrodynamic added mass of the barge in heave is quite 

different than the added mass in surge and sway (unlike the 

physical mass, which is identical in all directions). Our 

augmentation of the barge body mass properties ensured that 

the surge, sway, pitch, roll, and yaw elements (including offdiagonal elements)—but not the heave element—of the added 

mass matrix was accounted for in the ADAMS model. 

Table 4. Modal Frequencies of Platform-Supported Turbine. 

 Frequency (Hz) 

Mode 

Number

Mode 

Type 

BModes ADAMS 

Platform 

Inertia 

Only 

Platform Inertia + 

Hydrostatic & 

Mooring Stiffness 

Full 

Platform 

Model 

Full 

Platform 

Model 

1 Surge 0.0000 0.0081 0.0076 0.0076 

2 Sway 0.0000 0.0081 0.0076 0.0076 

3 Yaw 0.0000 0.0206 0.0198 0.0198 

4 Roll 0.0000 0.1106 0.0978 0.0966 

5 Pitch 0.0000 0.1109 0.0980 0.0968 

6 Heave 0.0000 0.2576 0.1283 0.2463 

7 1st SS 0.7349 0.7671 0.5489 0.5374 

8 1st FA 0.7494 0.7820 0.5556 0.5440 

9 1st Torsion 1.4836 1.4836 1.4826 1.4890 

10 2nd SS 1.9943 1.9962 1.9270 1.9327 

11 2nd FA 2.3652 2.3666 2.2942 2.2950 

12 3rd SS 4.7559 4.7562 4.7011 4.7742 

13 3rd FA 5.0799 5.0801 5.0293 5.2260 

14 1st Axial 8.5014 8.5017 8.2186 8.2759 

15 4th SS 11.3835 11.3835 11.3542 11.3138 

16 4th FA 11.5280 11.5280 11.4983 11.5167 

17 2nd Torsion 17.9683 17.9683 17.9679 17.9639 

18 5th SS 21.7584 21.7584 21.7406 21.3760 

19 5th FA 21.8153 21.8153 21.7975 21.4885 

20 2nd Axial 30.4368 30.4368 30.2625 30.3275 

0

0.2

0.4

0.6

0.8

1

-0.1 -0.05 0 0.05 0.1 0.15

Modal displacement

Tower section height / h

Surge

Pitch

1st F-A

2nd F-A

3rd F-A

h=87.6 

Figure 8a. Modes of platform-supported turbine. 

 Figures 8a–8c show BModes-computed mode shapes 

for the full platform-supported turbine model. Note that all 

modes in the longitudinal plane of symmetry of the turbine are 

uncoupled, whereas other modes are coupled. Note also that the 

 7 
low-frequency platform modes (surge, etc) are close to rigidbody modes as expected. 

0

0.2

0.4

0.6

0.8

1

-0.1 -0.05 0 0.05 0.1 0.15

Modal displacement

Tower section height / h

Sway

Roll

1st S-S

1st S-S (twist)

2nd S-S

2nd S-S (twist)

3rd S-S

3rd S-S (twist)

Figure 8b. Modes of platform-supported turbine. 

6.3. MONOPILE-SUPPORTED TURBINE 

As discussed in Section 4, three models have been 

proposed to represent the monopile foundation: the DS model, 

the EF model, and the ECS model. Figure 3 shows the three 

turbine configurations corresponding to these three models. We 

use BModes to model all these three models using the 

appropriate boundary conditions and the appropriate elastic 

foundation model. For the DS and ECS models, the axial and 

torsion motions were suppressed at the tower base. 

Table 5 compares BModes- and ADAMS-computed modal 

frequencies for the DS model. All frequencies agree well, 

thereby verifying BModes modeling of the elastic foundation. 

Table 6 compares modal frequencies obtained from the 

three monopile-supported turbine models. The DS model most 

closely represents the true monopile configuration and, 

therefore, must provide the most accurate frequencies and mode 

shapes. As seen in the table, the equivalent models (EF and 

ECS) provide reasonably accurate frequencies for the 1st foreaft and 1st side-to-side modes. However, other frequencies differ 

appreciably. Results from the ECS model in particular diverge 

considerably because the ECS model, while partially accounting 

for the foundation stiffness, totally ignores the inertia of the 

tower foundation. 

0

0.2

0.4

0.6

0.8

1

-0.05 0 0.05 0.1 0.15 0.2

Modal displacement

Tower section height / h

Yaw

1st Twist

2ndTwist

Figure 8c. Modes of platform-supported turbine. 

Figures 9a–9c compare BModes-computed mode shapes 

for the three monopile-supported turbine models. In these 

figures, which show tower modal deflection versus tower 

section height, the tower section height has been normalized 

with respect to H, the full height of the flexible tower, which is 

143.6 m (see Figure 3). Thus, zero represents the flexible tower 

base and one represents the tower top. The figures also show 

the EF model fixity line, the mudline, and the MSL line 

locations on the tower axis. As seen in Figure 3, the flexibletower base is located at one of these lines depending on which 

model we are considering. Mode shapes in Figures 9a–9c, 

which represent deflected shapes of only the flexible tower part 

of the turbine, originate at different reference lines. The 

reference line is the zero-tower-height line for the DS model, 

EF fixity line for the EF model, and mudline for the ECS 

model. 

 As the modal plots show, mode shapes of the three models 

agree reasonably for the 1st fore-aft, 1st side-to-side, and the 1st

twist modes. Higher modes differ appreciably. This clearly 

implies that if higher modes participate in turbine dynamics, 

then equivalent EF and ECS models may lead to erroneous 

loads and stability predictions. The DS model would be the 

appropriate choice for such a case. 

 8 
Table 5. Comparison of BModes- and ADAMS-Predicted 

Frequencies for the DS Model. 

0

0.2

0.4

0.6

0.8

1

-0.08 -0.04 0 0.04 0.08 0.12

Modal displacement

Tower section height / 

Mode 

r 

e Dif

Numbe (H

Mod

Type

Frequency (Hz) ference

BModes ADAMS z) 

1 1st SS 0.2513 0.2457 0.01 

2 1st FA 0.2530 0.2472 0.01 

3 n 1st Torsio 1.2752 1.2777 0.00 

4 2nd SS 1.3680 1.3549 0.01 

5 2nd FA 1.5316 1.5056 0.03 

6 3rd SS 2.7425 2.7810 0.04 

7 3rd FA 3.0874 3.1788 0.09 

8 4th SS 5.9778 6.0090 0.03 

9 4th FA 6.0506 6.2269 0.18 

10 1st Axial 6.7671 6.5515 0.22 

11 n 2nd Torsio 10.3875 10.3448 0.04 

12 5th SS 11.4049 11.2947 0.11 

13 5th FA 11.4758 11.4022 0.07 

14 6th SS 17.9595 17.6518 0.31 

15 6th FA 17.9704 17.7208 0.25 

16 2nd Axial 18.1887 18.0404 0.15 

17 3rd Torsion 21.1075 21.1944 0.09 

18 7th SS 26.3980 25.7959 0.60 

19 7th FA 26.4215 25.8452 0.58 

20 4th Torsion 32.9711 32.8559 0.12 

Table 6. Comparison of Modal Frequencies for the DS, EF, 

and ECS Turbine Models. 

Mode 

Number 

Mode 

Type 

Frequency (Hz) 

Distributed 

Stiffness 

Apparent 

Fixity 

Equivalent

Stiffness 

1 1st SS 0.2513 0.2513 0.2584 

2 1st FA 0.253 0.2530 0.2604 

3 1st Torsion 1.2752 1.3039 1.3223 

4 2nd SS 1.368 1.3672 1.5051 

5 2nd FA 1.5316 1.5307 1.7468 

6 3rd SS 2.7425 2.7430 3.3313 

7 3rd FA 3.0874 3.0895 3.6600 

8 4th SS 5.9778 6.0125 7.1579 

9 4th FA 6.0506 6.1083 7.6287 

10 1st Axial 6.7671 7.0695 7.8420 

11 2nd Torsion 10.3875 11.6387 13.1516 

12 5th SS 11.4049 11.7126 13.1865 

13 5th FA 11.4758 13.1636 15.9651 

14 6th SS 17.9595 18.7032 16.6629 

15 6th FA 17.9704 18.7399 16.6988 

16 2nd Axial 18.1887 22.2298 25.9700 

17 3rd Torsion 21.1075 23.3796 25.9937 

18 7th SS 26.398 28.0710 26.8848 

19 7th FA 26.4215 28.0961 28.2832 

20 4th Torsion 32.9711 38.1141 38.7023 

H

" "

2nd S-S (EF)

2nd S-S (ECS)

3rd S-S (DS)

3rd S-S (EF)

xx

DS Model

EF Model

ECS Model

1st S-S 

3rd S-S Modes

2nd S-S

Mud Line

MSL

EF Model Fixity Line

Figure 9a. Side-to-side modes of monopile-supported turbine 

models. 

0

0.2

0.4

0.6

0.8

1

-0.08 -0.04 0 0.04 0.08 0.12

Modal displacement

Tower section height / H

" "

2nd S-S (EF)

2nd S-S (ECS)

3rd F-A (DS)

3rd F-A (EF)

xx

DS Model

EF Model

ECS Model

1st F-A 

Modes

3rd F-A

2nd F-A

Mud Line

MSL

EF Model Fixity Line

Figure 9b. Fore-aft modes of monopile-supported turbine 

models. 

 9 
0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3

Modal displacement

Tower section height / H

" "

2nd S-S (EF)

2nd S-S (ECS)

DS Model

EF Model

ECS Model

1st Twist 

Modes

2nd Twist

Mud Line

MSL

EF Model Fixity Line

Figure 9c. Torsion modes of monopile-supported turbine 

models. 

7. CONCLUSIONS 

We successfully used BModes, a finite element code 

upgraded recently, to compute modal characteristics of three 

turbine configurations: a land-based turbine, a floatingplatform-supported offshore turbine, and a monopile-supported 

offshore turbine. Results show that hydrodynamic effects for the 

floating-platform-supported turbine and elastic foundation 

effects for the monopile-supported turbine have substantial 

influence on the turbine modes. For the monopile-supported 

turbine, we considered three models proposed in the literature: 

the DS model, the EF model, and the ECS model. Results 

suggest that if higher modes play a role in turbine dynamics 

under certain operating conditions, then the equivalent EF and 

ECS models may lead to erroneous loads and stability 

predictions. The DS model would be the appropriate choice for 

such cases. 

In the near future, we plan to write user’s manual for the 

recently upgraded BModes and then post the manual and the 

code on the NREL website. 

ACKNOWLEDGMENTS 

Thanks to Sandy Butterfield for motivating the development of 

BModes, and to Marshall Buhl for his software-related support. 

DOE supported this work under contract number DE-AC36-

83CH10093. 

REFERENCES 

1. Jonkman, J.M.; Buhl Jr., M.L. FAST User's Guide. 

NREL/EL-500-29798. Golden, Colorado: National Renewable 

Energy Laboratory, 2005. 

2. Bir, G.S. User’s Guide to BModes: Software for 

Computing Rotating Beam Coupled Modes. NREL TP-500-

38976. Golden, Colorado: National Renewable Energy 

Laboratory, 2005. 

3. Jonkman, J.; Butterfield, S.; Musial, W.; and Scott, G. 

Definition of a 5-MW Reference Wind Turbine for Offshore 

System Development. NREL/TP-500-38060. Golden, CO: 

National Renewable Energy Laboratory, February 2007. 

4. Musial, W. and Butterfield, S. “Future for Offshore 

Wind Energy in the United States.” EnergyOcean Proceedings; 

June 2004, Palm Beach, Florida, USA. CP-500-36313. 

Golden, CO: National Renewable Energy Laboratory, 2004. 

5. Butterfield, Sandy; Musial, Walt; Jonkman, Jason; 

Sclavounos, Paul; and Wayman, Libby. “Engineering 

Challenges for Floating Offshore Wind Turbines.” Copenhagen 

Offshore Wind 2005 Conference and Expedition Proceedings, 

26–28 October 2005. Copenhagen, Denmark: Danish Wind 

Energy Association, October 2005. 

6. Lee, Kwang Hyun. Responses of Floating Wind 

Turbines to Wind and Wave Excitation. M.S. Dissertation. 

Cambridge, Massachusetts: Department of Ocean Engineering, 

Massachusetts Institute of Technology, January 2005. 

7. Wayman, E. N.; Sclavounos, P. D.; Butterfield, S.; 

Jonkman, J.; and Musial, W. “Coupled Dynamic Modeling of 

Floating Wind Turbine Systems.” 2006 Offshore Technology 

Conference Proceedings, 1-4 May 2006, Houston, TX, 

NREL/CP-500-39481. Richardson, TX: Offshore Technology 

Conference, May 2006, OTC 18287. 

8. Wayman, Elizabeth. Coupled Dynamics and Economic 

Analysis of Floating Wind Turbine Systems. M.S. Dissertation. 

Cambridge, Massachusetts: Department of Mechanical 

Engineering, Massachusetts Institute of Technology, June 2006. 

9. Henderson, Andrew R. and Patel, Minoo H. “On the 

Modelling of a Floating Offshore Wind Turbine.” Wind Energy, 

Vol. 6, No. 1, February 2003; pp. 53–86. 

10. Withee, John E. Fully Coupled Dynamic Analysis of a 

Floating Wind Turbine System. Ph.D. Dissertation. Cambridge, 

Massachusetts: Department of Ocean Engineering, 

Massachusetts Institute of Technology, 2004. 

11. Jonkman, J.M. Dynamics Modeling and Loads 

Analysis of an Offshore Floating Wind Turbine. Ph.D. Thesis. 

Boulder, CO: Department of Aerospace Engineering Sciences, 

University of Colorado, 2007; National Renewable Energy 

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Laboratory/TP-500-41958, Golden, CO: National Renewable 

Energy Laboratory. 

12. Vijfhuizen, W. J. M. J. Design of a Wind and Wave 

Power Barge. M.S. Dissertation. Glasgow, Scotland: 

Department of Naval Architecture and Mechanical Engineering, 

Universities of Glasgow and Strathclyde, September 2006. 

13. Passon, P. “Memorandum: Derivation and Description 

of the Soil-Pile-Interaction Models.” Endowed Chair of Wind 

Energy, University of Stuttgart, Stuttgart, Germany, 2006 

(unpublished). 

14. Jonkman, J.; Butterfield, S.; Passon, P.; Larsen, T.; 

Camp, T.; Nichols, J.; Azcona, J.; and Martinez, A. “Offshore 

Code Comparison Collaboration within IEA Wind Annex 

XXIII: Phase II Results Regarding Monopile Foundation 

Modeling.” NREL/CP-500-42471. Golden, CO: National 

Renewable Energy Laboratory, 2008. 

15. Bir, G. S., and Chopra, I. “Status of the University of 

Maryland Advanced Rotorcraft Code (UMARC).” Presented at 

the American Helicopter Society Aeromechanics Specialist 

Conference. San Francisco, California, January 19-21, 1994. 

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Rotorcraft Comprehensive Analysis System (RCAS). 

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Energy Laboratory, 2005. 

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Manual, Versions 6.3, 6.3PC, 6.3S, 6.3S-PC. Chestnut Hill, 

MA: WAMIT, Inc., 2006. 
F1147-E(09/2007) 

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Modal Dynamics of Large Wind Turbines with Different Support 

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This paper presents modal dynamics of floating-platform-supported and monopile-supported offshore wind turbines. 

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