Vibration Mitigation of Wind Turbine Towers with Tuned Mass Dampers - Wind Turbine Control and Monitoring - page 334

extended FEM are the large size of the model, as the soil boundary must be located
far away from the structure and the residual error caused by the wave energy
reflection at the model boundary.
Besides advanced numerical methods, the most popular approach in practice for
SSI analysis applied to wind turbine is the spring-dashpot analog model. Here, the
foundation-soil system can be converted into a mechanical model of springs,
dashpots, and masses (Lysmer's analog), also called lumped parameter model
(LPM). This model represents the soil trough in just two free parameters, the
stiffness K FS and the damping C FS coefficients, and gives good results for the low
and medium frequencies. The mass parameter M FS can be added to obtain a better
fit between the real system and the LPM. The dynamic stiffness S FS of the LPM
can be expressed as a function of the excitation frequency X as

S FS ð X Þ¼ K FS X 2 M FS þ iXC FS ð 12 : 1 Þ

The dynamic stiffness relates the displacements of the foundation u F (X) to the
applied harmonic load P F (X)as

u F ð X Þ¼ P F ð X Þ
S FS ð X Þ

ð 12 : 2 Þ

The model can be enriched with additional lumped masses, dashpots, and
springs, increasing the number of free parameters. This is especially important for
layered half-space or stratum over bedrock.
Previous research works [ 1 , 7 , 8 , 28 , 33 ] proved that LPMs can predict accu-
rately the dynamic response of soil-turbine systems in the case of a homogeneous
isotropic medium. They confirmed that if the soil compliance is included, the
natural frequencies of the system decrease with respect to the fixed base system
and the most affected frequencies are those related to the second and third bending
modes. Investigation of the influence of soil layering on the turbine dynamics can
be found in [ 5 , 30 , 31 ], where rigorous methods were applied.
Standard codes usually suggest a representation of the foundation-soil influence
in terms of a set of linear frequency-independent springs, connected the turbine
model at the foot of the tower (Fig. 12.3 ).
Stiffness coefficients can be computed according to the DNV/Risø Guidelines
[ 14 ] or to the DIBt Provisions [ 13 ], which refer to the recommendations of the
Building Ground Dynamics Work Group [ 12 ]. Alternative coefficient formulas
may be used if justified by rational engineering analysis.
The LPMs proposed by standard codes are generally made up of six uncoupled
springs, one along each of the six degrees of freedom. They are frequency inde-
pendent and no coupling between translational and rotational degrees of freedom is
considered. The LPM can be implemented in structural multidegrees of freedom
model in the form of diagonal stiffness and damping matrices. The matrix coef-
ficients depend on the soil properties (shear modulus G S , density q s , Poisson's ratio
t S ) and on the foundation geometry (a representative length of the footing and