Vibration Mitigation of Wind Turbine Towers with Tuned Mass Dampers - Wind Turbine Control and Monitoring - page 338

oscillation energy locally at installation spots of the turbine similar to the buffers
used by the automobile industry. Hereby, due to their adaptation characteristic,
semiactive dampers can mitigate vibrations over a broader frequency range com-
pared with passive elements. In order to control tower vibrations in all directions,
both passive and semiactive dampers are to be positioned in the inner side of the
turbine tower in polar formation, which blocks the tower shaft and disturbs
the accessibility of the nacelle. Material costs and necessary maintenance effort
make the effective application of the auxiliary dampers difficult.

12.3.3 Tuned Mass Dampers

For conventional slender structures, the mitigation of wind-induced periodic
vibrations is commonly achieved through TMD. A standard TMD consists of an
auxiliary mass, which is attached to the main structure by means of spring and
dashpot elements. The natural frequency of a TMD is defined by its spring con-
stant and the damping ratio caused by the dashpot. The tuned parameter of the
TMD enables the auxiliary mass to oscillate with a phase shift with respect to the
motion of the structure, leading to damping forces on the structure. TMD can
suppress especially periodic vibrations very effectively. Nevertheless, because of
mechanical challenges, it is not easy to find a suitable spring element, which can
be tuned to the fundamental frequencies of wind turbines, as they are generally
lower than 0.4 Hz. Therefore, TMD can mainly be used to mitigate higher tower
modes.
A pendulum damper counts also as a TMD and consists of an auxiliary mass,
which can be hung below the nacelle of a wind turbine and supported by dampers or
friction plates. The pendulum length is tuned to the natural frequencies of the turbine
tower modes. For a wind turbine with a fundamental frequency of 0.4 Hz, the
resulting pendulum length is according to Eq. 12.3 more than 1.5 m. Hereby, f D is
the damper frequency, L pendulum length, and g acceleration due to gravity. For
lower frequencies this value increases exponentially. To solve this problem, mul-
tistep pendulum dampers can be used. Hereby, the auxiliary mass is attached to
multiple pendula, which are interlinked to each other by various mechanical joints.
Figure 12.6 shows a wind turbine with TMD and pendulum damper.

r g

L

f D ¼ 1
2p

ð 12 : 3 Þ

12.3.3.1 Calculation of Optimal Parameters of Tuned Mass Damper

For the calculation of optimal TMD parameters, especially the criteria developed by
Den Hartog and Warburton are commonly used [ 12 , 32 ]. The results of these applied
criteria are optimal values for the natural frequency and damping ratio of TMD.