Tower design and analysis - Wind Power Generation and Wind Turbine Design - page 533

Figure 2 : Rotationally sampled turbulence spectra.

Using the loading from the rotationally sampled spectra of turbulence and using
a mode-acceleration method, Murtagh et al. [31] estimated the wind-induced
dynamic time-history response of tapered rotating wind turbine blades. The mode-
acceleration method was initially implemented by Williams [32] and Craig [33]
reported that it has superior convergence characteristics compared to the mode-
displacement method. Singh [34] presented a method for obtaining the spectral
response of a non-classically damped system, based on the mode-acceleration
technique. Akgun [35] presented an augmented algorithm based on the mode-
acceleration method which has improved convergence for computation of stresses
in large models.

2.5 Loading on tower-nacelle

The tower can be modelled as a lumped mass multi-degree-of-freedom (MDOF)
fl exible entity, which includes a lumped mass at the top of the tower, to represent
the mass of the nacelle and the effect of the blades. An eigenvalue analysis can be
performed to obtain the natural frequencies and mode shapes. As the tower-nacelle
is a MDOF system, it is convenient to obtain modal force time-histories associated
with each mode for analysis. This allows the spatial correlation or coherence of
drag forces along the height of the tower to be included. Nigam and Narayanan
[36] presented an expression for the modal fl uctuating drag force power spectrum,
for a continuous line-like structure, which can be used following modifi cation for
a discretized MDOF system [30].
The wind velocity auto and cross power spectral density (PSD) terms may be
evaluated as

S () f = S () f S ()coh(,; ) f k l f

(5)

V V V

k kVk lVl

V l