Tower design and analysis - Wind Power Generation and Wind Turbine Design - page 538

Hence, when this factor is applied to the responses from the mean wind loading,
it yields the maximum design values.
The methodology developed by Davenport and, Velozzi and Cohen calculated
the GRF using a ratio of displacements, and while this yielded accurate maximum
expected response for displacement, it was found to fall short in providing esti-
mates of other response parameters, such as bending moment and shear force.
Following the work by [38, 39] several new models of the GRF have been pro-
posed by Holmes [40] and Zhou and Kareem [41], with the latter being based on
base bending moment, rather than displacement. The GRF methodology has also
become the basis of most modern design codes worldwide [42].

3.1 Gust factor approach

The traditional Davenport-type GRF assumes that the fl exible structure may be rep-
resented by a single degree-of-freedom (SDOF) representing the fundamental mode
of vibration, and this is usually suffi cient. However, if a structural system like a
wind turbine tower (with coupled tower-rotor interaction) has more than one mode
contributing to the response, the traditional GRF methodology may yield inaccurate
representations of the energy contained in the response. Thus an extension of the
traditional GRF methodology to include the effects of higher modes in the derivation
of the GRF is required for application in the case of a wind turbine tower.
A GRF for evaluating the along-wind response of wind turbine towers has been
proposed by Murtagh et al. [43]. The approach presented differs from the conven-
tional GRF methods as the GRF contains contributions from two resonant modes,
mainly due to rotor blade-tower interaction effects. The wind turbine tower model
considered contains two inter-connected fl exible sub-systems, representing the
tower and a three-bladed rotor system. It is assumed that all the blades vibrate
identically in the fl apwise mode (out-of-plane) coupled with the tower. Each com-
ponent is initially modelled as a separate degree-of-freedom (DOF) and these are
coupled together to form an equivalent reduced order model of the coupled tower-
rotor system considering the fi rst two dominant modes. Thus, the resonant compo-
nent of the response contains energy output from the two modes of the coupled
system. This is an approximate way to account for the effect of the blades fed back
to the tower including the coupled tower-blade interaction. The GRF is obtained
for both tower tip displacement and base bending moment through numerical
integration, with a closed form expression included for the former.

3.2 Displacement GRF

The displacement GRF [43], G DISP , is obtained as a ratio of the expecte d maxi-
mum displacement response, X MAX ( t ) divided by the mean displacement, x , with
the latter being represented by the equation:

Φ f Φ f

CS ,1 - TT D,1 CS ,2 - TT D,2

x = +

(10 )

K K

CS,1 CS,2