Upp í vindinn - 01.05.2017, Síða 52

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linear elastic beam-column elements (100 elements in the tower). The damp-
ing ratio used is 1% of critical, which is the recommended value used for most
standards [6]. The translational and rotational head mass applied at the tip along
with other relevant parameters of the model are listed in [4].
Undamped natural frequencies obtained from eigenvalue analysis of the fi-
nite element model are presented in Table 1 along with the effective modal mass.
The fundamental modes are displayed both for side-to-side (SS) and for-aft (FA)
motion in Fig, 1. The effective modal mass for the perpendicular directions are
computed separately. For verification, the frequencies obtained by Bir and Jonk-
man [1] using the BModes and ADAMS software are presented in the correspond-
ing columns in Table 1. The dynamic analysis presented here considers ground
shaking in one horizontal direction only: due to the symmetry of the simplified
structured, and since pulse like ground motions are significantly stronger in one
direction, this simplifieation is justified.
As seen from Table 1 the effective modal mass is nearly the same in both
direetions, and the 2 first modes account almost 80% of effective modal mass
in both cases. Subsequently linear elastic dynamic analysis is performed us-
ing time-histories and response spectral methods. The near-fault ground mo-
tion data used in this study is a subset of data described in [7] For a site close to
tectonic plate boundaries or known earthquake faults, a consideration to near
fault effects could be incorporated by use of near fault response spectra. For this
study the near fault response spectra [7], which will henceforth be referred to as
RR2011, is used and its effectiveness evaluated against the simulated time histo-
ry, ground motion response spectra obtained using the SRSS combination rule
(GM SRSS), and the Eurocode 8 response spectra (EC8) scaled by the PGA of each
ground motion record.
Using time history analysis, the maximum horizontal displacement of the
nacelle is obtained using 70 near fault ground motions. The results are shown
in Figure 2 a) as a function of the normalized pulse period of ground motion
(pulse period divided by the fundamental structural period). The average value
of maximum displacement is roughly 0.5 meters and its maximum is almost 1.5
m. As is evident from Figure 2, the larger displacements are caused by ground
motions with a pulse period close to the fundamental structural period. These
is due to resonance effects. Interestingly, some of the earthquakes in the smaller
magnitude bins produce a larger response than in the larger magnitude ones.
The main reason appears to be the result of the scaling effect of the pulse period
with earthquake magnitude. For this specific type of structure with a long
fundamental period the pulse period generated from the second bin is closest
to the fundamental structural period. Therefore, the ground motions in the
second magnitude bins seem to produce, on the average, larger response than
earthquakes of greater magnitude.
Average maximum displacement demands at the top of the tower for each
magnitude bin are shown in Figure 2 b). It is evident that the two larger bins
produce significantly larger displacement demands than the bin with smaller
size earthquakes. Time history and GM SRSS results are very close to each
other, implying that response spectral analysis is appropriate. RR2011 results,
for average displacement in each bin, seem to adequately simulate the response
of the structure. EC8 spectral shapes seem to over-estimate the response for
small magnitude earthquakes, and significantly under-estimate it for larger
earthquakes. This is not surprising considering the EC8 spectral shape is based
mostly on far-fault ground motion records.
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