ct al. I99K,. Mci. & Agrawal. 1998). Considcrable rescareh effort has been dc- voted to a .... harmonic wavelet schcrne (Newland I 994a). Fur- .!her, the liltcrcd .... ti and freq looalimtion. However. 00 accurate spectral estimates are ob- tai~ ~f1@ ...
X
510
5809
90
ISBN
LisS9.
Zeitlinger;
&
Swets
2002
C
Structural Dynamics. EURODYN2002. Grundmann & SchutJller(eds.)
Waveletsapplicationsin structural dynamics P. D. Spanos RJ!fJn Chair, Rice Uni~sity, Houston,USA. P, Tratskas
Failla
de-
structural
tools
of and
response concepts
dynamic
the
pertinent
of
review
investigating
brief
a
After
presented.
is
for
USA.
methods
Houslon,
wavelets-based
on random
perspective
A non-stationary
to
systems
ABSTRACT:
Visiting Scholar, Rice Univers;I}',
input
G.
Research Engineer,ShellInternational, London,UK.
veloped by various researchers, attention is focused on the harmonic wavelet transform. Specifically, it is
shownthatthe non-overlappingfrcqucncycontentofharrnonic waveletsat different scalesleadsto significant simplificatioos in the description of both input and output processes in structural dynamics applications. Fur-
ther. it shownthat the wavelet reprcscntationof a stochasticprocesscan be interpretedin context with the evolutionary spectrum theory. and explicit relationships can be derived between the mean-square value of the wavelet transform. and the timc-depcndcnt spectrum of the process. Also, to estimate the response spectrum of linear systems, a scale-dependent wavelet transfer function can be introduced, by which the response waveIct transform is derived from the input wavclet transform by means of a convolution schcmc. Finally, a wavelet linearization method can bc formulated to (.'Omputcthe response spectrum of nonlinear systems. in which a scale-dependentequivalent linear system is constructed to approximate the wavelet transform of the nonlinear response.
have been proposed (Gasparini & DebChaudhury 1980, Borino
nalsand,in this context,to thepredictionof
a number
Hart
&
Conte
1990,
(Saragoni Papadimitriou
structures 1990,
Wen
nonlinear &
and Yeh
linear
1992). Therefore,
of st\Kiies have been
1987,
Yong
& 1997).
Lin Peng
&
1979, Conte
Penzien
& al.
et
(Kubo Grigoriu
In this context, wavelet analysis has received
slruC-
tural responsestatistics.Early studics have focused on modificationsof the well-establishcdtheory of stationary signals. In this contcxt. for excitation processesthat can be divided inlo long stationary segments, time-dependent damping paramete~ havc been used to predict the stationary rcsp
