Wavelets applications in structural dynamics

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