This article deals with reliability assessment of mechanical structures sub
jected to random excitation. The probability of failure is formulated as fi
rst passage probability of a given threshold within the observation period.
A solution for arbitrary structures exhibiting nonlinear behaviour can be
obtained by the Monte Carlo simulation. In order to reduce the sample size,
an importance sampling concept is proposed, which automatically adapts the
simulation densities in two subsequent simulation runs. The excitation pro
cess is simulated by the so-called spectral representation method, where th
e random variables are the amplitudes and phase angles of a Fourier series
expansion. It is proposed to adapt the simulation densities of the amplitud
es with respect to the power spectral density of the observed structural re
sponse. An example demonstrates the applicability of the procedure. (C) 199
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