Extreme Response of Nonlinear Structures with Low Damping Subjected to Stochastic Loading

The response of structures with low damping to random loading is generally characterized by significant clumping of the large response peaks. This clumping is known to affect the extreme responses of the structure. In the paper we shall propose an approximate method to account for this effect on first passage times and extreme values of narrow-band random vibrations, both Gaussian and non-Gaussian. The method is based on the concept of joint crossing rates of a stochastic process. This makes it possible to introduce a correlation structure to the sequence of peak values, allowing the introduction of an approximate estimate of the effect of clumping on large excursions of the underlying narrow-band process. The advantage of the proposed method is that explicit, closed-form expressons for the clumping effect on first passage times and extreme values are obtained. The method is illustrated by application to specific examples including a nonlinearly moored offshore structure in waves.