On Combination of Slamming-and Wave-Induced Responses

Abstract

Attempts to solve the combination problem of the low-frequency wave-induced bending and the high frequency slamming induced bending moments in ships have so far been based on a Poisson pulse train model for the occurrence of the slamming impacts. Embedded in the Poisson pulse model is the assumption that the time of occurrence and the intensity of a slamming impact are independent of the corresponding quantities of the previous impact. This assumption is not valid because the periodic character of the ship motion tends to concentrate the slamming impacts in clusters. Further, the times of occurrence of the slamming impact and the wave-induced stress peaks are highly correlated. Slamming impact usually generates the first peak of a compressive (sagging) slamming stress in the deck, as the wave-induced stress passes from hogging to sagging. The magnitude of the wave-induced and slamming-induced stress peaks, however, tends to be slightly negatively correlated. The work in the present paper is based on the so-called Slepian model process. This is a non-Gaussian and nonstationary process that gives a complete description of the original ergodic Gaussian process after an arbitrary upcrossing into a critical interval. By use of the Slepian model process, the joint distribution of the wave amplitude and the frequency is established at the occurrence of maximum slamming response within a cluster of slamming impacts. Thereafter the response is calculated for regular sinusoidal waves at selected wave amplitudes and frequencies. Response statistics are obtained by weighing the calculated response by the probability densities of the various pairs of wave amplitude and frequency.