ON COMBINATION OF SLAMMING-INDUCED AND WAVE-INDUCED RESPONSES

Attempts to solve the combination problem of the low-frequency wave-in duced 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 mod el is the assumption that the time of occurrence and the intensity of a slamming impact are independent of the corresponding quantities of t he 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 impa ct usually generates the first peak of a compressive (sagging) slammin g stress in the deck, as the wave-induced stress passes from hogging t o sagging. The magnitude of the wave-induced and slamming-induced stre ss peaks. however, tends to be slightly negatively correlated. The wor k in the present paper is based on the so-called Slepian model process . This is a non-Gaussian and nonstationary process that gives a comple te description of the original ergodic Gaussian process after an arbit rary upcrossing into a critical interval. By use of the Slepian model process, the joint distribution of the wave amplitude and the frequenc y 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 frequenci es. Response statistics are obtained by weighing the calculated respon se by the probability densities of the various pairs of wave amplitude and frequency.