The present paper focuses on the analysis of impact pressure registrations from repeated model scale sloshing experiments under harmonic rotational excitation. A series of more than 100 experiments, each one encompassing more than 100 impact events, has been conducted seeking the highest feasible repeatability. Different excitation periods, that cover the main features of the impact dynamics, have been considered in a preliminary screening, describing the main features of the impact dynamics. Since, even under a nominally deterministic excitation, the pressure at each impact is characterized by a high variability, a statistical approach is used treating the impact pressure as a stochastic process. For one selected excitation period, the statistical analysis focuses on the ensemble distribution of the maximum pressure during each impact event. Particular attention is given to the evolution of such distributions, in order to detect the variations in the statistical characteristics of the process. This is achieved by, first, identifying the presence and the length of the transient phase and, second, by characterizing the process at stationary state. The statistics of impact pressure for different peaks are discussed mostly in the ensemble domain. Linking the latter with the time domain analysis is made by checking that the problem can be considered “practically ergodic.” The “practical ergodicity” of the process is dealt with by checking to what extent steady state ensemble statistical information can be obtained from a single long run experiment. Statistical checks for correlation and independence of maximum impact pressures are also carried out to test the hypothesis of independent identically distributed random variables. The method of analysis presented in this paper through the considered example case is general in nature and is considered to be highly portable. In particular, it is considered to allow for a more thorough understanding of non-deterministic events such as those considered herein, by looking at them from a sound statistical perspective. The thorough description of the whole experimental setup makes the presented data suitable for comparison purposes and for validation of theoretical/numerical approaches
In this work a combined analytical-numerical approach is proposed to address the problem of the ship roll motion under the combined action of wind and waves. Roll motion is modelled as a one-degree-of-freedom system non-linear in both damping and restoring. The approach is modular, allowing an easy update of the methodology on the basis of new research outcomes. Realistic environmental conditions regarding the effects of both wind and waves are taken into account and can be easily changed. The spatial correlation of wind gusts is taken into account by means of an 'aerodynamic admittance' function, whereas the moment due to waves is obtained from the sea slope spectrum using the concept of effective wave slope, leading to a 'hydrodynamic admittance' function. Both static and dynamic aspects of the problems are taken into account. The proposed analytical procedure, based on statistical linearization technique, allows approximate statistical averages of the roll motion, assumed to be Gaussian, to be obtained without necessarily resorting to time-consuming Monte Carlo simulations. On the basis of the results obtained, an estimation of the capsize probability can be carried out. It seems that the effect of wind gustiness could be considered very small when compared with the effects of waves and mean wind speed when the metacentric height is sufficiently large. Finally, the presented approach moves towards the concept of 'performance-based analysis', recently introduced at the International Maritime Organization as the basis for future developments of intact stability, in a clear and formal way.
The roll motion response of a single degree of freedom (SDOF) structural system to which a rigid rectangular partially filled liquid tank has been attached is considered. The SDOF structural system with the empty tank is first described with a mathematical model and this model is validated by performing decay experiments as well as experiments in which periodic excitations are applied to the system. The responses are accurately predicted by the model. The accuracy of these predictions allows us to study both experimentally and numericaily, with weakly compressible SPH, the performance of the partially filled tank as a tuned liquid damper (TLD). The sloshing flows inside the tank comprise the onset of breaking waves which make the TLDs devices extremely difficult to model, especially for the potential flow multimodal approaches commonly used to simúlate these sorts of coupled systems. In order to characterise the wave breaking effects on the response curves, tests have been performed with liquids of different viscosity, the increasing viscosity preventing the onset of breaking waves. The capabilities of SPH to treat this coupling problem are assessed and the results show that SPH is able to capture a substantial part of the physics involved in the addressed phenomena but further work remains still to be done relating to a more accurate treatment of the laminar viscosity and turbulence effects. RESUME La réponse en roulis d'un systéme a un degré de liberté (SDOF), auquel est fixée une cuve rectangulaire partiellement remplie de liquide, est étudiée dans cet article. Dans une premiére partie, un modele mathématique est proposé pour le systéme SDOF, calibré a l'aide de résultats expérimentaux d'oscillations libres et forcees, avec une excitation périodique. La réponse du systéme est reproduite avec precisión par le modele. L'efficacité de la cuve en tant qu' amortisseur liquide (TLD) est ensuite analysée expérimentalement et numériquement en utilisant la méthode de simulation SPH. Pour résoudre ees problémes de couplage, des méthodes basées sur la théorie du potentiel sont généralement utilisées. Dans le cas présent, leur utilisation est limitée a cause de la formation de vagues déferlantes lors du ballotement du liquide dans la cuve. Une plus grande viscosité du liquide réduisant la formation de ees vagues, des expériences ont été effectuées avec des liquides de différentes viscosités pour quantifier l'impact des déferlantes sur la réponse globale du systéme couplé. La capacité de la méthode SPH pour résoudre ce probléme est discutée et les résultats montrent que les principaux phénoménes physiques sont reproduits avec SPH. Cependant, des travaux restent nécessaires quant au traitement de la viscosité laminaire et a la partie turbulente de l'écoulement.
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