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In this work the problem of slamming on the cross structure of catamarans is studied. An introduction and overview of the problem is given.Methods for predicting the slamming occurrence of high-speed power catamarans and sailing catamarans are presented. Emphasis is placed ondeveloping methods that are practical to use in order to facilitate prediction of slamming occurrence at the design stage. The methods used consist of three steps: Ship motion prediction, slamming identification and slamming pressurecalculations. Existing linear and non-linear ship motion prediction theories are used for high-speed power catamarans while a new strip theory has been developed specifically for motion prediction of sailing multihulls. Predicted shipmotion results are compared to full-scale experiments, both for high-speed powercatamarans and sailing catamarans. A new direct method for identification of slamming occurrence in the time domain is presented, as well as results using probabilistic methods. A comparison between the two methods is presented.Slamming pressure calculations are done using an existing two dimensional slamming theory and are compared with analytical results. A parametric study is done on two case study ships to investigate the effect of various hullformparameters on the slamming occurrence. The methods and results presented are of use to designers of high-speed power catamarans and sailing catamarans.

For high speed vessels and offshore structures, wave impact, a main source of environmental loads, causes high local stresses and structural failure. However, the prediction of wave impact loads presents numerous challenges due to the complex nature of the instant structure-fluid interaction. The purpose of the present study is to develop an effective wave impact model to investigate the dynamic behaviors of specific shaped elements as they impact waves. To achieve this objective, a wave impact model with a body swinging on a pendulum system is developed. The body on the pendulum goes through a wave free surface driven by gravity at the pendulum's natural frequency. The system's motion and impact force during the entire oscillation time beginning from the instant of impact are of interest. The impact force is calculated by applying von Karman's method, which is based on momentum considerations. The usual wave forces are presented in the Morison's equation and incorporated into dynamic systems with other wave forces. For each body shape, the dynamic system is described by a strongly nonlinear ordinary differential equation and then solved by a Runge-Kutta differential equation solver. The dynamic response behavior and the impact force time history are obtained numerically and the numerical results show support the selection of a pendulum model as an efficient approach to study slamming loads. The numerical prediction of this model is compared to previous experiments and classification society codes. Moreover, a basic design of wave impact experiments using this pendulum model is proposed to provide a more accurate comparison between numerical results and experimental data for this model. This design will also serve as a first look at the experimental application of the pendulum model for the purpose of forecasting slamming force.

High-speed planing craft operating in waves are subject to frequent water impact, or slamming, as a portion or whole of the craft exits the water and re-enters at high velocity. The global load induced by slamming can cause fatigue-related damages to structures. The local slamming can cause local damage to structures and its induced acceleration can cause damage to equipment and personnel aboard. Therefore the slamming loads in high-speed craft are critical design loads. Nowadays, due to the increasing use of composite materials in high-speed craft, the interaction between the hydrodynamic loading and structural response, or hydroelasticity, must be considered. In this work, a flexible V-shaped wedge, which vertically enters the calm water with an impact velocity, was examined experimentally and numerically to characterize the slamming of a representative cross-section of high-speed craft. Physical quantities of interest include rigid-body kinematic motions, spray root propagation, hydrodynamic loading, and structural response. In the experimental work, with varied impact velocity and flexural rigidity of the wedge bottom plate, a wide range of hydroelasticity factors were investigated. The intersection between the bottom plate and side plate is called chine. The phases before and after the spray root reached the chine are called chine-unwetted and chine-wetted phase, respectively. It was found that the maximum deflection and strain occur in the chine-unwetted phase while a structural vibration with rapidly decaying magnitude is observed in the chine-wetted phase. Furthermore, the kinematic effect of hydroelasticity changes the spray root propagation and hence the pressure, while the inertial effect elongates the natural period of the plate. Inspired by the experimental work, a computational framework was proposed to focus on the chine-unwetted phase. Several hydroelastic models can be obtained from this framework. The hydroelastic models were validated to show reasonable agreement with experiments. Various parameters were studied through the computational framework. The hydroelasticity factor was modified to account for the mass and boundary conditions. It was found that the nondimensional rigid-body kinematic motions and maximum deflection showed little dependence on the hydroelasticity factor. Hydroelastic effects increased the time it takes for the peak maximum deflection to be reached for small values of the hydroelasticity factor. Hydroelastic effects also have little influence on the magnitude of the maximum deflection. These discoveries further the understanding of hydroelastic slamming and show the potential to guide the structural optimization and design of high-speed craft. / Doctor of Philosophy / High-speed planing craft operating in waves are prone to frequent water impact, or slamming, as a portion or whole of the craft exits the water and re-enters at high velocity. The slamming loads in high-speed craft are critical design loads as the slamming can cause damage to the structures and equipment as well as injure personnel aboard. Nowadays, due to the increasing use of composite materials in high-speed craft, the interaction between the hydrodynamic loading and structural response, or hydroelasticity, must be considered. In this work, a flexible V-shaped wedge entering water is studied experimentally and computationally to characterize the slamming of a representative cross-section of high-speed craft. The contact point between the water surface and the wedge bottom is called the spray root. It was found that the hydrodynamic loading and structural response interact with each other through the spray root. The maximum deflection and strain occur when the wedge bottom is partially submerged while a structural vibration with rapidly decaying magnitude is observed when the wedge bottom is fully submerged. Using the hydroelasticity factor proposed by other researchers, the extent of fluid-structure interaction was quantified. Hydroelastic effects manifest themselves when the hydroelasticity factor is small These discoveries further the understanding of hydroelastic slamming and show the potential to guide the structural optimization and design of high-speed craft.

Local and global loadings, which may cause the local damage and/or global failure and collapse of offshore structures and ships, are experimentally investigated in this study. The big research question is how the aeration of water and the elasticity of the structural section affect loading during severe environmental conditions. A further question is how the scattered waves from ships and offshore structures, the mooring line force and the structural response, which are known to affect local load and contribute to global load, will be affected by wave-structure interaction of a ship or offshore structure under non-breaking wave conditions. Three different experiments were undertaken in this study to try to answer these questions: (i) slamming impacts of a square flat rigid/elastic plate, which represents a plate section of the bottom or bow of ship structure, onto pure and aerated water surface with zero degree deadrise angle; (ii) wave impacts on a truncated vertical rigid/elastic wall in pure and aerated water, where the wall represents a plate section of a hull; and (iii) wave-structure interactions of different FPSO-shaped models, where the models were fixed or taut moored. The experiments were carried out at Plymouth University’s COAST Laboratory. Spatial impact pressure distributions on the square plate have been characterised under different impact velocities. It was found that the impact pressures and force in pure water were proportional to the square of impact velocity. There was a significant reduction in both the maximum impact pressure and force for slamming in aerated water compared to that in pure water. An exponential relationship of the maximum force and the void fraction is proposed and its coefficients are found from drop test in this study. There was also a significant reduction in the first phase of the pressure and force impulse for slamming into aerated water compared with pure water. On the truncated wall, aeration also significantly reduced peak wave loads (both pressure and force) but impulses were not reduced by very much. For the case considered here, elasticity of the impact plate has a significant effect on the impact loads, though only at high impact velocities; here the impact loads were considerably reduced with increasing elasticity. Wave loading on the truncated wall was found to reduce with increasing elasticity of the wall for all investigated breaking wave types: high aeration, flip-through and slightly breaking wave impacts. In particular, impact pressure decreases with increasing elasticity of the wall under flip-through wave impact. As elasticity increases, the impulse of the first positive phase of pressure and force decreases significantly. This significant effect of hydroelasticity is also found for the total force impulse on the vertical wall under wave impacts. Scattered waves were generated from the interaction of focused wave groups with an FPSO model. The results show that close to the bow of the FPSO model, the highest amplitude scattered waves are observed with the most compact model, and the third- and fourth-harmonics are significantly larger than the incident bound harmonic components. At the locations close to the stern, the linear harmonic was found to increase as the model length was decreased, although the nonlinear harmonics were similar for all three tested lengths, and the second- and third-harmonics were strongest with the medium length model. The nonlinear scattered waves increased with increasing wave steepness and a second pulse was evident in the higher-order scattered wave fields for the fixed and free floating models. In addition, the higher harmonics of the mooring line force, and the heave and pitch motions all increased with increasing wave steepness. Incident wave angles of 0 (head-on), 10 and 20 degrees were experimentally investigated in this study. As the incident wave angle between the waves and the long axis of the vessel was increased from 0 to 20 degrees, the third- and fourth-harmonic scattered waves reduced on the upstream side. These third- and fourth-harmonic diffracted waves are important in assessing wave run-up and loading for offshore structure design and ringing-type structural response in fixed and taut moored structures. The second-, third- and fourth-harmonics of the mooring line force, and the heave and pitch motions decreased as the incident wave angle increased from 0 to 20 degrees.

Slamming loads are the critical structural design load for high-speed craft. In addition to damaging the hull structure, payload, and injuring personnel, slamming events can also significantly limit operating envelopes and decrease performance. To better characterize slamming events and the factors affecting their severity, a parametric study will be carried out in the Virginia Tech Hydroelasticity Lab. This thesis provides the groundwork for this longitudinal project through meticulous analysis of irregular wave tow tank experiments. Through the modification of machine learning techniques and taking inspiration from facial recognition algorithms, key parameters were identified to form an experimental matrix which captures intricacies of the complex interdependent relation of variables in the slamming problem. The independent effects of parameters to be evaluated include hull flexural rigidity, LCG location, heave and surge velocity, and impact trim, angular velocity and acceleration. In preparation for this parametric study, an innovative experimental setup was designed to simulate the impact of a deep-vee planing hull into waves, through a controlled motion slam into calm water. To provide a baseline to compare data from future controlled motion experiments to, a model drop experiment was completed to characterize the relationships of impact velocity and trim to slamming event severity. During this experiment, the position, acceleration, strain, and pressure were measured. These measurements illustrated a decrease in peak acceleration, pressure, and strain magnitude with an increase in impact trim. Additionally, as trim was increased a delay in the time of peak magnitude for all measurements was observed. These results are attributed to the change in buoyancy with the change in impact angle. At non-zero angles of trim, a pitching moment was generated by the misalignment of the longitudinal center of buoyancy and center of gravity. This moment caused racking in the setup which was observed in the acceleration time histories immediately after impact. This finding furthers the need to investigate the angular velocity and acceleration of the model at impact, through the proposed series of experiments, as they are crucial naturally occurring motions inherent to slamming events. / Master of Science / Slamming loads are the critical structural design load for high-speed craft. Slamming events occur when a boat or ship impacts the water. This impact causes high peak pressures and accelerations. In addition to damaging the hull structure, payload, and injuring personnel, slamming events can also significantly limit operating envelopes and decrease performance. To better characterize slamming events and the factors affecting their severity, a parametric study will be carried out in the Virginia Tech Hydroelasticity Lab. This thesis provides the groundwork for this longitudinal project through meticulous analysis of irregular wave tow tank experiments, which mimic actual conditions in a sea way. Through the modification of machine learning techniques and taking inspiration from facial recognition algorithms, key parameters were identified to form an experimental matrix which captures intricacies of the complex interdependent relation of variables in the slamming problem. The independent effects of parameters to be evaluated include hull structural stiffness, location of the longitudinal center of gravity, vertical and forward velocity at impact, and impact angle, angular velocity and angular acceleration. In preparation for this parametric study, an innovative experimental setup was designed to simulate the impact of a generic high-speed boat into waves, through prescribing a motion path to the boat as it slams into calm water. To provide a baseline to compare data from future controlled motion experiments to, a precursor experiment dropping a boat into calm water was completed to characterize the relationships of impact velocity and trim to slamming event severity. During this experiment, the position, acceleration, strain, and pressure were measured. These measurements illustrated a decrease in peak acceleration, pressure, and strain magnitude with an increase in impact trim. Additionally, as trim was increased a delay in the time of peak magnitude for all measurements was observed. These results are attributed to the change in buoyancy with the change in impact angle. At non-zero angles of trim, a pitching moment was generated by the misalignment of the longitudinal center of buoyancy and center of gravity. This moment caused racking in the setup which was observed in the acceleration time histories immediately after impact. This finding furthers the need to investigate the angular velocity and acceleration of the model at impact, through the proposed series of experiments, as they are crucial naturally occurring motions inherent to slamming events.

Water entry of compliant structures is a major area of interest within different fields of engineering. In the case of highly flexible panels, an application for this topic is on drag reduction due to shape reconfiguration of panels near the free surface to support further development of undulatory propulsors. Moreover, it has been an important concept in the study of the slamming of small high-speed craft with flexible bottom structures, such as those made of composites. In this work, this fluid-structure interaction problem is experimentally investigated in different stages. In Stage I, free-falling water entry experiments are conducted on wedges that have bottom panels with different flexural rigidities. Kinematics, hydrodynamics, spray root propagation, and structural response of the model are measured during the experiments. Results are interpreted to evaluate the effect of flexural rigidity on the slamming characteristics. The comparison between the rigid and flexible wedges shows that the evolution of the spray root on a flexible wedge is influenced due to fluid-structure interaction. In Stage II, a hybrid approach is proposed that incorporates spray root measurements with the existing analytical models in order to estimate the hydrodynamic loads in water entry of wedges with different boundary conditions. The validity of this approach is evaluated using a case study of a flexible wedge drop experiment. The results of this analysis show that the proposed approach can reasonably predict the wedge kinematics and hydrodynamic pressure due to impact. Future components of this study will further develop this tool to be used for highly-flexible structures, where it is not easy to install traditional pressure sensors. Stage III of this work is on analysis of a tow-tank test of a rigid composite planing-hull model performed at the U.S. Naval Academy. Experiments conducted in regular waves were examined in terms of their kinematics and pressure loads. The goal of this analysis is to begin planning of the towing-tank tests that will be conducted at the VT Advanced Towing Tank Facility. These future VT experiments will combine the flexible composite panel with the hull form and motions, which are analyzed in the tow-tank study to investigate the fluid-structure interaction in the slamming of a flexible-planing hull. In stage IV, The findings of experimental investigations on wedge water entry are utilized in a 2D+t method to predict the hydrodynamics and motions of a prismatic planing craft. In this approach, the hydrodynamic loading on each V-type section of the vessel is calculated employing wedge water entry experiments (Stage I) and existing theoretical models (Stage II). A modified strip theory, also known as 2D+t, is then implemented to use these data and solve for the hydrodynamics and motion of the high-speed craft in calm water. Results show a good agreement with that of Savitsky prediction method and existing towing tank measurements. / Doctor of Philosophy / Water entry of compliant structures is a major area of interest within different fields of engineering. One application is to study the motion of highly-flexible plates near the free surface. This is inspired by the manta rays that change the stiffness of their flapping fins during swimming in the ocean in order to have a more smooth motion. Another application is related to small high-speed craft that repeatedly become airborne and impact the water surface in waves. These individual impacts, called slamming, can adversely influence the maneuverability, cause failure to the structure or injure the crew on board. Thus, it is crucial to study and understand this phenomenon in order to mitigate its negative effects. The problem becomes more challenging when the vessel structure, such as those made of composites, can endure some deflections in order to dampen the slams. The interaction between this deflection and the water impact can deviate the slamming characteristics from the traditional theoretical predictions. Therefore, more investigation is needed to study this fluid-structure interaction. In this work, this problem is experimentally investigated in different stages. In Stage I, water entry of a wedge is analyzed, where the wedge represents a section of the high-speed craft. Different bottom panels, including a composite panel, are studied and results are compared in order to understand the effects of deflection of the panel on the slamming characteristics. In Stage II, a new approach is proposed to estimate the hydrodynamic loading in water entry of objects with arbitrary shapes. This approach is developed to estimate the slamming loads during the impact without using any sensors. In fact, the high-speed videos of the water contact around the object during the impact is used to predict the slamming characteristics on the model. This technique can be so useful for the water entry of the objects that have very thin panels, which restrict mounting the pressure sensors. In Stage III, an analysis is conducted on the tow-tank tests of a composite planing-hull model. In these experiments, a small model is tested in regular waves and slamming is examined in terms of the kinematics and pressure loads on the model. The future experiments in VT Advanced Towing Tank will combine the flexible composite panel with the hull form and motions, which are analyzed in the tow-tank study to evaluate the fluid-structure interaction in the slamming of a flexible-planing hull. In Stage IV, the findings of experimental investigations on wedge water entry are utilized to predict the hydrodynamics and motions of a high-speed craft. In this approach, the hydrodynamic loading on each V-type cross section of the vessel is estimated employing wedge water entry measurements (Stage I) and existing theoretical models (Stage II). The calculated hydrodynamic loading on the vessel sections are then used to solve for the hydrodynamics and motion of the entire vessel.

Slamming of marine planing craft is expected to arise due to the high speed nature of their operating conditions. High hydrodynamic forces are inevitably induced causing the shell plating to deflect, which in turn can influence the flow physics surrounding the hull. In order to study the hull’s hydroelastic response due to a slamming event, wedge drop experiments were performed with an aluminum wedge of 57 inches in length, 47 inches in breadth, and 20 degree deadrise with 1/4 in. thick unstiffened bottom panels. The elastic behavior of the hull plating was measured via two methods. The first method uses strain gages to analyze the wedge’s deadrise panel deflections, and the second method is a Stereoscopic- Digital Image Correlation (S-DIC) technique. In the present investigation, an S-DIC code has been developed and utilized to study the deflections and to advance the capabilities of future research. Comparisons are made between the methods and also with theoretical studies. The deflections measured are approximately 0.1 in. on a panel spanning 24.5 inches, and the predictions made using S-DIC and strain gages differ by approximately 23%.