• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.513-521
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• 2018

In this paper, the resonance response of spar-type floating platform in coupled heave and pitch motion is investigated using a CPU time-effective numerical method. A coupled nonlinear 2-DOF equation of motion is derived based on the potential wave theory and the rigid-body hydrodynamics. The transient responses are solved by the fourth-order Runge-Kutta (RK4) method and transformed to the frequency responses by the digital Fourier transform (DFT), and the first-order approximation of heave response is analytically derived. Through the numerical experiments, the theoretical derivation and the numerical formulation are verified from the comparison with the commercial software AQWA. And, the frequencies of resonance arising from the nonlinear coupling between heave and pitch motions are investigated and justified from the comparison with the analytically derived first-order approximation of heave response.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.37-46
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• 2017

This paper is concerned with the numerical study on the resonance response of a rigid spar-type floating platform in coupled heave and pitch motion. Spar-type floating platforms, widely used for supporting the offshore structures, offer an economic advantage but those exhibit the dynamically high sensitivity to external excitations due to their shape at the same time. Hence, the investigation of their dynamic responses, particularly at resonance, is prerequisite for the design of spar-type floating platforms which secure the dynamic stability. Spar-type floating platform in 2-D surface wave is assumed to be a rigid body having 2-DOFs, and its coupled dynamic equations are analytically derived using the geometric and kinematic relations. The motion-variance of the metacentric height and the moment of inertia of floating platform are taken into consideration, and the hydrodynamic interaction between the wave and platform motions is reflected into the hydrodynamic force and moment and the frequency-dependent added masses. The coupled nonlinear equations governing the heave and pitch motions are solved by the RK4 method, and the frequency responses are obtained by the digital Fourier transform. Through the numerical experiments to the wave frequency, the resonance responses and the coupling in resonance between heave and pitch motions are investigated in time and frequency domains.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.633-646
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• 2014

A semi-analytical numerical approach for the effective structural dynamic response analysis of spar floating substructure for offshore wind turbine subject to wave-induced excitation is introduced in this paper. The wave-induced rigid body motions at the center of mass are analytically solved using the dynamic equations of rigid ship motion. After that, the flexible structural dynamic responses of spar floating substructure for offshore wind turbine are numerically analyzed by letting the analytically derived rigid body motions be the external dynamic loading. Restricted to one-dimensional sinusoidal wave excitation at sea state 3, pitch and heave motions are considered. Through the numerical experiments, the time responses of heave and pitch motions are solved and the wave-induced dynamic displacement and effective stress of flexible floating substructure are investigated. The hydrodynamic interaction between wave and structure is modeled by means of added mass and wave damping, and its modeling accuracy is verified from the comparison of natural frequencies obtained by experiment with a 1/100 scale model.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.12
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• pp.1111-1118
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• 2013

In this paper, the disturbance applied to launcher hatch by ship motions is introduced to identify the vertical ship motion disturbance. Basically, ship motions are comprised of 6 degrees of freedom: roll, pitch, yaw, heave, surge and sway. In the case of the shipboard launcher hatch the coupled pitch, heave and roll are significant motions to be transformed to a vertical direction motion. The maximum acceleration values are obtained from the vertical motion model and the ship motion data in accordance with ship type and hatch location on the ship. We verify that the maximum pitch motion mainly influences the launcher hatch and also present the quantity of the maximum load disturbance by the ship's motion acceleration.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.2 s.140
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• pp.124-128
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• 2005

This paper describes motion stability of a spar platform with and without a damping plate in regular waves. The heave and pitch motion equation is derived in terms of Mathieu equation and the stability diagram is obtained. It is shown that the spar platform with damping plate has smaller unstable region than that without damping plate in the stability diagram. Model tests are carried out to verify the mathematical analysis. Under the condition that the pitch natural period is approximately double the heave natural period and the heave motion is amplified at heave resonance, unstable pitch motions are evoked. However the unstable motion is stabilized in cases of spar platform with damping plate. Therefore the damping plate is an effective device to stabilize the motion of spar platform.

• Journal of Ocean Engineering and Technology
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• v.37 no.1
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• pp.1-7
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• 2023

The motion of small fishing vessels is significantly affected by small waves, leading to accidents, such as capsizing or sinking. This paper presents the results of two types of basin tests. The first test analyzed the characteristics of roll and pitch motions among regular waves with the same wave steepness using the drifting state of three (3G/T, 7G/T, 10G/T) small fishing vessels. The second test analyzed the motion characteristics of the 7G/T fishing vessel under different wave steepness. The first test showed that heave and roll motions are significant in the beam sea, while pitch motion is significant in the bow and stern seas. The second test shows that wave steepness has a linear relationship with roll and pitch motions in the bow and stern seas.

• Ocean Systems Engineering
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• v.3 no.3
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• pp.203-217
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• 2013

A PTO (power-take-off) mechanism by using relative heave motions between a floating buoy and its inner mass (magnet or amateur) is suggested. The inner power take-off system is characterized by a mass with linear stiffness and damping. A vertical truncated cylinder is selected as a buoy and a special station-keeping system is proposed to minimize pitch motions while not affecting heave motions. By numerical examples, it is seen that the maximum power can actually be obtained at the optimal spring and damper condition, as predicted by the developed WEC(wave energy converter) theory. Then, based on the developed theory, several design strategies are proposed to further enhance the maximum PTO, which includes the intentional mismatching among heave natural frequency of the buoy, natural frequency of the inner dynamic system, and peak frequency of input wave spectrum. By using the intentional mismatching strategy, the generated power is actually increased and the required damping value is significantly reduced, which is a big advantage in designing the proposed WEC with practical inner LEG (linear electric generator) system.

• Bulletin of the Society of Naval Architects of Korea
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• v.12 no.2
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• pp.59-66
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• 1975

Recently, as the dimensions of energy carriers increase, especially in draft, a reliable prediction of the ship motions at finite depths of water becomes necessary. The purpose of this paper is to probe the effect of finite water depth on the hydrodynamic forces and ship motions, particularly heave and pitch, in longitudinal regular head waves, by comparing the experimental value of Freakes and Keay with the author's theoretical value obtained by applying the modified strip theory to the Mariner class ship. It is confirmed that generally the hydrodynamic coefficients in the equations of motion increase with decreasing water depth, and the wave exciting forces and moments decrease with decreasing water depth. Amplitudes of heave and pitch in longitudinal regular head waves decrease as the water depth in the range where the length of the incident wave is comparatively long. The effects of Froude Number on the hydrodynamic coefficients increase with decreasing water depth and is more noticeable in the case of heave than pitch. In heave, generally the discrepancy between the experimental value and the theoretical value is relatively small in the case of $F_n=O$, but it is very large in the case of $F_n=0.2$. It is considered that the trend stems from the ignorance of the three dimensional effect and the other effects due to shallowness of water on the hydrodynamic coefficients in the theoretical calculation. An extension of methods for calculating the two dimensional hydrodynamic forces to included the effect of forward speed should be recommended. It is required that more experimental works in finite water depths will be carried out for correlation studies between the theoretical calculation, according tp modified strip theory, and model experiments.

• Journal of the Korean Society of Marine Environment & Safety
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• v.25 no.3
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• pp.366-372
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• 2019

This study performed a numerical analysis of a 3D unsteady viscous flow in order to investigate ship motion responses running through regular waves of the platform supply vessel. The feasibility of numerical analysis was tested under the three regular wave conditions of the KRISO container ship (KCS) suggested at the 2010 Gothenburg CFD Workshop. The resulting resistance coefficient, heave motion, and pitch angle were compared with the model test of the harmonic analysis. Also, the ship motion response characteristics of the platform supply vessel were performed using the proven method of the KRISO container ship (KCS). The ship motions including the resistance coefficient, heave motion, and pitch angle according to the time series were investigated via harmonic analysis under regular waves condition of ${\lambda}/LPP=1.87$ and $H_S=0.078m$.

• Journal of the Korean Society of Marine Environment & Safety
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• v.20 no.4
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• pp.443-450
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• 2014

In this study, we have discussed about the effect of hydrofoil arrangement and longitudinal moment characteristic on longitudinal motion stability of fully-submerged hydrofoil by the experiment of tandem hydrofoil model. First of all, tandem hydrofoil model that has canard wing arrangement has been made and characteristics of lift force and drag force by performing the lift force and drag force measuring experiment has also been estimated. Besides, tandem hydrofoil model's wing arrangement which has the initial stability and self stability of longitudinal motion has also been determined. In longitudinal stability experiment of tandem hydrofoil model, the motion characteristic of pitch and heave and the longitudinal stability of foil borne condition by variation of self stability of longitudinal moment and longitudinal distance are estimated. The result from the experiment and it's important conclusion can be described as below; Increase the self stability for longitudinal moment, the higher self stability for pitch motions in a constant pitch angles. By increasing the self stability for longitudinal moment, the range of fluctuation of pitch motion and heave motion for pitch angle also will change relatively small and longitudinal stability is excellent. Lastly, when the lift force of hydrofoil is remain constants, we can conclude that securing the enough self stability for longitudinal moment is essential for stable foil borne condition of tandem hydrofoil.