: The subject of cylinders oscillating in or below the free surface of very deep fluids is developed as a boundary value problem within the framework of linear free-surface theory by distributing source singularities over the submerged portion of the cylinders. A computer program for calculating the hydrodynamic pressure, force, and moment of fluids on these cylinders was devised. The results for various two-dimensional shapes are given in graphical form. (Author)

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Oscillation of cylinders in or below the free surface of deep fluids

This article presents a unified state-space model for ship maneuvering, station-keeping, and control in a seaway. The frequency-dependent potential and viscous damping terms, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using a state-space formulation. The separation of the vessel model into a low-frequency model (represented by zero-frequency added mass and damping) and a wave-frequency model (represented by motion transfer functions or RAOs), which is commonly used for simulation, is hence made superfluous.

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A nonlinear unified state-space model for ship maneuvering and control in a seaway

This paper presents a computer effective nonlinear time-domain strip theory formulation for dynamic positioning (DP) and low-speed manoeuvring. Strip theory or 2D potential theory, where the ship is divided in 20 to 30 cross sections, can be used to compute the potential coefficients (added mass and potential damping) and the exciting wave loads (Froude-Krylov and diffraction forces). Commercially available programs are ShipX (VERES) by Marintek (Fathi, 2004) and SEAWAY by Amarcon (Journee & Adegeest, 2003), for instance. The proposed method can easily be extended to utilize other strip theory formulations or 3-D potential programs like WAMIT (2004). The frequency dependent potential damping, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using the state-space formulation of Kristiansen & Egeland (2003). The separation of the vessel model into a low-frequency model (represented by zero- frequency added mass and damping) and a wave-frequency model (represented by motion transfer functions or RAOs), which is commonly used for simulation, is hence made superfluous. Transformations of motions and coefficients between different coordinate systems and origins, i.e. data frame, hydrodynamic frame, body frame, inertial frame etc., are put into the rigid framework of Fossen (1994, 2002). The kinematic equations of motion are formulated in a compact nonlinear vector representation and the classical kinematic assumption that the Euler angles are small is removed. This is important for computation of accurate control forces at higher roll and pitch angles. The hydrodynamic forces in the steadily translating hydrodynamic reference frame (equilibrium axes) are, however, assumed tobe linear. Recipes for computation of retardation functions are presented and frequency dependent viscous damping is included. Emphasis is placed on numerical computations and representation of the data from VERES and SEAWAY in Matlab/Simulink. For this purpose a Simulink add-in to the Marine Systems Simulator (MSS) at the Norwegian University of Science and Technology has been developed (Fossen et al., 2004).

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Nonlinear Time-Domain Strip Theory Formulation for Low-Speed Manoeuvring and Station-Keeping

Wave-induced ship hull vibrations in stochastic seaways

Shiphandling simulation: application to waterway design

When cylinders of Lewis Form sections heave and pitch on the free surface, their damping force and the added mass were exactly calculated by Ursell's Method. And many figures in this report show the results of the calculation. Then the reporter calculated, applying the results of the above-mentioned calculation and by Strip Method, the damping force and the added mass of the two ships, which were respectively put to test by Golovato and Gerritsuma. The added mass and the added moment of inertia which the reporter gained by Strip Method showed good coincidence with the results of Golovato's and Gerritsuma's experiments. To get better estimation on the damping force by Strip Method, it is necessary to calculate more closely the three dimensional effect, non-linear effect, etc. As to the added mass the three dimensional correction could be negligible except for small ξ1*.

On the Damping Force and added Mass of Ships Heaving and Pitching

Hydrodynamic Force and Moment Produced by Swaying Oscillation of Cylinders on the Surface of a Fluid

We measured the two dimensional progressive wave height produced by forced heaving of the miscellaneous cylinders, and compared the amplitude ratio A with the F. Ursell's results [1] and author's theoretical calculations [2]. As the result we could find that the measured A showed generally fair coincidence wih that of the theoretical results. Moreover, the author studied the wedge effect, the effect of the deviation from the Lewis forms, and the effect of the heaving amplitude.Many figures in this paper shows these results.

Fukuzo Tasai

Papers

On the Damping Force and added Mass of Ships Heaving and Pitching

Hydrodynamic Force and Moment Produced by Swaying Oscillation of Cylinders on the Surface of a Fluid

Measurement of the Wave Height Produced by Forced Heaving of the Cylinders