• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.45-64
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• 1993

This paper dealt with the application of a numerical method developed by the authors using the matching method proposed in the previous paper on "The Nonlinear motions of cylinders(I)[16]", and Cauchy's theorem to the problems associated with hydrodynamic forces acting on a heaving cylinders translating in a calm water and also motions of cylinders in waves. In spectral method. body boundary condition in submerged case is satisfied exactly but one in floating case is not satisfied exactly. In the numerical code developed here, the boundary condition at the free-surface and body surface is satisfied exactly at its instaneous position. It is of interest to note that the present scheme could be applied to a free-surface-piercing body without experiencing a difficulty in the numerical convergence. The computed results are compared with other results([6], [12]).

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.1
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• pp.63-72
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• 1990

The linear hydrodynamic forces, acting on a forced oscillating cylinder from its mean position on a free surface with a small amplitude, are calculated in the time domain. The integral equation method using a time dependent Green function is employed. The numerical results for the heaving and swaying circular cylinder are shown and give good agreements with others Furthermore it is shown that the use of the Green function, which is expressed by a series expansion or asymptotic expansion according to time range, reduces computing time greatly.

• Bulletin of the Society of Naval Architects of Korea
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• v.10 no.1
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• pp.33-44
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• 1973

Chine형 선체단면 주상체의 자유표면에서의 상하운동에 수반되는 부가질량과 감쇠력을 Ursell-Tasai 방법에 의하여 계산하였다. Chine형에서 구하여진 결과는 같은 선체단면적 계수와 반폭흘수비를 갖는 등가 Lewis형의 결과와 비교하였고 선체단면의 형상이 부가질량 및 감쇠력에 미치는 영향을 고찰하였다. Chine형과 등가 Lewis형 선체단면 주상체에 파고가 일정한 횡파가 입사할 때의 상하운동을 고찰하였다. 이상과 같은 계산 및 고찰을 통하여 다음 결과를 얻었다. 1) 자유표면이 부가질량에 미치는 영향은 chine형이 등가 Lewis형단면보다 큰 값을 갖는다. 2) 선체단면적계수와 반폭흘수비가 같은 경우에 감쇠력의 크기는 Lewis form, single chine, double chine순서이다. 3) 선체단면계수와 반폭흘수비는 상하운동에 가장 큰 영향을 미치는 것으로 생각되며, 선체단면의 기하학적인 변형이 운동에 미치는 영향은 중요한 요소가 되질 못한다. 4) 감쇠력계수와 선체단면계수와의 관계는 간단한 관계를 유지한다.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.1
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• pp.25-33
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• 2015

Following the previous works on the natural frequency of heaving circular cylinder, i.e. Lee and Lee (2013) and Kim and Lee (2013), an investigation of the same spirit on the 2-dimensional cylinder of Lewis form has been conducted. As before, the natural frequency is defined as that corresponding to the local maximum of the MCFR (Modulus of Complex Frequency Response), which is given by the equation of motion in the frequency domain analysis. Hydrodynamic coefficients were found by using the Ursell-Tasai method, and numerical results for them were obtained up to much higher frequencies than before, for which the method was known as numerically unstable in the past. For a wide range of H, the beam-draft ratio, and ${\sigma}$, the sectional area coefficient, including their practical ranges for a ship, results for the natural frequency were computed and presented in this work. Two approximate values for the natural frequency, one proposed by Lee (2008) and another one by the damped harmonic oscillator, were also compared with the current results, and for most cases it was observed that the current result is between the two values. Our numerical results showed that the values of the local maximum of MCFR as well as the natural frequencye increase as ${\sigma}$ increases while H decreases. At present, extension of the present finding to the 3-dimensional ship via the approximate theory like the strip method looks promising.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.86-97
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• 1993

A numerical method is developed for the nonlinear motion of two-dimensional wedges and axisymmetric-forced-heaving motion using Semi-Largrangian scheme under assumption of potential flows. In two-dimensional-problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary. In three-dimensional-problem Rankine ring sources are used in a Green's theorem boundary integral formulation to salve the field equation. The solution is stepped forward numerically in time by integrating the exact kinematic and dynamic free-surface boundary condition. Numerical computations are made for the entry of a wedge with a constant velocity and for the forced harmonic heaving motion from rest. The problem of the entry of wedge compared with the calculated results of Champan[4] and Kim[11]. By Fourier transform of forces in time domain, added mass coefficient, damping coefficient, second harmonic forces are obtained and compared with Yamashita's experiment[5].

• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.114-131
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• 1992

In the present work, a two-dimensional boundary-value problem for a large amplitude motion is treated as an initial-value problem by satisfying the exact body-boundary and nonlinear free-surface boundary conditions. The present nonlinear numerical scheme is similar to that described by Vinje and Brevig(1981) who utilized the Cauchy's theorem and assumed the periodicity in the horizontal coordinate. In the present thesis, however, the periodicity in the horizontal coordinate is not assumed. Thus the present method can treat more realistic problems, which allow radiating waves to infinities. In the present method of solution, the original infinite fluid domain, is divided into two subdomains ; ie the inner and outer subdomains which are a local nonlinear subdomain and the truncated infinite linear subdomain, respectively. By imposing an appropriate matching condition, the computation is carried out only in the inner domain which includes the body. Here we adopt the nonlinear scheme of Vinje & Brevig only in the inner domain and respresent the solution in the truncated infinite subdomains by distributing the time-dependent Green function on the matching boundaries. The matching condition is that the velocity potential and stream function are required to be continuous across the matching boundary. In the computations we used, if necessary, a regriding algorithm on the free surface which could give converged stable solutions successfully even for the breaking waves. In harmonic oscillation problem, each harmonic component and time-mean force are obtained by the Fourier transform of the computed forces in the time domain. The numerical calculations are made for the following problems. $\cdot$ Forced harmonic large-amplitude oscillation(${\omega}{\neq}0,\;U=0$) $\cdot$ Translation with a uniform speed(${\omega}=0,\;U{\neq}0$) The computed results are compared with available experimental data and other analytical results.