• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-44
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• 2000

We study a free boundary problem satisfying Bernoulli type boundary condition along which the gradient of a piecewise harmonic solution jumps zero to a given constant value. In such problem, the free boundary splits the domain into two regions, the zero set and the harmonic region. Our main interest is to identify the global shape and the location of the zero set. In this paper, we find the lower and the upper bound of the zero set. In a convex domain, easier estimation of the upper bound and faster disk test technique are given to find a rough shape of the zero set. Also a simple proof on the convexity of zero set is given for a connected zero set in a convex domain.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.965-970
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• 2002

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass with translational elastic support at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a wide range of section ratio, dimensionless spring constant and mass ratio.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.394.1-394
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• 2002

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. (omitted)

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.995-999
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• 2001

This paper deals with the free vibrations of arches with general boundary condition. Based on the dynamic equilibrium equations of a arch element acting the stress resultants and the inertia forces, the governing differential equation is derived for the in-plane free vibration of such arches. Differential equations are solved numerically to calculate natural frequencies. In numerical examples, the parabolic arch is considered. The effects of the arch rise to span length ratio, the slenderness ratio, the vertical spring coefficient and the rotational spring coefficient on the natural frequencies are analyzed.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.71.3-71.3
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• 2019

Previously we developed a method of coronal force-free field construction using vector potentials. In this method, the boundary normal component of the vector potential should be adjusted at every iteration step to implement the boundary normal current density, which is provided by observations. The method was a variational method in the sense that the excessive kinetic energy is removed from the system at every iteration step. The boundary condition imposing the normal current density, however, is not compatible with the variational procedure seeking for the minimum energy state, which is employed by most force-free field solvers currently being used. To resolve this problem, we have developed a totally new method of force-free field construction. Our new method uses a unique magnetic field description using two scalar functions. Our procedure is non-variational and can impose the boundary normal current density exactly. We have tested the new force-free solver for standard Low & Lou fields and Titov-Demoulin flux ropes. Our code excels others in both examples, especially in Titov-Demoulin flux ropes, for which most codes available now yield poor results. Application to a real active region will also be presented.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.2
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• pp.13-18
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• 1982

The method of Rankine source distribution is emerging as a powerful yet simple alternative for the solution of complicated free surface problems. But it has been uncertain whether the radiation condition could be satisfied exactly by distributing the simple sources on the free surface only. In this paper, it is proved rigorously that the Rankine sources, whose intensities are varying sinusoidally along the axis satisfying the free surface boundary condition, generate the radiation waves both in the infinite and finite-depth flows. A formula is derived to give the upper and lower bounds of the errors in the induced velocity computation that will be introduced by truncating the extent of source distribution on the free surface. Since the truncation is inevitable in the numerical analysis, this formula may be used as a criterion to limit the position of the field points, where velocity computation is made, away from the truncation boundary. A typical analysis shows that the maximum error will be 3.4 percent of the exact induced velocity when the field point is on the free surface two wave lengths away from the truncation boundary.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.831-836
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• 2000

In this study, the Rayleigh inextensional theory and extensional theory for thin shells was employed to predict the natural frequencies of the hemi-spherical shell with free and simply. supported boundary condition. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. Modal test and FEM analysis of the free, simply supported and clamped boundary condition was also carried out.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.2
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• pp.186-193
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• 2011

The NDIF method(non-dimensional dynamic influence function method) for free vibration analysis of arbitrarily shaped plates with the simply supported edge is newly developed in the paper. In order to extract the system matrix that gives the natural frequencies and natural modes of the plate of interest, the difficulty of measuring higher differential terms involved in the simply supported boundary condition is successfully overcome. Finally, the excellence of the characteristics of convergence and accuracy of the proposed method is shown through two verification examples, which indicate that natural frequencies and natural modes obtained by the proposed method are very accurate and swiftly converged even though a small number of nodes are used compared with FEM.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.698-703
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• 2000

In a computational fluid dynamics, the imposition of open boundary condition has an important part of the accuracy but it is not easy to find the optimal boundary rendition. This difficult is introduced by making artificial boundary in unbounded domairs. Such open boundary requires us to ensure the continuity of all primitive variables because the nature is in continuum. Here we introduce a revised well-conditioned open boundary condition particularly in FEM and apply it to various problems-entrainment, body force, short domains.

• International Journal of Ocean System Engineering
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• v.2 no.1
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• pp.32-36
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• 2012

This paper presents a comparison of potential and viscous computational codes for the water entry problem. A po-tential code was developed which adopted the boundary element method to solve the problem. A nonlinear free surface boundary condition was integrated to find new locations of free surface. The dynamic boundary condition was simplified by taking constant potential values for every time steps. The simplified dynamic boundary condition was applied in the new position of the free surface not at the mean level, which is the usual practice for linearized theory. The commercial code FLUENT was used to solve the water entry problem from the viscosity point of view. The movement of the air-liquid interface is traced by distribution of the volume fraction of water in a computational cell. The pressure coefficients were compared with each other, while experimental results published by other researchers were also examined. The characteristics of each method were discussed to clarify merits and limitations when they were applied to the water entry problems.