• Journal of the Society of Naval Architects of Korea
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• v.50 no.2
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• pp.111-119
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• 2013

The concept of the natural frequency is useful for understanding the characters of oscillating systems. However, when a circular cylinder floating horizontally on the water surface is heaving, due to the hydrodynamic forces, the system is not governed by the equation like that of the harmonic one. In this paper, in order to shed some lights on the more correct use of the concept of the natural frequency, a problem of the heaving circular cylinder is analyzed in the frequency domain. Previously, it was thought that the theory of Ursell (1949) could not be used to get the added mass and wave-making damping for short waves, however, they were obtained by applying an accurate collocation method to the theory in this study. Using the so developed numerical method, we found the added mass and wave-making damping of the circular cylinder for the entire range of the frequency. Then, the MCFR(Modulus of Complex Frequency Response) was used to locate the frequency corresponding to the local maximum of MCFR and we define it as the natural frequency. Comparing our results with the previous investigation, we found that the pressure distribution on the cylinder gets close asymptotically to that of a cylinder in infinite fluid OR close to that of the cylinder, that the approximation of the natural frequency by Lee (2008) is different from our new value only by 0.64%, and that the approximation of the heaving system by an equivalent damped harmonic oscillation is not proper by the reason that is clearly shown from the comparison of the shape of the corresponding MCFRs.

• Journal of the Society of Naval Architects of Korea
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• v.50 no.4
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• pp.224-231
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• 2013

The concept of the natural frequency is useful for understanding the characters of oscillating systems. However, when a circular cylinder floating horizontally on the water surface is heaving, due to the hydrodynamic forces, the system is not governed by the equation like that of the harmonic one. In this paper, in order to shed some lights on the more correct use of the concept of the natural frequency, a problem of the heaving circular cylinder is analyzed in the time domain. The equation of motion, an integro-differential equation, was derived following the fashion of Cummins (1962), and its coefficients including the retardation function were obtained using the numerical solution of Lee (2012). The equation was solved numerically, and the experiment was also carried out in the CNU flume. Using our numerical and experimental results, the natural frequency was defined as its average value given by the motion data excluding those of the initial stage. Our results were then compared with those of the existing investigations such as Maskell and Ursell (1970), Ito (1977) and Yeung (1982) as well as the newly obtained results of Lee (2012). Comparison showed that the natural frequency obtained here agrees well with that of Lee (2012), which was found through the frequency domain analysis. It was also shown that the approximation of heaving motion by a damped harmonic oscillation, which was regarded as suitable by most previous investigators, is not physically suitable for the reason that can be clearly shown through comparing the shape of MCFRs(Modulus of Complex Frequency Response). Furthermore, we found that although the previous approximations yield the damping ratio significantly different from our result the magnitude of natural frequency is not much different from our result.

• Bulletin of the Society of Naval Architects of Korea
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• v.14 no.3
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• pp.13-22
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• 1977

The hydrodynamic forces acting on a forced oscillating 2-dimensional cylinder on a free surface of a fluid of a finite depth are calculated by distributing singularities on the immersed body surface. And the Haskind-Newman relation in a fluid of a finite depth is derived. The wave exciting force of the cylinder to an oscillation is also calculated by using the above relation. The method is applied to a circular cylinder swaying in a water of finite depth, and then, to a rectangular cylinder heaving, swaying, and rolling. The results of above cases give a good agreement with those by earlier investigators such as Bai, Keil, and Yeung. Also, this method is applied to a Lewis form cylinder with a half beam-to-draft ratio of 1.0 and a sectional area coefficient of 0.941, and to a bulbous section cylinder which is hard to represent by a mapping function. The results reveal that the hydrodynamic forces in heave increase as the depth of a water decrease, but in sway or roll, the tendency of the hydrodynamic forces is difficult to say in a few words. The exciting force to heave for a bulbous section cylinder becomes zero at two frequencies. The added mass moment of inertia for roll is seemed to mainly depend on the sectional shape than the water depth.

• Journal of Ocean Engineering and Technology
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• v.31 no.1
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• pp.1-7
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• 2017

There are two wave modes induced by an oscillating body on the free surface of a two-layer fluid: the barotropic and baroclinic modes. To investigate the generated waves composed of two modes, a radiation problem involving a heaving rectangular body was solved in a numerical wave tank. A new artificial damping zone scheme was developed and applied in the frequency-domain analysis. The performance of this damping scheme was compared with given radiation boundary conditions for various conditions. The added mass and radiation damping coefficients for the heaving rectangular body were also calculated for various fluid-density ratios.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.4
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• pp.389-395
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• 2008

It is very well known that the natural frequency of an oscillating body on the free surface is determinable only after the added mass is given. However, it is hard to find analytical investigations in which actually the natural frequency is obtained. Difficulties arise from the fact that in order to determine the natural frequency we need to compute the added mass at least for a range of frequencies, and to solve an equation where the frequency is a variable. In this study, first, a formula is obtained for the added mass, and then an equation for finding the natural frequency is defined and solved by Newton's iteration. It is confirmed that the formula shows a good agreement with the results given by Ursell(1949), and the value of natural frequency is reduced by 21.5% compared to the pre-natural frequency, which is obtained without considering the effect of added mass.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.369-372
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• 2002

Under the assumption of potential flow, free-surface flows around a 2-dimensional hydrofoil are calculated by high-order spoctral/boundary-integral method. This method is one of the most efficient numerical methods by which the nonlinear interactions between hydrofoil and free-surface can be simulated in time-domain. Comparisons of the calculated free-surface profiles with other experimental results show relatively good agreements. As another example, free-surface flow generated by the heaving and translating hydrofoil is calculated and discussed.

• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.6
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• pp.85-91
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• 2011

This study aims at evaluating feasibility of Bottom ash-mixed Foam Cement Banking(BFCB) Method on the enhancement of soft soil, which is developed to reduce self-weight of banking by applying bottom ash and foam. to cement slurry. In order to measure the behavior of soil when BFCB layer was covered to soft ground, a testing equipment for mock-up test was fabricated and phased loads were applied up to measurement of yielding and ultimate strengths as well as movement of ground particles. In addition, these measured values such as settlement and heaving were compared with ones of surface-hardening method prevailing on soil improvement. As the result through mock-up test, BFCB showed lower values of ground deformation, while wider range of deformation was observed in compare to the other method. And settlement and heaving were measured lower, which implies the method developed is very effective to applicability of soft ground.

• Journal of the Korean Geotechnical Society
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• v.23 no.5
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• pp.43-51
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• 2007

Frost action may cause extensive damage to building, structures, roads, railways and utility lines in seasonal frost. The research about frost heave of natural ground has been considerably performed. In late years various structures have become complicated with the development of social infrastructure maintenance. Therefore countermeasure to frost heave becomes a matter of great importance from a new viewpoint. This study was aimed at catching natural ground frost heaving force quantitatively. Frost heaving forces on circular steel plates which were set on ground surface were measured in field test. The frost heaving forces arise at freezing front propagates to the structures through frozen soil layer. Besides, a full scale model of multi-anchored retaining wall was installed in field, and the freezing lines, frost heave pressure to act on a wall block, and so on were measured. Finally, the position and shape of frost line were estimated by using numerical simulation and a method to determine replacement range was suggested with soil properties and weather data.

• 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]).

• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.3
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• pp.281-290
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• 2012

Hydrodynamic analysis of a surface-piercing body with an open chamber was performed with incident regular waves and forced-heaving body motions. The floating body was simulated in the time domain using a 2D fully nonlinear numerical wave tank (NWT) technique based on potential theory. This paper focuses on the hydrodynamic behavior of the free surfaces inside the chamber for various input conditions, including a two-input system: both incident wave profiles and forced body velocities were implemented in order to calculate the maximum surface elevations for the respective inputs and evaluate their interactions. An appropriate equivalent linear or quadratic viscous damping coefficient, which was selected from experimental data, was employed on the free surface boundary inside the chamber to account for the viscous energy loss on the system. Then a comprehensive parametric study was performed to investigate the nonlinear behavior of the wave-body interaction.