• Journal of Ship and Ocean Technology
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• v.1 no.2
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• pp.11-18
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• 1997

The leading edge of a low-drag super-cavitating foil has been made to be thick enough by using a point drag which is supposed to be a linear model of the Kirchhoff lamina. In the present paper, the relation between the point drag and the Kirchhoff lamina is made clear by analyzing the cavity drag of both models and the leading edge radius of the point drag model and the lamina thickness of Kirchhoff\`s profile K. The matched asymptotic expansion is effectively made use of in designing a practical super-cavitating fool which is not only of low drag but also structurally sound. Also it has a distinct leading edge cavity separation point. The cavity foil shapes of trans-cavitating propeller blade sections designed by present method are shown.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.81-86
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• 1989

Herein the surge-heave-pitch motion of a ship has been analyzed within the framework of linear potential theory. The ship is assumed slender weakly moored along the centerline of a rectangular harbor with constant depth and straight coastline. The method of matched asymptotic expansion is us-ed to obtain the leading-order solution. The ship and harbor responses to incident long waves can be re-presented in terms of Green's function, which is the solution of the Helmholtz equation satisfying necessary boundary conditions. Numerical results clearly indicate the importance of the surge motion.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.56-63
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• 1985

Methods for evaluating the added masses of square and hexagonal structures with fluid gap are presented. For a sufficiently small fluid gap, an analytical expression for the added mass is found using the method of matched asymptotic expansion. Experimental data and numerical results using finite element method are also obtained for various sizes of fluid gap. It is shown that added masses increase in inverse proportion to the fluid gap as it becomes smaller. Experimental data, theoretical and numerical results are in good agreement.

• Steel and Composite Structures
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• v.43 no.2
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• pp.241-256
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• 2022

In this article, an analytical procedure is presented for static analysis of composite cylinders with the geometrically nonlinear behavior, and non-uniform thickness profiles under different loading conditions by considering moderately large deformation. The composite cylinder includes two inner and outer isotropic layers and one honeycomb core layer with adjustable Poisson's ratio. The Mirsky-Herman theory in conjunction with the von-Karman nonlinear theory is employed to extract the governing equations which are a system of nonlinear differential equations with variable coefficients. The governing equations are solved analytically using the matched asymptotic expansion (MAE) method of the perturbation technique and the effects of moderately large deformations are studied. The presented method obtains the results with fast convergence and high accuracy even in the regions near the boundaries. Highlights: • An analytical procedure based on the matched asymptotic expansion method is proposed for the static nonlinear analysis of composite cylindrical shells with a honeycomb core layer and non-uniform thickness. • The effect of moderately large deformation has been considered in the kinematic relations by assuming the nonlinear von Karman theory. • By conducting a parametric study, the effect of the honeycomb structure on the results is studied. • By adjusting the Poisson ratio, the effect of auxetic behavior on the nonlinear results is investigated.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.1
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• pp.28-35
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• 2002

In cavity flow, the rectangular step generates so strong sound that many researchers have investigated method to suppress the nois during interaction between vortical flow and rectangular forward step. In this study the flow noise from the vortex motion in two-dimentional low Mach number flow past a forward step with various chamfering angle is calculated numerically. Inviscid incompressible discrete vortex model and matched asymptotic expansion(MAE) theory are applied to obtain the inner flow field and the outer noise field. Both source acoustic pressure and sound intensity are obtained with various chamfering height, chamfering angle and initial vortex position. The pressure amplitude is most suppressed when the chamfering angle is between $15^{\circ}C$ and $30^{\circC}$ at the chamfering length of 30% of the step height.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.3
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• pp.286-293
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• 1996

This paper established the analytical model of sea surface oscilation of simple type fishing port with vertical wave absorbor. This model is composed by MAEM(Matched Asymptotic Expansion Method) for wave amplification in fishing port and EEM(Eigen - function Expansion Method) for wave absorbing characteristics against vertical perforated plates. Dimensionless porosity by adopting Darcy's law was introduced to evaluate wave absorbing characteristics of the perforated structure. Using the model, the efficiency of the vertical perforated plates was studied for fishing port tranqulity with number of plates, array method and plate intervals. Optimal design and arrangement of perforated plates can be applied to develop multipurpose fishing ports and villages.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.1
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• pp.72-80
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• 1996

Two analytical solutions for oscillations in a rectangular harbour are presented. In this paper, the correct solution is obtained by use of matched asymptotic expansion method, which was first derived by Mei(1989). The other solution derived from eigenfunction expansion method is also presented, in which more accurate numerical integration is employed. In order to check the solutions, amplification factors inside the harbor are calculated and plotted by both analytical methods and numerical boundary integral equation method.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.4
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• pp.3-13
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• 1989

In recent towing tank experiments, it has been observed that a ship moving near the critical speed $\sqrt{gh}$(g=gravitational acceleration, h=water depth) radiates solitons upstream in an almost periodic manner. As a ,consequence, the ship experiences considerable changes in resistance, trim and sinkage, or better known as squat. Mei and Choi(1987) developed a nonlinear theory for a slender ship by using the method of matched asymptotic expansions. For a certain class of channel width and ship slenderness, they found that the waves generated can be described by an inhomogeneous Korteweg-de Vries(KdV) equation. The leading-order solution properly predicts solitons propagating upstream, but it fails to render three-dimensional waves in the wake. In this paper a new approach has been made by choosing a different class of channel width and ship slenderness. The wave equation in the farfield turns out to be a homogeneous Kadomtsev-Petviashvili(KP) equation, which predicts solitons upstream and three-dimensional waves in the wake. Numerical results for the wave resistance, sinkage and trim reflect the experimentally identified phenomena.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.89-99
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• 2001

In the present paper, Helmholtz resonator, which is widely used as a sound-amplification device, is applied to the development of seawater-exchanging breakwater. The incident waves can induce a large response in the resonator when incident wave frequency is close to one of natural modes of the resonator. Largely amplified potential energy due to the resonance supplies clean seawater into the harbor side throughout the channel. Flow supplied by the resonator circulates the seawater of harbor and helps to improve water quality. Within the framework of linear potential theory, matched asymptotic expansion method is employed to analyze the wave responses in a resonator. The semi-circular shape of the resonator has been chosen as an analytic model for mathematical simplicity. The wave responses of both single and arrays of Helmholtz resonator are investi¬gated. To validate an analytic solution, model test is conducted at 2-dimensional wave tanle Wave hcights in the resonator and velocity at the channel are measured for the state of valve-on and valve-off.