• 대한수학회보
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• 제58권1호
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2008년도 춘계종합학술대회 A
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• pp.677-680
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• 2008

본 논문에서는 다층매질 안에 위치한 안테나의 방사특성을 해석하고 있다. 접지면이 없는 유전체 기판에 인쇄된 안테나의 경우, 매질의 구성은 공기층을 포함하여 3층매질이 되며 이러한 3층매질의 Green 함수은 Sommerfeld적분식으로 표현되기 때문에 해석이 매우 복잡해진다. 그러나 안테나위 방사특성을 해석하는데 있어서는 적분식의 조건이 잘 일치한다면 Sadddle-point법을 이용하여 근사할 수 있다. 본 연구에서는 이와 같은 근사법을 적용하여 접지면이 없는 유전체 기판에 놓인 각종 안테나의 방사패턴 특성을 해석한다. 또한 기판으로 사용하는 유전체의 파라미터를 달리하여 방사특성을 검토한다.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.73-91
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• 2005

The application of Green's function in calculation of flow characteristics around submerged and floating bodies due to a regular wave is presented. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and all body motions are small. Two methods based on the boundary integral equation method (BIEM) are applied to solve associated problems. The first is a low order panel method with triangular flat patches and uniform distribution of velocity potential on each panel. The second method is a high order panel method in which the kernels of the integral equations are modified to make it nonsingular and amenable to solution by the Gaussian quadrature formula. The calculations are performed on a submerged sphere and some floating spheroids of different aspect ratios. The excellent level of agreement with the analytical solutions shows that the second method is more accurate and reliable.

• 한국해안해양공학회지
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• 제7권2호
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• pp.156-162
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• 1995

스커트의 유연성을 고려한 2차원 오일붐 모델에 대한 수치해법을 개발하였다. 본 수치모델에서는 부체를 강체로, 스커트를 장력이 걸려 있는 막으로, 스커트의 아래끝엔 집중질량이 놓여 있다고 가정하였다. 유동은 포텐셜이라고 가정하였으며 부체와 스커트의 연결부에서는 변위가 연속이라는 운동학적 조건을 그리고 스커트의 아래끝에는 집중질량에 대한 동력학적인 조건을 부가하였다. 수치해법은 선형포텐셜유동 이론에 근거한 Green 함수방법에 기초를 두고 있다. 스커트의 변형을 미리 알 수 없으므로 방사 포텐셜(radiation potential)과 부체의 변위 그러고 스커트의 변형을 동시에 구하는 방식을 택하였다. Green 정리를 적용하여 얻은 적분방정식과 부체의 운동방정식 그리고 스커트의 변형 관계식을 이산화하여 방사포텐셜과 부체의 변위 그리고 스커트의 변위에 대한 선형대수 방정식을 얻었다. 수치계산결과에 의하면 스커트의 유연성이 부체의 운동응답을 다소 줄일 수 있으며 부체의 공진체계를 바꿀 수 있음을 확인하였다. 그리고 오일붐의 운동응답특성에 영향을 주는 인자들 중에서 스커트의 길이와 집중질량을 파라미터로 하여 오일붐 모델의 운동응답특성을 비교해 보았다. 스커트가 유연한 경우와 스커트가 강체인 경우의 저주파수 극한해는 거의 일치하고 있어 수치해의 타당성을 간접적으로 확인할 수 있었다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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• pp.292-292
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• 2004

There are many difficulties to get the scattered field generated by obstacle which has arbitrary shape or irregular surface impedance by using analytic solution or numerical methods. In this study, we propose experimental method of acoustic scattering holography that can predict the far-field scattered field based on nearfield measurements. First of all, we express scattered field using K-H integral equation and compare the differences of which green's function we use. Also we consider analytic solution of scattered field by infinite cylinder to analysis for the errors due to apply cylinderical holography. So the errors which caused by holography due to frequency (ka) and microphone spacing are also analyzed by numerical simulation.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1317-1322
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• 2001

What changes in the eigen values and eigen functions are produced if the boundary surface S is no longer rigid but has a specific acoustic admittance which may vary from point to point on S. In this paper, changes in eigen values and eigen functions are derived by using Kirchhoff-Helmholtz integral equation. And acoustic potential energy, which is representative measure describing the physical quantity in cavity, is defined. Acoustic potential energy can be divided into primary one and secondary one. Primary one is the acoustic potential energy through unchanged eigen functions, and secondary one is through changed eigen functions. Using these two term, we can find the eigenvalue problem, which gives the control performance when the boundary condition is changed.

• 전자공학회논문지A
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• 제32A권12호
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• pp.55-63
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• 1995

By employing the concept of superimposing the induced current on partial scattere roled as a secondary source, matrix Green's function was derived. The procedure in the way of derivation presented here was based on the equivalence principle and the induction theorem and applying moment methods to the resulting electric field integral equation. As examples, the induced current on scatterers consisted of wire/plate conductor, the input impedance and gain patterns of corner reflector antenna were calculated. And computing times required for solving matrix equation were compared with those of conventional method.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제51권8호
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• pp.375-381
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• 2002

A rigorous analysis of a broad wall slot array is presented. The slot is longitudinal and offset from the center line in the rectangular waveguide. Pertinent integral equations are developed, taking into account finite wall thickness. The mothed of moment with entire basis function is used to solve a pair of coupled-integral equations, derived from the electromagnetic boundary conditions using modified Green's function, to find the tangential electric field on the upper and lower surfaces of the slot. Numerical results for resonant length and scattering parameters of the slots are Presented over a range of offset. Computed results are compared with experimental result.

• 산업기술연구
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• 제9권
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• pp.79-85
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• 1989

In this paper, the static limit of Helmhortz equation is discussed in the analysis of acoustic wave scattering in a waveguide. Boundary integral equation method is used to formulate the scattering process in the exerior of the scatterer and finite element method in the interior of the scatterer. And hybrid Ray-Mode Method is used the provide the Green's function of the waveguide. The proposed algorithm is applied to a sample poblem with arbitrary scatterer in a waveguide. The results are compared with those of Laplace's equation which is the governing equation in the static problems.

• Smart Structures and Systems
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• 제17권5호
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.