• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.213-219
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• 2001

This paper deals with the free vibration of two identical circular plates coupled with a bounded fluid. An analytical method based on the [mite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. In the theory, it is assumed that the ideal fluid is filled in a rigid cylindrical container and the two plates are clamped along the plate edges. The proposed method is verified by the finite element analysis using commercial software with a good accuracy. Two transverse vibration modes, namely in-phase and out-of-phase, are observed alternately in the fluid-coupled system when the number of nodal circles increases for the fixed nodal diameter. The effect of gap between the plates on the fluid-coupled natural frequency is also investigated.

• Nuclear Engineering and Technology
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• 제41권3호
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• pp.355-364
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• 2009

Circular plates with holes are extensively used in mechanical components. The existence of a hole in a circular plate results in a significant change in the natural frequencies and mode shapes of the structure. Especially if the hole is located eccentrically, the vibration behavior of these structures is expected to deviate significantly from that of a plate with a concentric hole. In addition, if the plate is in contact with or submerged in fluid, the situation is more complex. Therefore, in this study, an analytical method to determine the modal characteristics of a plate submerged in fluid is developed based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method and is verified by the finite element analysis using a commercial program. Also, the relationship between parameter variations and vibration modes is investigated. These results can be used as guidance for the modal analysis and damage detection of a circular plate with a hole.

• 대한기계학회논문집
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• 제16권8호
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• pp.1451-1457
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• 1992

본 연구에서는 작업롤의 온도분포를 정상 상태에서 롤의 길이 방향만을 고려 한 경우에 대하여 구한 다음 Fouries 급수로 전개하여 이 온도분포에 따른 작업롤의 축대칭 3차원 열-탄성문제를 해석함으로서 롤의 크라운 양과 열응력을 구하여 이 결과 를 유한요소법에 의한 결과와 비교 검토 하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.603-608
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• 2001

This paper deals with the free vibration of two identical circular plates coupled with a bounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. In the theory, it is assumed that the ideal fluid is filled between the two plates and the plates are simply supported along the plate edges. The proposed method is verified by the finite element analysis using commercial software with an excellent accuracy. The effect of the plate boundary conditions on the fluid-coupled natural frequency is investigated.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.267-281
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• 2022

Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Chebyshev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA^® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical examples are given in support of our theoretical analysis.

• 한국해안해양공학회지
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• 제12권3호
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• pp.116-129
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• 2000

자유수면 아래 일정한 초기장력이 작용한 원형 박막이 수평으로 놓여있을 때 3차원 선형 유탄성 이론을 적용하여 파와 구조물의 상호작용문제를 고찰하였다. 속도포텐셜을 회절포텐셜과 방사포텐셜로 분리하여 각각의 경계치 문제를 푼다. 유체영열을 3개의 영역으로 나누어 각 영역에서 회절포텐셜과 방사포텐셜을 Bessel 함수의 전개식으로 표현하고 부족한 경계조건으로 생기는 미지수는 인접한 영역이 만나는 정합면에서 속도와 압력이 같다는 정합조건식을 적용하여 구해진다. 원형막의 크기와 잠긴 깊이 그리고 추기장력이 변함에 따라 원형 유연막 주위의 파의 형태가 달라짐을 볼 수 있었다. 즉, 적절히 설계된 몰수형 원형 유연막은 파 에너지를 집중시키는데 활용될 수 있다.

• 한국지진공학회논문집
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• 제1권4호
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• pp.59-68
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• 1997

터널 등과 같은 지하구조계를 유한요소법 등의 수치적 방법으로 해석할 경우 인위적인 경제에서 파의 반사가 발생하게 되어 실제 결과의 큰 차이를 발생시킨다. 따라서 동역학적 하중을 받는 지하구조계는 실질적인 반무한 구조계로 고려되어야 한다. 특히 지하구조계는 실제 다층구조로 구성되어 있으므로 이러한 다층문제를 고려할 수 있어야 한다. 이를 위해 본 연구에서는 외부영역 경제적문제로 해석하기 위한 동적 수치기본해를 개발하였다. 주파수영역의 정적인 경우에 대한 엄밀 적분해와 Bessel 함수의 점근식을 이용한 적분을 통해 축대치문제를 2차원 문제로 보다 쉽게 적용할 수 있도록 하였다. 이와 같이 개발된 동적 수치기본해를 경제 적분 방정식에 적용하여 해석한 결과와 기존 해석결과와의 비교를 통해 그 효율성을 입증하였다. 또한 다층지반내 지하구조물에 대해 지반매체의 각 물성 및 공동의 깊이에 따른 민감도분석을 수해하여 지하구조계의 동적 거동특성 파악의 적용성을 다루었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.69-81
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• 2015

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t > 0 heat is generated within the circular disk at a rate of g(r, z, t) $Btu/hr.ft^3$. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature $Q_3(r,t)$ and the upper surface ($Z={\infty}$) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.

• 한국해양공학회지
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• 제18권5호
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• pp.7-14
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• 2004

The interaction of incident manochromatic waves with an array of N surface-piercing porous dual cylindrical structures is investigated in the frame of three-dimensional linear potential theory. The dual cylindrical structure is camposed of concentric two cylinders. The exterior cylinder is porous and the interior cylinder is impermeable. The fluid domain is divided into N+1 regions i.e. a single exterior region and N interior regions. The diffraction potentials in each region representing the scattering of incident waves by an array of porous cylindrical structures are expressed by the Fourier Bessel series. The unknown coefficients in each region are determined by applying the porous boundary condition and continuity of mass flux at the matching boundary. It is found that an array of porous cylindrical structures reduces both the wave forces and the wave run-up, and shows the excellent performance of wave blocking. The results show that various types of breakwater exchanging seawater are prospective by controlling the porosity and the configuration of cylindrical structures.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.634-639
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• 2003

It has been studied the flow near a rotating disk with surface topography. The system Ekman number is assumed very small, i.e., $E[{\equiv}\frac{\nu}{{\Omega}^{\ast}L^{\ast2}}]<<1$ in which $L^{\ast}$ denotes a disk radius, ${\nu}$ kinematic viscosity of the fluid and ${\Omega}^{\ast}$ angular velocity of the basic state. Disk surface has a sinusoidal topographic variation along radial coordinate, i.e., $z={\delta}cos(2{\pi}{\omega}r)$, where ${\delta}$ and ${\omega}$ are, respectively, nondimensional amplitude and wave number of the disk surface. Analytic solutions, being useful over the parametric ranges of ${\delta}{\sim}O$( $E^{1/2}$ ) and ${\omega}{\leq}O$ ( $E^{1/2}$ ), are secured in a series-function form of Fourier-Bessel type. An asymptotic behavior, when $E{\rightarrow}0$, is clarified as : for a disk with surface roughness, in contrast to the case of a flat disk, the azimuthal velocity increases in magnitude, together with the thickening boundary layer. The radial velocity, however, decreases in magnitude as the amplitude of surface waviness increases. Consequently, the overall Ekman pumping at the edge of the boundary layer remains unchanged, maintaining the constant value equal to that of the flat disk.