• 제목/요약/키워드: Fourier Bessel series

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유체로 채워진 강체 실린더에 잠긴 원판의 고유진동 해석 (Free Vibration Analysis of a Circular Plate Submerged in a Fluid-filled Rigid Cylinder)

  • 정경훈;최순;정명조
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2003년도 춘계학술대회논문집
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    • pp.921-925
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    • 2003
  • An analytical method for the free vibration of single circular plate submerged in a fluid-filled rigid cylindrical vessel was developed by the Rayleigh-Ritz method based on the Fourier-Bessel series expansion. It was assumed that the plate is clamped at an offcentered location of the cylinder, and the non-viscous incompressible fluid contained in the cylinder is bisected by the plate. It was found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis results. The offcentered distance effect on the natural frequencies was also observed.

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갇힌 유체로 연성된 두 원판의 고유진동 해석 (Natural Vibration Analysis of Two Circular Plates Coupled with Bounded Fluid)

  • 정명조;정경훈
    • 한국소음진동공학회논문집
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    • 제11권9호
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    • pp.439-453
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    • 2001
  • This study 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 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 program 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 frequencies sis also investigated.

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Natural vibration characteristics of a clamped circular plate in contact with fluid

  • Jhung, Myung Jo;Choi, Young Hwan;Kim, Hho Jung;Jeong, Kyeong Hoon
    • Structural Engineering and Mechanics
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    • 제21권2호
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    • pp.169-184
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    • 2005
  • This study deals with the free vibration of a circular plate in contact with a fluid; submerged in fluid, beneath fluid or on fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. The normalized natural frequencies are obtained in order to estimate the relative added mass effect of fluid on each vibration mode of the plate. Also, the location of plate coupled with fluid and the cases of free and bounded fluid surface are studied for the effect on the vibration characteristics.

Fluid Bounding Effect on Natural Frequencies of Fluid-Coupled Circular Plates

  • Jhung, Myung-Jo;Park, Young-Hwan;Jeong, Kyeong-Hoon
    • Journal of Mechanical Science and Technology
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    • 제17권9호
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    • pp.1297-1315
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    • 2003
  • This study deals with the free vibration of two identical circular plates coupled with a bounded or unbounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy The case of bounded or unbounded fluid is studied for the effect on the vibration characteristics of two circular plates. Also, the effect of gap between the plates on the fluid-coupled natural frequencies is investigated.

AN EFFICIENT AND STABLE ALGORITHM FOR NUMERICAL EVALUATION OF HANKEL TRANSFORMS

  • Singh, Om P.;Singh, Vineet K.;Pandey, Rajesh K.
    • Journal of applied mathematics & informatics
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    • 제28권5_6호
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    • pp.1055-1071
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    • 2010
  • Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.

A Three-Dimensional Calculation of the Reactor Impedance for Planar-Type Cylindrical Inductively Coupled Plasma Sources

  • Kwon, Deuk-Chul;Yoon, Nam-Sik
    • Applied Science and Convergence Technology
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    • 제24권6호
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    • pp.237-241
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    • 2015
  • The reactor impedance is calculated for a planar-type cylindrical inductively coupled plasma source by expanding the electromagnetic fields into their Fourier-Bessel series forms including the three-dimensional shape of the antenna. The mode excitation method is utilized to determine the electromagnetic fields based on a Poynting theorem-like relationship. From the obtained electromagnetic fields, a tractable form of the reactor impedance is obtained as a function of various plasma and geometrical parameters and applied to carry out a parametric study.

Exact solution for asymmetric transient thermal and mechanical stresses in FGM hollow cylinders with heat source

  • Jabbari, M.;Vaghari, A.R.;Bahtui, A.;Eslami, M.R.
    • Structural Engineering and Mechanics
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    • 제29권5호
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    • pp.551-565
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    • 2008
  • Transient solution of asymmetric mechanical and thermal stresses for hollow cylinders made of functionally graded material is presented. Temperature distribution, as function of radial and circumferential directions and time, is analytically obtained, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler equation and complex Fourier series.

동심 원통형 용기내에서의 플라즈마 회전 (Plasma Rotation in Plasma Centrifuge with an Annular Gap)

  • Hue Yeon Lee;Sang Hee Hong
    • Nuclear Engineering and Technology
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    • 제14권2호
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    • pp.78-85
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    • 1982
  • 정상상태의 플라즈마의 이론적 해석을 통해서 플라즈마의 회전과 동위원소 분리기로서의 적합성을 분석하였다. 이 장치는 두개의 동심원통형 전극과 이들 사이의 원통형 공동으로 구성되었으며, 축 방향으로 외부자장이 걸려 있다. 두 전극사이에 생성되는 전류밀도는 전기방전의 형태로 동위원소 혼합물로부터 플라즈마를 생성하고, 자장과 교차되어 발생하는 Lorentz힘에 의해서 플라즈마를 회전시킨다. 자기 유체역학 방정식을 바탕으로 이 계를 설명하는 두개의 연립편미분방정식을 얻었고, 네 경계조건을 사용하여 Fourier-Bessel로 표현된 이차원적 전류밀도와 속도분포의 해를 얻었다. 실제로 가능한 조건하에서 플라즈마 회전속도는 $10^4$m/sec 정도에 달하고, Hartmann수가 커짐에 따라 플라즈마회전 속도도 커진다. 이 같은 고속의 회전속도를 감안해 볼때 플라즈마 원심분리기는 기계적으로 회전되는 가스원심분리기보다 훨씬 높은 효율을 가지게 될 것이다.

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Free Vibration Analysis of Perforated Plate Submerged in Fluid

  • Jhung, Myung-Jo;Jo, Jong-Chull;Jeong, Kyeong-Hoon
    • Journal of Mechanical Science and Technology
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    • 제20권9호
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    • pp.1323-1338
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    • 2006
  • An analytical method to estimate the coupled frequencies of the circular plate submerged in fluid is developed using the finite Fourier-Bessel series expansion and Rayleigh-Ritz method. To verify the validity of the analytical method developed, finite element method is used and the frequency comparisons between them are found to be in good agreement. For the perforated plate submerged in fluid, it is almost impossible to develop a finite element model due to the necessity of the fine meshing of the plate and the fluid at the same time. This necessitates the use of solid plate with equivalent material properties. Unfortunately the effective elastic constants suggested by the ASME code are found to be not valid for the modal analysis. Therefore in this study the equivalent material properties of perforated plate are suggested by performing several finite element analyses with respect to the ligament efficiencies.