• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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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.

• Structural Engineering and Mechanics
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• v.21 no.2
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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.

• Journal of Mechanical Science and Technology
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• v.17 no.9
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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.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.15-21
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• 2007

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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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.

• Applied Science and Convergence Technology
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• v.24 no.6
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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.

• Structural Engineering and Mechanics
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• v.29 no.5
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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.

• Nuclear Engineering and Technology
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• v.14 no.2
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• pp.78-85
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• 1982

The steady-state rotation of plasma centrifuge is theoretically analyzed to understand the physics of rotating plasmas and its feasibility for isotope separation. The centrifuge system under consideration consists of an annular gap between coaxial cylindrical anode and cathode in the presence of an externally-applied axial magnetic field. A problem for coupled partial differential equations describing centrifuge fields is formulated on the basis of the magnetohydrodynamic equations. Two-dimensional solutions are found analytically in the form of Fourier-Bessel series. The current density and velocity distributions are discussed in terms of the Hartmann number and the geometrical parameter of the system. At typical conditions, rotational speeds of the plasma up to the order of 10$^4$m/sec are achievable, and increase either with increasing Hartmann number, or with increasing ratio of the axial length to the inner radius of the cylinder. In view of much higher speeds of rotation which can be achieved in plasma centrifuge, it is expected that its efficiency is superior to mechanically driven gas centrifuges.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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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.