• Transactions of the Korean Society of Automotive Engineers
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• v.17 no.4
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• pp.108-117
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• 2009

Leissa claimed in his article that the Rayleigh method is not the same as the Ritz method for determining natural frequencies and its corresponding mode shapes and contended that Rayleigh's name should not be attached to the method. The present article examines the methods in viewpoint of admissible functions and its minimization process, and of the historical developments. It concludes that Leissa's assertion is relevant, although Rayleigh did apply a conceptual theory systematized from the Lagrange method, and given 38 years earlier than Ritz's 'masterly exposition of theory'.

• Nuclear Engineering and Technology
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• v.54 no.9
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• pp.3540-3550
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• 2022

The supercritical carbon dioxide (S-CO₂) Brayton cycle is an important energy conversion technology for the fourth generation of nuclear energy. Since the printed circuit heat exchanger (PCHE) used in the S-CO₂ Brayton cycle has narrow channels, Rayleigh-Bénard (RB) convection is likely to exist in the tiny channels. However, there are very few studies on RB convection in supercritical fluids. Current research on RB convection mainly focuses on conventional fluids such as water and air that meet the Boussinesq assumption. It is necessary to study non-Boussinesq fluids. PRB convection refers to RB convection that is affected by horizontal incoming flow. In this paper, the computational fluid dynamics simulation method is used to study the PRB convection phenomenon of non-Boussinesq fluid-supercritical carbon dioxide. The result shows that the inlet Reynolds number (Re) of the horizontal incoming flow significantly affects the PRB convection. When the inlet Re remains unchanged, with the increase of Rayleigh number (Ra), the steady-state convective pattern of the fluid layer is shown in order: horizontal flow, local traveling wave, traveling wave convection. If Ra remains unchanged, as the inlet Re increases, three convection patterns of traveling wave convection, local traveling wave, and horizontal flow will appear in sequence. To characterize the relationship between traveling wave convection and horizontal incoming flow, this paper proposes the relationship between critical Reynolds number and relative Rayleigh number (r).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.47-55
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• 2003

This paper Presents active control algorithm using probability density function of structural energy. It is assumed that the structural energy under excitation has Rayleigh probability distribution. This assumption is based on the fact that Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of control force is determined by Lyapunov controller design method. Proposed control algorithm shows much reduction of peak responses under seismic excitation compared to LQR controller, and it can consider control force limit in the controller design. Also, chattering problem which sometimes occurs in Lyapunov controller can be avoided.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.3
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• pp.35-42
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• 1987

For the analysis of natural vibrations of a rectangular stiffened plate with inner cutouts, an application of the Rayleigh-Ritz method is investigated. In construction of the trial function for the Rayleigh quotient, only the outer boundary conditions are satisfied with combination of Euler beam functions. As to the modeling of stiffened plates for the energy calculations, a lumping stiffener-effects method and the orthotropic plate analogy are considered for the purpose of comparison. Some numerical results obtained by the Rayleigh-Ritz method are compared with results by experiments and the finite element method. The following are major conclusions; (1) With the lumping stiffener-effects modeling the Rayleigh-Ritz method gives good results of both natural frequencies and mode shapes. The orthotropic plate analogy in cases of regularly stiffened plates is of restrictive use i.e. acceptable for a small cutout. (2) The natural frequency of a stiffened plate with inner cutouts between stiffeners is higher than that of without cutouts and increase as the hole area ratio increases as long as there are no discontinuous stiffeners due to the cutout.

• Water for future
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• v.22 no.4
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• pp.441-451
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• 1989

Using the wave data by typhoons LEE, VERA, THELMA which gave great damages in the Korean penisula, the significant waves based on zero-up & down crossing and Tucker-Draper method are compared with those from the wave energy spectrum. And the histograms of individual waves obtained from zero-up crossing method are presented and compared with the Rayleigh, Weibull, Gluhovski, Ibrageemov and Goda distributions, and also the Chi-square goodness of fit test is applied to each theoretical distributions. It is shown that the significant wave heights by zero-up crossing method are very well agreed to those by energy spectrum method. The wave heights are found to well follow the Rayleigh and Goda distributions by the Chi-square test.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.295-300
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• 2005

An analytical method for the hydroelastic vibration of a vessel composed of an upper annular plate and a lower circular plate is developed by the Rayleigh-Ritz method. The two plates are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.42-47
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• 2007

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh.Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the water bounded by rigid walls is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid.coupled natural frequencies comparing with the finite element analysis result.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.258-262
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• 2004

An analytical method for the free vibration of two circular plates coupled with a fluid was developed by the Rayleigh-Ritz method. The two plates with unequal thickness and diameter are clamped along the cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the circular plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives a eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis result.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.906-910
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• 2004

An analytical method for the free vibration of two annular plates coupled with water was developed by the Rayleigh-Ritz method. The two plates with unequal thickness are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the annular plates Is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Korean Chemical Engineering Research
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• v.57 no.1
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• pp.142-147
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• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.