• 한국자동차공학회논문집
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• 제17권4호
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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'.

• 대한조선학회지
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• 제24권3호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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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.

• 한국소음진동공학회논문집
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• 제15권8호
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• pp.968-974
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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.

• Steel and Composite Structures
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• 제29권6호
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• pp.785-802
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• 2018

In this paper, two different computational methods, called Rayleigh-Ritz and collocation are developed to estimate the ultimate strength of composite plates. Progressive damage behavior of moderately thick composite laminated plates is studied under in-plane compressive load and uniform lateral pressure. The formulations of both methods are based on the concept of the principle of minimum potential energy. First order shear deformation theory and the assumption of large deflections are used to develop the equilibrium equations of laminated plates. Therefore, Newton-Raphson technique will be used to solve the obtained system of nonlinear algebraic equations. In Rayleigh-Ritz method, two degradation models called complete and region degradation models are used to estimate the degradation zone around the failure location. In the second method, a new energy based collocation technique is introduced in which the domain of the plate is discretized into the Legendre-Gauss-Lobatto points. In this new method, in addition to the two previous models, the new model named node degradation model will also be used in which the material properties of the area just around the failed node are reduced. To predict the failure location, Hashin failure criteria have been used and the corresponding material properties of the failed zone are reduced instantaneously. Approximation of the displacement fields is performed by suitable harmonic functions in the Rayleigh-Ritz method and by Legendre basis functions (LBFs) in the second method. Finally, the results will be calculated and discussions will be conducted on the methods.

• 한국소음진동공학회논문집
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• 제18권1호
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• pp.123-130
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• 2008

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 contained water 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.

• Structural Engineering and Mechanics
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• 제4권5호
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• pp.541-552
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• 1996

This paper is concerned with the structural optimization problem of maximizing the compressive buckling load of orthotropic rectangular plates for a given volume of material. The optimality condition is first derived via variational calculus. It states that the thickness distribution is proportional to the strain energy density contrary to popular claims of constant strain energy density at the optimum. An engineers physical meaning of the optimality condition would be to make the average strain energy density with respect to the depth a constant. A double cosine thickness varying plate and a double sine thickness varying plate are then fine tuned in a one parameter optimization using the Rayleigh-Ritz method of analysis. Results for simply supported square plates indicate an increase of 89% in capacity for an orthotropic plate having 100% of its fibers in $0^{\circ}$ direction.