• 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'.

• 한국소음진동공학회논문집
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• 제21권5호
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• pp.430-436
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• 2011

The purpose of this study is to analyze the vibration and sound generation characteristics of the sandwich panel. Two thick panels were assumed to be separated by a compliant viscoelastic core. The transverse vibration induced by an external impact was analyzed using the Rayleigh-Ritz method. For applying arbitrary boundary condition of the panels, the edges were assumed to be supported by the translational and rotational springs. The beam functions were used as the trial functions. The effect of the boundary condition and viscoelastic core on the resulting vibration characteristics was investigated. The radiated sound power was analyzed using the proposed numerical model and the Rayleigh integral. The dynamic properties of the core and the mass-stiffness-mass resonance frequency had significant influence on the impact sound.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.869-872
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• 2005

The purpose of this study is on the prediction of the acoustic performance of the lined rectangular plenum chamber which can be used in the HVAC systems. The lined plenum chamber is modeled as a piston driven rectangular tube without mean flow and the acoustic pressure in the lined chamber is obtained by superposing the three dimensional pressure due to each of uniformly and harmonically fluctuating pistons. The arbitrary locations of inlet/outlet ports as well as the acoustic higher order modes generated at the area discontinuities of the port chamber interfaces are taken into consideration. The four-pole parameters can be derived by imposing the proper boundary conditions on each inlet and outlet ports. The lining material on the internal wall is assumed to be a bulk-reacting model. A single weak variation statement which satisfies the fluctuating rigid piston condition and the pressure and displacement continuity condition at the interface between the lining material and the airway was developed. The set of cosine functions were used as the admissible function when applying the Rayleigh-Ritz method. Computed results are compared with those predicted by using the locally-reacting lining material and experimental results, respectively. There are a good agreement shown between the results by the Rayleigh-Ritz method and the experiment results. The derived transfer matrices can be easily combined with other four-pole parameters of different types of mufflers for the calculation of the whole system performance.

• 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.

• 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.

• 대한조선학회논문집
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• 제30권1호
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• pp.125-133
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• 1993

중간구속조건을 갖는 보 및 보-기둥의 진동에 관한 기존연구들의 대부분은 Euler 보이론틀에서 다루었다. 세장비가 작은 경우 또는 세장비가 큰 경우일지라도 고차진동에 대해서는 Timoshenko 이론들에 의한 해석이 요구되나, Timoshenko 보 및 보-기둥에 관한 연구사례는 적은 편이다. 본 연구에서는 Timoshenko 보-기둥에 대해서 양단경계조건을 병진스프링 회전스프링 구속으로, 중간구속조건을 임의 갯수의 집중질량 병진스프링 회전스프링으로 일반화하여 정식화한 다음 엄밀해법을 제시하고, 아울러 엄밀해법의 연산부담이 매우 큰 점을 고려하여 적정한 Rayleigh-Ritz 해석에 대해서도 검토하였다. Rayleigh-Ritz 해석에 있어서는 우선 기준계의 고유함수를 이용하는 방법이 고려될 수 있으나 이 경우에도 Euler 보이론과는 달라서 연산부담이 역시 큰 편이다. 따라서 기준계의 고유함수와 같은 성질을 갖는 다항식을 도출하고 이를 이용하는 Rayleigh-Ritz 해석의 유용성에 관해 검토했다. 한편, 본 연구의 대상계와 같은 복합계에 대해서는 최적설계관점에서 설계변수변경에 따른 재해석문제 또한 중요한 과제임을 고려하여, 특성다항식 이용 Rayleigh-Ritz 방법에 기초하여 계산되는 동특성 1차 감도의 유용성도 검토되었다. 수치 계산예를 통해 전기 특성 다항식을 이용한 Rayleigh-Ritz 해석이 정확도면에서 엄밀해와 부합성이 양호하고, 계산 효율은 매우 높음이 확인되었다.

• 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.