• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.1
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• pp.23-34
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• 1998

A dynamic fluid-structure-soil interaction analysis method is developed to investigate the effects of translational and/or rocking motions on the seismic response of flexible rectangular liquid storage tanks founded on the deformable ground. The governing equation for the dynamics of 3-D rectangular tanks subjected to the translational and/or rocking motion is abtained by applying Rayleigh-Ritz method. The dynamic stiffness matrices of a rigid rectangular foundation resting on the surface of a stratum overlaid bedrock are calculated by hyperelement method. The seismic responses of 3-D flexible tank model founded on the deformable ground is calculated by combining the governing equation for the fluid-tank system with the dynamic stiffness matrix of th rigid surface foundation.

• Composites Research
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• v.33 no.6
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• pp.377-382
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• 2020

The free vibration characteristics of corrugated laminated composite plates with axial stiffeners is investigated using the Rayleigh-Ritz method. The plate is stiffened by beams with open cross-section area. The equivalent homogenization model is used for the corrugated laminated composite plates. This homogenization model is treated a corrugated plate as an orthotropic plate that has different material properties in two perpendicular directions. The motion of equivalent plate is represented on the basis of the first order shear deformation theory (FSDT) to account for the effect of rotary inertia and transverse shear deformation. Stiffeners are considered as discrete elements to predict the local vibration mode to be generated by the presence of stiffeners. To validate the proposed analytical approach, natural frequencies and vibration mode shapes from the analytical method are compared with those from the FEA by ANSYS.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.116-125
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• 1995

In ship and of offshore structures, there exist many local panels of various shapes having many kinds of attachments reducible to damped spring-mass systems. For the vibration analysis of panels, analytical methods such as Rayleight-Ritz method or the assumed mode method can be efficiently applied. There have been many studies on the vibration analysis of rectangular panels using the analytical methods but relatively few for arbitrary shape panels. An efficient formulation based on the assumed mode method is presented for the vibration analysis of an arbitrary quadrangular plate having concentrated masses, supporting springs such as pillars and spring-mass systems. In the formulation, the natural coordinate system is used for the efficient treatment of an arbitrary quadrangular shape. Through some numerical calculations, accuracy and efficiency of the presented method are shown.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.1
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• pp.63-73
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• 1987

This study is a part of the research on the coupled vibration of train wheel with the stepped thickness and rail. The research was conducted for the purpose of examining the dynamic characteristics of train wheel at the running state and preventing the vibrations of the high speed railway. The stress at the boundary surface of web and rim, .sigma.$_{c}$, was analyzed in consideration of the uniform In-plane compressive stress depending on the conditions of rolling and the In-plane compressive stress depending on the rotation of train wheel. Then the equation of transverse vibration of the annular plate with the stepped thickness was analyzed by Rayleigh-Ritz's method. As a result of study, it was known that the rotational speed increase the natural frequency slightly and the acceleration level highly while the reaction force between train wheel and rail decrease the natural frequency linearly and the critical buckling is generated at n=1.

• Journal of Korean Society of Steel Construction
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• v.18 no.5
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• pp.615-624
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• 2006

In the present paper, an extended composite beam theory that has no restriction on the lay-up and can account for Poisson effect which is significant for composite materials is proposed. Buckling equations for composite thin-walled members which are subjected to axial compression are derived based on the composite beam theory. In order to check the validity of the derived buckling equations, the results of experiments on the flexural-torsional buckling of vinylester/E-glass and polyester/E-glass pultruded T-section members and the flexural buckling of vinylester/E-glass pultruded H-section members are used as numerical examples. The comparison of the analytical results to the experimental and FE analysis results reveals that the proposed buckling equations predict the buckling loads of pultruded members conservatively by about 7%.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.7
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• pp.622-628
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• 2011

The purpose of this study was to analyze the vibro-acoustic characteristics of a stiffened rectangular plate at high frequencies. The stiffeners attached along the plate surface were assumed to have rotational and translational stiffness and inertia. The harmonic response of the stiffened plate were predicted and compared using the Rayleigh-Ritz method with two different trial functions - polynomial and beam functions. The variation of the spatially averaged mean square velocity and the modal characteristics with the number of stiffeners were obtained. The use of the beam function ensured fast convergence which was essential for analyzing the high frequency vibration responses. Using the calculated modal characteristics and the Rayleigh-integral, the radiated sound power was predicted, and the effects of stiffeners were investigated. The proposed model can be applied to study optimal layout of stiffeners for minimal noise generation of the stiffened structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.3
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• pp.251-260
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• 2003

A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.140-148
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• 1992

The free vibration problem of symmetrically laminated composite rectangular plates is formulated based on anisotropic thick plate theory including the effects of shear deformation and rotary inertia. Considering the difficulty of obtaining closed-form solutions, Rayleigh-Ritz analysis using polynomials having the property of Timoshenko beam functions as trial functions is adopted. The boundary conditions elastically restrained against rotation are accomodated as well as classical boundary conditions. From the results of numerical studies, the validity of the present method is verified. And it is also found that the adoption of thick plate theory for the vibration analysis of laminated composite plates is essential because of the relatively large shear deformation effect, and that the convergence of the Rayleigh quotient to the stationary value is less rapid in anisotropic composite plates than that in the orthotropic ones due to more complicated mode shapes of the former.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.04a
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• pp.67-72
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• 1995

본 연구에서는 섬유강화 복합재료로 구성된 항공기 날개를 외팔보 형태 구조물로 모델링하고 동특성 해석을 위해 횡전단변형 이론과 고전 적층판 이론을 적용, Rayleigh-Ritz 방법에 의한 진동해석을 수행한뒤 진동 발생시 효과적으로 제어할 수 있는 방법을 제시하고 시뮬레이션을 통하여 동특성 향상을 정량적으로 제시하였다. 진동을 제어하기 위한 방법으로서 수동적, 능동적 방법을 모두 사용하고 있는데, (보다 자세한 사항은 참고문헌[12] 참조) 본 연구에서는 TMD(Tuned Mass Damper)를 사용하지 않고 복합소재 구조물의 성질을 이용한 탄성배열설계(Structural Tailoring)로 수동적 의미의 면진효과를 거둘 수 있게 하였다. 능동 제어의 경우 되먹임(feedback) 제어기를 이용, 이산(discret) 작동기(actuator)를 통하여 외팔보의 휨 및 비틀림 모우드를 함께 제어하여 효과적인 제어기를 설계하였다.

• The Journal of the Acoustical Society of Korea
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• v.34 no.3
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• pp.219-226
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• 2015

In this paper, derivation of the STL (Sound Transmission Loss) of a square plate installed in an impedance tube is discussed using an analytic method. Coupled motion of the plate vibration and acoustic field is considered. Vibration of the plate and pressure field inside the tube are expressed in terms of the infinite series of modal functions. Under the plane wave assumption, it is shown that consideration of the first few modes yields sufficiently accurate results. When the boundary of the plate is clamped, vibration mode is assumed as a multiplication of the beam modes corresponding to the crosswise directions. The natural frequencies of the clamped plate are calculated using the Rayleigh-Ritz method. It is found that the STL shows a dip at the lowest natural frequency of the plate, and increases as the frequency decreases below the natural frequency. Comparison of the result in this paper with the STL obtained by measurements and FE computations in the reference shows an excellent agreement.