• 소음진동
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• 제6권5호
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• pp.617-624
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• 1996

Finite Element Method(FEM) is one of the most popularly used method in analyzing the dynamic behaviors of structures. But unless the number of finite elements is large enough, the results from FEM are somewhat different form exact analytical solutions, especially at high frequency range. On the other hand, as the Spectral Element Method(SEM) deals directly with the governing equations of structures, the results from this method cannot but be exact regardless of any frequency range. However, despite two dimensional structures are more general, the SEM has been applied only to the analysis of one dimensional structures so far. In this paper, therefore, new methodologies are introduced to analyze the two dimensional plate structure using SEM. The results from this new method are compared with the exact analytical solutions by letting the two dimensional plate structure be one dimensional and showed the dynamic responses of two dimensional plate by including various waves propagated into x-direction.

• 대한기계학회논문집A
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• 제20권6호
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• pp.1773-1783
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• 1996

Finite element method(FEM) is one of the most popularly used method analyzing the dynamic behaviors of structures. But unless number of finite elements is large enough, the results from FEM some what different from exact analytical solutions, especially at high frequency range. On the other hand, as the spectral analysis method(SAM) deals directly with the governing equations of a structure, the results from this melthod cannot but be exact regardless of any frequency range. However, the SAM can be applied only to the case where a structure is subjected to the concentrated loads, despite a structure could be unddergone distributed loads more generally. In this paper, therefore, new spectral analysis algorithm is introduced through the spectral element method(SEM), so that it can be applied to anlystructures whether they are subjected to the concentrated loads or to the distributed loads. The results from this new SEM are compared with both the results from FEM and the exact analytical solutions. As expected, the results from new SEM algorithm are found to be almost identical to the exact analytical solutions while those from FEM are not agreed well with the exact analytical solutions as the mode number increases.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.45-48
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• 2008

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.

• Geomechanics and Engineering
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• 제1권2호
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• 대한기계학회논문집A
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• 제22권3호
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• pp.635-643
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• 1998

A spectral element method(SEM) is introduced for the vibration analysis of a rectangular plate subject to dynamic concentrated loads. First, the spectral plate element is derived from the relations between the forces and displacements along the two opposite edges of plate element. The global spectral matrix equation is then formulated by assembling two spectral plate elements so that the dynamic concentrated load is located at the connection nodal line between two plate elements. the concentrated load is then spatially Fourier transformed in the direction of the connection nodal line to transform the two-dimensional plate problem into a simplified equivalent one-dimensional beam-like problem. We may benefit from these procedures in that the spectral results from the present SEM is compared with the exact analytical solutions to prove the remarkable accuracy of the present SEM, while this is not true for conventional finite element solutions, especially at high frequency.

• 한국음향학회지
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• 제33권3호
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• pp.191-199
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• 2014

파이프, 평판과 같이 단면의 형상이 길이 방향으로 일정한 도파관 구조물을 따라 전파되는 진동의 반사 및 투과 특성은 여러 공학 분야에서 응용되는 중요한 주제이다. 도파관에 조인트 또는 균열 등의 국부적 불연속이 있는 경우, 스펙트럴 요소(spectral element)와 유한 요소(finite elment)를 결합한 SE/FE 방법이 주로 사용되고 있다. 그러나 이 방법은 보 이론에 기반한 스펙트럴 요소가 사용되므로 저주파수 대역 해석에 국한되는 단점이 있다. 고주파수 대역 해석에는 스펙트럴 수퍼 요소(spectral super element)와 유한 요소를 결합한 SSE/FE 방법이 제안되었으나 유한요소와 스펙트럼 요소의 연성으로 인해 많은 연산 시간이 요구된다. 이러한 문제점을 개선하고자, 본 연구에서는 국부적 불연속 구간의 단면이 일정한 경우에 대해 국부적 불연속 구간을 스펙트럴 수퍼 요소로 대체한 SSE/SSE 연성 해석을 시도하였다. 적용 모델로는 국부적 결함을 가진 레일의 파동 반사 및 투과, 그리고 주기적 보강재를 가진 평판의 진동전파에 대해 적용하였다. 결함을 가진 레일의 해석 예를 통해, 본 논문에서 사용한 SSE/SSE 방법과 기존의 SSE/FE 방법의 성능을 비교하였다. 보강재를 가진 평판의 예를 통해서는 반복 구조를 가진 도파관의 파동 전파 특성 해석에 SSE/SSE 방법이 유용함을 확인하였다.

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.551-561
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• 2017

As FGM (functionally graded material) bars which vibrate in axial or longitudinal direction have great potential for applications in diverse engineering fields, developing a reliable mathematical model that provides very reliable vibration and wave characteristics of a FGM axial bar, especially at high frequencies, has been an important research issue during last decades. Thus, as an extension of the previous works (Hong et al. 2014, Hong and Lee 2015) on three-layered FGM axial bars (hereafter called FGM bars), an enhanced spectral element model is proposed for a FGM bar model in which axial and radial displacements in the radial direction are treated more realistic by representing the inner FGM layer by multiple sub-layers. The accuracy and performance of the proposed enhanced spectral element model is evaluated by comparison with the solutions obtained by using the commercial finite element package ANSYS. The proposed enhanced spectral element model is also evaluated by comparison with the author's previous spectral element model. In addition, the effects of Poisson's ratio on the dynamics and wave characteristics in example FGM bars are numerically investigated.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.1066-1071
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• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2008년도 춘계학술대회 논문집
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• pp.831-834
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• 2008

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model with variational method for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is the verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2009년도 춘계학술대회 논문집
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• pp.1092-1096
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• 2009

스펙트럴요소법 (SEM)은 계산되는 행렬의 크기를 줄여 비용과 시간을 절감하면서 구조물의 동역학적 특성을 정확하게 알 수 있는 해석법이다. 본 연구에서는 변분법을 이용하여 양단에서 축 방향으로 장력을 받으며 같은 방향으로 이동하는 현을 스펙트럴요소법 (SEM) 을 이용하여 해석하였다. 또 결과의 정확도를 비교하기 위하여 스펙트럴요소법 (SEM)과 유한요소법 (FEM)과 엄밀해를 비교하였다. 그리고 현이 움직이는 속도와 양단에 작용하는 장력이 진동특성, 파동특성 그리고 정, 동적 안정성에 어떤 영향을 미치는지 연구하였다.