• 대한조선학회논문집
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• 제46권2호
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• pp.155-164
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• 2009

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

• Structural Engineering and Mechanics
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• 제4권3호
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• pp.209-226
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• 1996

One of the major divisions in the mathematical modelling of a tubular structure is to include the effect of the transverse shear stress and rotary inertia in vibration of members. During the past three decades, problems of vibration of tubular structures have been considered by some authors, and special attention has been devoted to the Timoshenko theory. There have been considerable efforts, also, to apply the method of spectral analysis to vibration of a structure with rectangular section beams. The purpose of this paper is to compare the results of the spectrally formulated finite element analyses for the Timoshenko theory with those derived from the conventional finite element method for a tubular structure. The spectrally formulated finite element starts at the same starting point as the conventional finite element formulation. However, it works in the frequency domain. Using a computer program, the proposed formulation has been extended to derive the dynamic response of a tubular structure under an impact load.

• 대한수학회보
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• 제51권2호
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• pp.595-612
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• 2014

The spectral collocation method for a second order elliptic boundary value problem on a domain ${\Omega}$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] ${\times}$ [0, h], h > 0. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

• 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.

• 소음진동
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• 제6권1호
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• pp.83-88
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• 1996

The significance of spectral element method is that it can treat the mass and stiffness distribution exactly in contrast to the conventional finite element method, and therefore the dynamic behaviors within each spectral element can be obtained exactly. The present study provides the derivation of the spectral element of a curved beam, while the previous ones presented that of a straight structure. Further, in order to verify the derived spectral element, the natural frequencies of a ring by the spectral element method are compared with those by the analytical method and those by the FEM. From the verification, derived spectral element is admissible. And the dynamic behaviors of curved beam are simulated by using the derived spectral element of a curved beam.

• 한국소음진동공학회논문집
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• 제19권12호
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• pp.1347-1355
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• 2009

This paper demonstrates the validity of spectral element analysis for modeling the high-frequency dynamic behaviors of a beam with a surface-bonded piezoelectric wafer through a laboratory test. In the spectral element analysis, the high-frequency electro-mechanical interaction can be considered properly with relatively low computational cost compared to the finite element analysis. In the verification test, a cantilever beam with a surface-bonded piezoelectric wafer is forced to be in steady-state motion by exerting the harmonic driving voltage signal on the piezoelectric wafer. A laser scanning vibrometer is used to obtain the overall dynamic responses of the structure such as resonance frequencies, the associated mode shapes, and frequency response functions up to 20 kHz. Then, these dynamic responses from the test are compared to those computed by the spectral element analysis. A two-dimensional finite analysis is conducted to obtain the asymptotic solutions for the comparison purpose as well.

• 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.

• 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.

• 한국음향학회지
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• 제29권5호
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• pp.314-324
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• 2010

도파관 (waveguide structures)에 지지구조 또는 균열과 같은 국부적 불연속이 존재하는 경우, 도파관을 따라 전파되는 파동은 이러한 국부적 불연속으로 인해 반사가 발생한다. 빔과 같이 단면의 형상이 단순한 도파관에서는 국부적 불연속에 의한 저주파수 대역 반사 및 투과 특성을 스펙트럴요소(spectral element, SE)와 유한요소(finite element, FE)를 연결한 스펙트럴요소/유한요소법 (SE/FE method)으로 해석 할 수 있다. 그러나 도파관의 단면 형상이 복잡하거나 또는 고주파수 대역 해석에서는 빔 이론에 근거한 스펙트럴 요소를 이용하는 것이 부적합하다. 본 논문에서는 고주파수 대역 파동 반사 및 투과 특성 해석을 위해 스펙트럴요소 대신 스펙트럴수퍼요소 (spectral super element, SSE)를 도입하고, 이를 유한요소와 결합시킨 SSE/FE 방법을 제안한다. 이 방법은 도파관 모델링에 스펙트럴 수퍼요소를 이용하므로 레일과 같이 단면의 형상이 복잡한 도파관의 고주파수 대역 해석에 적합하다. 본 논문에서는 SSE/FE 해석에 필요한 반무한 SSE(semi-infinite spectral super element)에 대한 정식화를 먼저 수행하고, 이를 FE로 모델링한 국부적 불연속 구간과 연결하여 SSE/FE 모델을 구성하였다. 이 방법의 적용 예로써 단순 형상의 국부적 결함이 존재하는 철로 레일에 대하여 고주파수 대역 파동반사 및 투과계수를 계산하고 그 결과를 살펴보았다. 또한, 입사된 파워가 보존되어야 한다는 조건을 이용해 SSE/FE 방법의 수치오차를 추정하였다.

• 한국정보통신학회논문지
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• 제7권3호
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• pp.437-447
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• 2003

Circulant Matrix Factorization (CMF)는 covariance 행렬의 spectral factorization된 결과를 얻을 수 있다. 우리는 얻어진 결과를 가지고 일반적으로 잘 알려진 방법인 Schur algorithm을 이용하여 finite impulse response(FIR)와 infinite impulse response (IIR) lattice 필터를 설계하는 방법을 제안하였다. CMF는 기존에 많이 사용되는 root finding을 사용하지 않고 covariance polynomial로부터 minimum phase 특성을 가지는 polynomial을 얻는데 유용한 방법이다. 그리고 Schur algorithm은 toeplitz matrix를 빠르게 Cholesky factorization하기 위한 방법으로 이 방법을 이용하면 FIR/IIR lattice 필터의 계수를 쉽게 찾아낼 수 있다. 본 논문에서는 이러한 방법들을 이용하여 FIR과 IIR lattice 필터의 설계의 계산적인 예제를 제시했으며, 제안된 방법과 다른 기존에 제시되었던 방법 (polynomial root finding과 cepstral deconvolution)들과 성능을 비교 평가하였다.