• Title/Summary/Keyword: Spectral element method

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Study on the dynamic behaviors of curved beam structure using spectral element (스펙트럴 요소를 이용한 곡선 보 구조물의 동적거동 해석)

  • 이준근;이우식;박철희
    • Journal of KSNVE
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    • v.6 no.1
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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.

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The evaluation of applicability of spectral element method for the dynamic analysis of the spatial structures (대공간 구조 시스템의 동적 해석을 위한 스펙트럴 요소법의 적용성 평가)

  • Han, Sang-Eul;Lee, Sang-Ju;Cho, Jun-Yeong
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.789-794
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    • 2007
  • Recently, the necessity of efficient and exact method to analyze structures is increasing with the importance of the seismic analysis. But the finite element method used in many field do not give the exact solution unless the length of the element is very short enough to represent the deformation of the element. Because the amount of computer calculation increase with the increasing of the number of degree of freedoms, the finite element method for the exact dynamic analysis of structures would not be efficient. To solve these problems, spectral clement method combined spectral method using the principle of wave mechanics and finite element method for the analysis of discrete models is applied to evaluate the behavior of the spatial structures. As a result of analysis. it becomes clear that the spectral element method is faster and more exact than the finite clement method.

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Analysis of Simply Supported Rectangular Plate Using Spectral Finite Element Method (스펙트럴유한요소법을 이용한 네 변이 단순지지 된 직사각형평판의 진동해석)

  • Jo, Kyung-Lim;Hong, Suk-Yoon;Song, Ji-Hun;Kim, Dong-Jin
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11b
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    • pp.85-89
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    • 2005
  • For the analysis of a vibrating two dimensional structure such as the simply supported rectangular plate, Spectral Finite Element Method (SFEM) has been studied. Under the condition that two parallel edges are simply supported at least and the other two edges can be arbitrary, Spectral Finite Element has been developed. Using this element SFEM is applied to the vibrating rectangular plate which all edges are simply supported, and obtain the frequency response function in frequency domain and the dynamic response in time domain. To evaluate these results normal mode method and finite element method (FEM) are also accomplished and compared. It is seen that SFEM is more powerful analysis tool than FEM in high frequency range.

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Spectral Element modeling for the one-dimensional blood flow analysis (일차원 혈류해석을 위한 스펙트럴 요소 모델링)

  • Jang, In-Joon;Lee, U-Sik
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2008.04a
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    • pp.152-155
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    • 2008
  • The blood flow characteristics have been closely related to various cardiovascular diseases, it is very important to predict them accurate enough in an efficient way. Thus, this paper proposes a one-dimensional spectral element model for the blood flow through blood vessels. The spectral element model is formulated by using the variational method. The nonlinear terms in spectral element model are all treated as the pseudo-force and an iterative solution method is applied in the frequency domain.

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Spectral Element Vibration Analysis of the Pipeline Conveying Internal Flow (내부유동을 갖는 파이프 진동의 스펙트럴요소해석)

  • Oh, Hyuck-Jin;Kang, Kwan-Ho;Lee, U-Sik
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.2
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    • pp.294-301
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    • 2003
  • It is of often important to accurately predict the flow-induced vibration or dynamic instability of a pipeline conveying internal high speed flow in advance, which requires a very accurate solution method. In this study, first the dynamic equations for the axial and transverse vibrations of a pipeline are reduced from a set of pipe-dynamic equations derived in the previous study and then the spectral element model is formulated. The accuracy of the spectral element method (SEM) is then verified by comparing its results with the results obtained by finite element method (FEM). It is shown that the present spectral element model provides very accurate solutions by using an extremely small number of degrees-of-freedom when compared with FEM. The dynamics of a sample pipeline is investigated with varying the axial tension and the speed of internal flow.

Vibration Analysis of the Pipeline with Internal Unsteady Fluid Flow by Using Spectral Element Method (스펙트럴요소법을 이용한 내부 비정상류를 갖는 파이프에 대한 진동해석)

  • Seo, Bo-Sung;Cho, Joo-Yong;Lee, U-Sik
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.4 s.109
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    • pp.387-393
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    • 2006
  • In this paper, a spectral element model is developed for the uniform straight pipelines conveying internal unsteady fluid flow. The spectral element matrix is formulated by using the exact frequency-domain solutions of the pipe-dynamics equations. The spectral element dynamic analysis is then conducted to evaluate the accuracy of the present spectral element model and to investigate the vibration characteristics and internal fluid characteristics of an example pipeline system.

Vibration analysis of the plates subject to dynamic concentrated loads by using spectral element method (스펙트럴요소법을 이용한 동적집중하중을 받는 평판의 진동해석)

  • Lee, Joon-Keun;Lee, U-sik
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.3
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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.

NONCONFORMING SPECTRAL ELEMENT METHOD FOR ELASTICITY INTERFACE PROBLEMS

  • Kumar, N. Kishore
    • Journal of applied mathematics & informatics
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    • v.32 no.5_6
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    • pp.761-781
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    • 2014
  • An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

A natural frequency sensitivity-based stabilization in spectral stochastic finite element method for frequency response analysis

  • Lee, Gil-Yong;Jin, Seung-Seop;Park, Yong-Hwa
    • Structural Engineering and Mechanics
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    • v.75 no.3
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    • pp.311-325
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    • 2020
  • In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

Analysis of Vibration and Radiated Noise of Circular Cylindrical Shell in the Air Using Spectral Finite Element Method and Boundary Element Method (스펙트럴유한요소법과 경계요소법을 이용한 셸의 공기 중 진동 및 방사소음 해석)

  • Lee, Yung-Koo;Hong, Suk-Yoon;Song, Jee-Hun
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.11
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    • pp.1192-1201
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    • 2009
  • Analysis of the vibration characteristic for cylindrical shell is more complex than plates since the coupling effects are considered on three dimensions. Based on Love's equation, spectral finite element method(SFEM) is introduced to predict frequency response function of finite circular cylindrical shell in the air with simply supported - free boundary condition without simplifying the equation of motion. And for the radiated noise analysis of cylindrical shell, indirect boundary element method(BEM) is applied using out-of-plane displacements as an input from structural vibration analysis. Comparisons of the structural vibration results by the spectral finite element method and commercial code, NASTRAN(FEM based) are carried out. Likewise, for verification of radiated noise analysis results, commercial code, SYSNOISE(BEM based) are used.