• Title/Summary/Keyword: Eigenvalue Analysis

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Vibration Analysis of Thick Hyperboloidal Shells of Revolution from a Three-Dimensional Analysis (두꺼운 축대칭 쌍곡형 쉘의 3차원 진동해석)

  • 심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.4
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    • pp.419-429
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    • 2003
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells are formulated, and 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 hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

Prediction of Preliminary Pogo Instability on a Space Launch Vehicle (예비설계 단계 우주발사체의 공급/추진계 모델을 이용한 포고 불안정성 예측)

  • Lee, SangGu;Sim, JiSoo;Shin, SangJoon;Seo, Yongjun;Ann, Sungjun;Song, Huiseong;Kim, Youdan
    • Journal of the Korean Society of Propulsion Engineers
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    • v.21 no.6
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    • pp.64-72
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    • 2017
  • The longitudinal dynamic instability which can occur in the fueling process of a space launch vehicle is called pogo. It is caused by coupling between the fuselage and propulsion system and they would be formed as a closed-loop system. so that the amplitude of the response may increase or decrease. In this paper, a mathematical model which is applicable to the systematic pogo analysis of a general launch vehicle is developed for an example of space shuttle. The formulations are composed of the linearized second-order differential equation for the propulsion system, and of the pressure, weight displacement, and generalized displacement. Those are important parameters for pogo analysis, are derived through eigenvalue analysis. By the formulation suggested in this paper, it is expected that mathematical modeling method of the pogo system can be obtained and systematic pogo stability analysis for any launch vehicle will be enabled.

Analyses of Structural Performances for Reinforced Concrete Middle-Rise Residential Building under Construction (중층 규모 철근콘크리트 주거형 건물의 시공 중 구조성능 분석)

  • Ko, Jun-Young;Kim, Jae-Yo
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.23 no.5
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    • pp.96-103
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    • 2019
  • Middle-rise reinforced concrete residential buildings account for a large portion of the Korea, and structural performance analysis are needed for problems that could occur during the construction of such buildings. Thus, a middle-rise reinforced concrete residential building with 25 stories are selected as a sample model for structural performance analysis. The structural analyses are performed by dividing a sample model into the construction stage models of the 5th, 10th, 15th, 20th and 25th floors and the completion stage models with the design completed. For the comparisons of structural performances, Eigenvalue analysis results and lateral-load-resisting capabilities and structural design performances of structural members are analyzed. As a result of analyses, it was confirmed that both the construction and completion stage do not exceed KBC criteria limits at the lateral displacement and story drift ratio, and structural design performances of structural members confirm structural safety in all components except for some members of the wall. Therefore, it was concluded that if structural stability is obtained during the completion stage of a middle-rise reinforced concrete residential building, structural stability is secured under construction.

Application of a Fictitious Axial Force Factor to Determine Elastic and Inelastic Effective Lengths for Column Members of Steel Frames (강프레임 기둥 부재의 탄성 및 비탄성 유효좌굴길이 산정을 위한 가상축력계수의 적용)

  • Choi, Dong Ho;Yoo, Hoon;Lee, Yoon Seok
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.2A
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    • pp.81-92
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    • 2010
  • In design of steel frames, it is generally believed that elastic system buckling analysis cannot predict real behaviors of structures, while inelastic system buckling analysis can give informative buckling behaviors of individual members considering inelastic material behavior. However, the use of Euler buckling equation with these system buckling analyses have the inherent problem that the methods evaluate unexpectedly large effective lengths of members having relatively small axial forces. This paper proposes a new method of obtaining elastic and inelastic effective lengths of all members in steel frames. Considering a fictitious axial force factor for each story of frames, the proposed method determines the effective lengths using the inelastic stiffness reduction factor and the iterative eigenvalue analysis. In order to verify the validity of the proposed method, the effective lengths of example frames by the proposed method were compared to those of previously established methods. As a result, the proposed method gives reasonable effective lengths of all members in steel frames. The effect of inelastic material behavior on the effective lengths of members was also discussed.

Three-Dimensional Vibration Analysis of Solid and Hollow Hemispheres Having Varying Thickness (변두께를 갖는 두꺼운 반구형 쉘과 반구헝체의 3차원적 진동해석)

  • 심현주;장경호;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.2
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    • pp.197-206
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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 solid and hollow hemispherical shells of revolution of arbitrary wall thickness having arbitrary constraints on their boundaries. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components μ/sub Φ/, μ/sub z/, and μ/sub θ/ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the Φ and z directions. Potential (strain) and kinetic energies of the hemispherical shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for solid and hollow hemispheres with linear thickness variation. The effect on frequencies of a small axial conical hole is also discussed. Comparisons are made for the frequencies of completely free, thick hemispherical shells with uniform thickness from the present 3-D Ritz solutions and other 3-D finite element ones.

A Symbolic Manipulation Computer Program for Structural Analysis (구조해석(構造解析)을 위한 Symbolic Manipulation Program)

  • Shim, Jae Soo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.3 no.4
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    • pp.95-107
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    • 1983
  • The general purpose programs are in their fixed algorithm and theory of mechanics which can not be altered without painful program modifications. Users are usually guided by user's manual for data input. The several symbolic manipulation programs for structural analysis are introduced recently. These programs allow users to include a wide class of solution algorithm and to specify, by means of some symbolic manipulation, a combination of analytical steps to suit a particular problem. As they can solve a single domain problem, a large computer is usually needed. The scope of this study is to develop an efficient symbolic manipulation program with space beam element, plate bending element and eigen value routines. The incorporated Substructure capability and generation capability of finite element characteristic arrays (e.g., stiffness matrix, mass matrix) enables users to analyse multidomain problem with small computer. The program consists of modulized independent processors, each having its own specific function and is easily modified, eliminated and added. The processors are efficiently handling data by the Data base approach which is the concept of integrated program network(IPN).

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Three-Dimensional Vibration Analysis of Deep, Nonlinearly Tapered Rods and Beams with Circular Cross-Section (원형단면의 깊은 비선형 테이퍼 봉과 보의 3차원 진동해석)

  • 심현주;강재훈
    • 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.

Study on the Design and Usability factor analysis of Web Multimedia Contents (웹 멀티미디어 컨텐츠의 디자인과 유용성분석에 대한 연구)

  • Koh, Eun-Young;Shin, Soon-Ho
    • Archives of design research
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    • v.17 no.4
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    • pp.69-78
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    • 2004
  • This thesis is designed to investigate the relationship of Web Multimedia design. Web sites are needed to approach the lot of ways that increase the user intuitive lay over communicating information nowadays. In the digital era of today, multimedia is composed of such various elements as text, image, sound, animation, video. The method of the thesis is a research questions as this follow. First, the structuring element of the web site type was classified by a form and the contents in the web site. These types in this classified web site are HTML, flash and mixed type. Second, to study this thesis, we made up pose a questionnaire to students in the university as th method of random sampling. The goal of this survey is that user is how to understand about the web multimedia design. Results of analysis may be summarized as follows: 1) It was the image design in the NIKE web site that there would be evaluated the best design effected by flash, and it is finding that the NIDE web site will need more supporting Information, Interactive design through this studies. 2) It was information that there would be evaluated good design effect by text and image in SAMSUNG web site. Based on HTML, SAMSUNG need supporting motion image design by this studies. In conclusion, this thesis suggests that the each web medias should be constructed by the different web design component, according to information, Interactive, image design of web site.

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Three Dimensional Vibration Analysis of Thick, Circular and Annular Plates with Nonlinear Thickness Variation (비선형 두께 변분을 갖는 두꺼운 원형판과 환형판의 3차원적 진동해석)

  • 장승환;심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.17 no.2
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    • pp.119-129
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    • 2004
  • A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and 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 plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.

Free Vibration Analysis of Horizontally Curved I-Girder Bridges using the Finite Element Method (유한요소법을 이용한 수평곡선 I형교의 자유진동해석)

  • Yoon, Ki Yong;Kang, Young Jong
    • Journal of Korean Society of Steel Construction
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    • v.10 no.1 s.34
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    • pp.47-61
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    • 1998
  • The behavior of horizontally curved I-girder bridges is complex because the flexural and torsional behavior of curved girders are coupled due to their initial curvature. Also, the behavior is affected by cross beams. To investigate the behavior of horizontally curved I-girder bridges, it is necessary to consider curved girders with cross beams. In order to perform free vibration analyses of horizontally curved I-girder bridges, a finite element formulation is presented here and a finite element analysis program is developed. The formulation that is presented here consists of curved and straight beam elements, including the warping degree of freedom. Based on the theory of thin-walled curved beams, the shape functions of the curved beam elements are derived from homogeneous solutions of the static equilibrium equations. Third-order hermits polynomials are used to form the shape functions of the straight beam elements. In the finite element analysis program, global stiffness and mass matrix are composed, based on the Cartesian coordinate system. The Gupta method is used to efficiently solve the eigenvalue problem. Comparing the results of several examples here with those of previous studies, the formulation presented is verified. The validity of the program developed is shown by comparing results with those analyzed by the shell element.

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