• Title/Summary/Keyword: Eigenvalue equation

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Improved Static Element Stiffness Matrix of Thin-Walled Beam-Column Elements (박벽보-기둥 요소의 개선된 정적 요소강성행렬)

  • Yun, Hee Taek;Kim, Nam Il;Kim, Moon Young;Gil, Heung Bae
    • Journal of Korean Society of Steel Construction
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    • v.14 no.4
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    • pp.509-518
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    • 2002
  • In order to perform the spatial buckling and static analysis of the nonsymmetric thin-walled beam-column element, improved exact static stiffness matrices were evaluated using equilibrium equation and force-deformation relationships. This numerical technique was obtained using a generalized linear eigenvalue problem, by introducing 14 displacement parameters and system of linear algebraic equations with complex matrices. Unlike the evaluation of dynamic stiffness matrices, some zero eigenvalues were included. Thus, displacement parameters related to these zero eigenvalues were assumed as polynomials, with their exact distributions determined using the identity condition. The exact displacement functions corresponding to three loadingcases for initial stress-resultants were then derived, by consistently combining zero and nonzero eigenvalues and corresponding eigenvectors. Finally, exact static stiffness matrices were determined by applying member force-displacement relationships to these displacement functions. The buckling loads and displacement of thin-walled beam were evaluated and compared with analytic solutions and results using ABAQUS' shell element or straight beam element.

Determination of Eigenvalues of Sinusoidally Tapered Members by Finite Element Method (유한요소법을 이용한 정현상으로 taper진 부재의 고유치 산정)

  • Lee, Soo-Gon;Kim, Soon-Chul
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.13 no.1
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    • pp.87-95
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    • 2000
  • The two eigenvalues (elastic critical load and natural frequency of lateral vibration) of sinusoidally tapered bats with simply supported ends were determined by the finite element method. For the convenience of structural engineers who are engaged in the structural design or vibration analysis of tapered beam-columns, eigenvalue coefficients were expressed by simple algebraic equations. The validity of each algebraic equation was confirmed by the value of unity for each correlation coefficient. The influence of axial thrust on the lateral vibration frequency was also investigated. For this purpose, the axial thrust was increased successively and the corresponding frequency was calculated. The approximate linear relationship between the axial thrust and the square of the frequency was confirmed lot each of the tapered members.

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Derivation of Exact Dynamic Stiffness Matrix of a Beam-Column Element on Elastic Foundation (균일하게 탄성지지된 보-기둥요소의 엄밀한 동적강성행렬 유도)

  • 김문영;윤희택;곽태영
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.3
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    • pp.463-469
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    • 2002
  • The governing equation and force-displacement rotations of a beam-column element on elastic foundation we derived based on variational approach of total potential energy. An exact static and dynamic 4×4 element stiffness matrix of the beam-column element is established via a generalized lineal-eigenvalue problem by introducing 4 displacement parameters and a system of linear algebraic equations with complex matrices. The structure stiffness matrix is established by the conventional direct stiffness method. In addition the F. E. procedure is presented by using Hermitian polynomials as shape function and evaluating the corresponding elastic and geometric stiffness and the mass matrix. In order to verify the efficiency and accuracy of the beam-column element using exact dynamic stiffness matrix, buckling loads and natural frequencies are calculated for the continuous beam structures and the results are compared with F E. solutions.

Free vibration analysis of large sag catenary with application to catenary jumper

  • Klaycham, Karun;Nguantud, Panisara;Athisakul, Chainarong;Chucheepsakul, Somchai
    • Ocean Systems Engineering
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    • v.10 no.1
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    • pp.67-86
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    • 2020
  • The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

Resonant Mode Analysis of Microwave Film Bulk Acoustic Wave Resonator using 3D Finite Element Method (3차원 유한 요소법을 이용한 초고주파 압전 박막 공진기의 공진 모드해석)

  • 정재호;송영민;이용현;이정희;고광식;최현철
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.12 no.1
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    • pp.18-26
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    • 2001
  • In this paper, the resonant characteristics and modes of the film bulk acoustic wave resonator (FBAR) used in 1~2 GHz frequency region are analyzed by it's input impedance which was calculated by three dimensional finite element method formulated as eigenvalue problem using electro-mechanical wave equation and boundary condition. It was extracted that the resonant and the spurious characteristics considering the effects of electrode area and shape variation and unsymmetry of upper and lower electrode. Those effects couldn't be analyzed by on dimensional analysis, e.g. Mason equivalent model. The simulation result was confirmed by comparing with the simulation data from Mason model analysis and the measured data of the ZnO FBAR fabricated using micro-machining technique. Also, through the simulation of the area variations of FBAR, it was obtained that the optimum ratio of length and thickness is 20:1 and the minimum ratio is 5:1 to operate thickness vibration mode.

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Parametric study of the wave dispersion in the hydro-elastic system consisting of an inhomogeneously prestressed hollow cylinder containing compressible inviscid fluid

  • Surkay D. Akbarov;Gurbaneli J. Veliyev
    • Coupled systems mechanics
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    • v.12 no.1
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    • pp.41-68
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    • 2023
  • The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discrete-analytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.

An integral quasi-3D computational model for the hygro-thermal wave propagation of imperfect FGM sandwich plates

  • Abdelouahed Tounsi;Saeed I. Tahir;Mohammed A. Al-Osta;Trinh Do-Van;Fouad Bourada;Abdelmoumen Anis Bousahla;Abdeldjebbar Tounsi
    • Computers and Concrete
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    • v.32 no.1
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    • pp.61-74
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    • 2023
  • This article investigates the wave propagation analysis of the imperfect functionally graded (FG) sandwich plates based on a novel simple four-variable integral quasi-3D higher-order shear deformation theory (HSDT). The thickness stretching effect is considered in the transverse displacement component. The presented formulation ensures a parabolic variation of the transverse shear stresses with zero-stresses at the top and the bottom surfaces without requiring any shear correction factors. The studied sandwich plates can be used in several sectors as areas of aircraft, construction, naval/marine, aerospace and wind energy systems, the sandwich structure is composed from three layers (two FG face sheets and isotropic core). The material properties in the FG faces sheet are computed according to a modified power law function with considering the porosity which may appear during the manufacturing process in the form of micro-voids in the layer body. The Hamilton principle is utilized to determine the four governing differential equations for wave propagation in FG plates which is reduced in terms of computation time and cost compared to the other conventional quasi-3D models. An eigenvalue equation is formulated for the analytical solution using a generalized displacements' solution form for wave propagation. The effects of porosity, temperature, moisture concentration, core thickness, and the material exponent on the plates' dispersion relations are examined by considering the thickness stretching influence.

Omnichannel's Perception Effect on Omnichannel Use and Customer-Brand Relationship (옴니채널의 지각된 편리성과 유용성이 옴니채널 사용과 소비자-브랜드 관계에 미치는 영향)

  • Yim, Duk-Soon;Han, Sang-Seol
    • Journal of Distribution Science
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    • v.14 no.7
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    • pp.83-90
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    • 2016
  • Purpose - This study focuses on new type distribution channel that named as Omnichannel. Omnichannel is developed from Multichannel which is used in many distribution channels to buy or selling goods. Omnichannel basically needs an Information and Communications Technologies(ICT) to use, so researcher conduct a Technology Acceptance Model(TAM) to research model. Customer-brand relationship was used as dependent variable to focus on the role of Omnichannel. Research design, data, and methodology - The subject of this study is customer who purchase goods or service through omnichannel. Based on the literature from the preceding research analysis of TAM and customer-brand relationship, this study was constructed by the reference to previous studies, final research model design for figure out casual relationship among perceived ease of use, perceived usefulness, omnichannel use and customer-brand relationship. From 2016 February 3 to March 17, questionnaire survey targeted customers who use online and offline channels. 273 questionnaire survey had conducted, then, 252 survey data were available for empirical analysis. Researcher provide descriptive statistics for checking generality. Cronbach's alpha value was used to check the reliability of data. Exploratory factor analysis was used for purification of values and eigenvalue checking. After EFA, Confirmatory factor analysis was used to prepare structural equation modeling with executing structural equation modeling for confirming hypothesis which developed by researcher. Results - The main results of this empirical study are as follows. First, omnichannel's perceived ease of use has positive significant effect on perceived usefulness(estimate: 0.579). Moreover, omnichannel's perceived ease of use and perceived usefulness has positive significant effect on omnichannel use(estimate: 0.325,0.648). Second, using omnichannel has positive significant effect on brand-customer relationship(estimate: 0.521). Every hypothesis adopted as researcher designed. This study found out the intermediate relationship between perceived ease of use and omnichannel use by investigating hypothesis. Conclusions - Base on the empirical result, this study confirmed that TAM theory perceived has relation with omnichannel. First, factors of TAM has positive effect on omnichannel use, so it highlights the important role of customer based interface and usefulness. Especially, perceived usefulness has high indirect influence on ease of use and use of omnichannel. It seems that when customers try to decide use or not use omnichannel, customers focus on percept benefits from omnichannel. Thus, a provider should applicate attractive price table, accurate product or service information and high switching cost strategy to emphasize the usefulness of omnichannel. Second, using omnichannel enhances the relationship between customers and brand, because there are more time and frequency to serve customers. It is important because good relationship between customers can increase the future's financial performance through word of mouse, positive brand image and loyalty to brand or company. Finally, despite of empirical result and implications, this study has limitations. First, there are only a few previous studies about omnicahnnel, so literature reviews are restricted. While set up the factors which can affect the use of omnichannel, next study should be considered with broader theories or models(ex: contingency theory). Second, omnichannel has developed from multichannel, so comparative analysis is needed between these methods because there is a possibility about different forte character of each distribution system on customer's consuming patterns.

Groundwater Flow Model for the Pollutant Transport in Subsurface Porous Media Theory and Modeling (지하다공질(地下多孔質) 매체(媒體)속에서의 오염물질이동(汚染物質移動) 해석(解析)을 위한 지하수(地下水)흐름 모형(模型))

  • Cho, Won Cheal
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.9 no.3
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    • pp.97-106
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    • 1989
  • This paper is on the modeling of two-dimensional groundwater flow, which is the first step of the development of Dynamic System Model for groundwater flow and pollutant transport in subsurface porous media. The particular features of the model are its versatility and flexibility to deal with as many real-world problems as possible. Points as well as distributed sources/sinks are included to represent recharges/pumping and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Sources/sinks strength over each element and node, hydraulic head at each Dirichlet boundary node and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution methed for the matrix equation approximating the partial differential equation of groundwater flow. The model also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. The groundwater flow model shall be combined with the model of pollutant transport in subsurface porous media. Then the combined model, with the applications of the Eigenvalue technique and the Dynamic system theory, shall be improved to the Dynamic System Model which can simulate the real groundwater flow and the pollutant transport accurately and effectively for the analyses and predictions.

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Buckling Analysis of Laminated Composite Plates Longitudinally Stiffened with U-Shaped Ribs (축방향 압축을 받는 폐단면리브로 보강된 복합적층판의 좌굴 해석연구)

  • Choi, Byung-Ho;Choi, Su-Young;Park, Sang-Kyun
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.3 no.1
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    • pp.29-34
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    • 2012
  • Even though the longitudinally stiffened laminated composite plates with closed section ribs should be an effective system for axially compressed members, the existing researches on the applications of closed-section ribs, especially for the laminated composite plates, are not sufficient. This study is aimed to examine the influence of the sectional stiffness of U-shaped ribs on the buckling modes and strengths of laminated composite plates. Applying the orthotropic plates with eight layers of the layup $[(0^{\circ})_4]_s$ and $[(0^{\circ}/90^{\circ})_2]_s$, 3-dimensional finite element models for the U-rib stiffened plates were setup by using ABAQUS and then a series of eigenvalue analyses were conducted. From the parametric studies, the minimum required ply thicknesses as well as the buckling strengths were presented for the analysis models. The buckling strengths were compared with the theoretical critical stress equation for simply supported plates based on the Classical laminated plate theory. This study will contribute to the future study for evaluating the minimum required stiffness and optimum design of U-rib stiffened plates.