• Title/Summary/Keyword: Plate equation

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Computation of V-I characteristics in wire-plate electrostatic precipitators (선대 평판 전기 집진기의 V-I 특성 계산)

  • Kim, Kill-Sin;Shim, Jae-Hak;Ko, Kwang-Cheol;Kang, Hyung-Boo
    • Proceedings of the KIEE Conference
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    • 1997.07e
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    • pp.1675-1677
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    • 1997
  • In this paper we study the voltage-current characteristics inside the wire-plate precipitators by numerically solving the Poisson's equation and current continuity equation. The effects of a wire size, wire-wire spacing, wire-plate spacing and effective mobility have been considered.

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Press Molding Conditions for the Preparation of Bipolar Plate in Epoxy/Carbon System (에폭시/탄소계 Bipolar Plate 제조를 위한 Press Molding 조건 연구)

  • Choi, Bumchoul;Lee, Jaeyoung;Lee, Jijung;Lee, Hongki
    • 한국신재생에너지학회:학술대회논문집
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    • 2010.06a
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    • pp.144.2-144.2
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    • 2010
  • Bipolar plate는 고분자 전해질 연료전지(PEMFC)에서 핵심 부품 중의 하나이고, 전해질 막이나 촉매 등에 비해서는 상대적으로 쉽게 접근할 수 있기 때문에 많은 연구가 수행되고 있다. Bipolar plate를 제조하는 기술은 크게 금속을 프레스 가공하는 방법, graphite 판을 직접 밀링하는 방법 및 고분자/카본계의 press molding 법 등 3가지로 분류되며, 본 연구에서는 3번째 방법에 의해서 bipolar plate를 대량 생산하는 방법에 대해 연구하였다. 고분자 매트릭스는 에폭시계 수지를 사용하였고, 카본계 재료는 graphite 분말과 carbon nanotube를 사용하였다. 이들 재료들을 일정한 비율로 혼합한 후 differential scanning calorimetry(DSC)를 사용하여 열분석 하였고, 그 결과를 Kissinger equation에 대입하여 경화반응 속도론을 연구하였다. 또한, 경화된 에폭시/탄소 복합재료의 전기전도도, 유리전이온도, 표면에너지 특성 등을 분석하였다.

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Measurement of Near Field Sound Intensity and Loss Factor Using Plate Intensity Measurement (평판 인텐시티 측정을 통한 근접장 음향 인텐시티와 손실 계수 측정법)

  • 김용조;김양한
    • Journal of KSNVE
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    • v.7 no.4
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    • pp.589-596
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    • 1997
  • A energy equation for a thin plate and surrounding fluid is derived. The equation essentially determines the relation between internal loss of thin plate, energy of acoustic radiation, and structure intensity. We attempted to use this relation to measure internal loss of thin plate. The significance of this approach is that internal loss at any point of a thin plate can be measured. The quality of this measure is dicated by the accuracy of associated measurement systems such as structure and acoustic intensity measurements. A strain gauge bridge system has been developed to measure structure intensity of thin plate. Its performance is tested by experiments.

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Heat Transfer of an Evaporating Liquid on a Horizontal Plate

  • Joo, Sang-Woo;Park, Min-Soo;Kim, Min-Suk
    • Journal of Mechanical Science and Technology
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    • v.19 no.8
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    • pp.1649-1661
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    • 2005
  • We consider. a horizontal static liquid layer on a planar solid boundary. The layer is evaporating when the plate is heated. Vapor recoil and thermo-capillary are discussed along with the effect of mass loss and vapor convection due to evaporating liquid and non-equilibrium thermodynamic effects. These coupled systems of equations are reduced to a single evolution equation for the local thickness of the liquid layer by using a long-wave asymptotics. The partial differential equation is solved numerically.

On the Penetration Phenomena for Thin and Multi-Layered Finite Thickness Plates by a Long Rod Penetrator (긴 관통자에 의한 유한박판 및 적층표적재의 관통현상 연구)

  • 이창현;홍성인
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.7
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    • pp.1759-1772
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    • 1994
  • In this study, we re-examined the Tate's modified Bernoulli equation to study penetration phenomena for long rod projectile into single or multi-layered finite thickness plates. We used the force equlibrium equation at mushroomed nose/target interface instead of conventional pressure equation at the stagnation point. In our penetration model, we considered the velocity dependent $R_t$ value for semi-infinite target and considered only the back face effect for finite target. To compensate for $R_t$ value according to target's thickness and back face effect, we used the spherical cavity expansion theory for semi-infinite plate and used the cylindrical cavity expansion theory for finite plate. Also we developed the experimental technique using make screen to measure the penetration duration time at each layered plate. In 3-layered laminated RHA/mild steel/ A1 7039 plate, we observed that spall had occured around the back face of A1 7039 plate by the stress wave interaction. Through the comparison between theoretical and experimental data including Lambert's results, we conform that our study has good confidences.

A Method to Determine Optimum Viscoelastic Layer Thickness of Sandwich Plate for Maximum Modal Damping (샌드위치 평판의 모드 감쇠 최대화를 위한 점탄성층 두께 결정법)

  • Nam, Dae-Ho;Shin, Yun-Ho;Kim, Kwang-Joon
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.7 s.112
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    • pp.690-696
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    • 2006
  • Thickness of damping layer in sandwich plate needs to be optimized in order to make modal loss factor of the sandwich plate maximum. Since previous studies were interested in noise reductions over high frequency range, the modal properties were derived based on simply supported boundaries. This conventional formula is approximately applicable to other boundary conditions over high frequency range only. The purpose of this study is to propose a method to determine optimum damping layer thickness of sandwich plate for maximum modal damping in low frequency range when the boundary condition is not a simple support. The conventional RKU equation based on simply supported boundary is modified to reflect other boundary conditions and the modified RKU equation is subsequently applied to determine the optimum damping layer thickness for arbitrary conditions. In order to reflect frequency-dependent characteristics of elastic modulus of the damping layer, an iteration method is proposed in determining the modal properties. Test results on sandwich plates for optimum damping layer thickness are compared with predictions by the proposed method and conventional method.

Isogeometric Collocation Method to solve the strong form equation of UI-RM Plate Theory

  • Katili, Irwan;Aristio, Ricky;Setyanto, Samuel Budhi
    • Structural Engineering and Mechanics
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    • v.76 no.4
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    • pp.435-449
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    • 2020
  • This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.

Dynamic response of functionally graded annular/circular plate in contact with bounded fluid under harmonic load

  • Yousefzadeh, Sh.;Jafari, A.A.;Mohammadzadeh, A.;Najafi, M.
    • Structural Engineering and Mechanics
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    • v.65 no.5
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    • pp.523-533
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    • 2018
  • In this study, the dynamic response of a functionally graded material (FGM) circular plate in contact with incompressible fluid under the harmonic load is investigated. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT). The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. A new set of admissible functions, which satisfy both geometrical and natural boundary conditions, are developed for the free vibration analysis of moderately thick circular plate. The Chebyshev-Ritz Method is employed together with this set of admissible functions to determine the vibrational behaviors. The modal superposition approach is used to determine the dynamic response of the plate exposed to harmonic loading. Numerical results of the force vibrations and the effects of the different geometrical parameters on the dynamic response of the plate are investigated. Finally, the results of this research in the limit case are compared and validated with the results of other researches and finite element model (FEM).

Stability of multi-step flexural-shear plates with varying cross-section

  • Xu, J.Y.;Li, Q.S.
    • Structural Engineering and Mechanics
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    • v.16 no.5
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    • pp.597-612
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    • 2003
  • In this paper, multi-story buildings with shear-wall structures and with narrow rectangular plane configuration are modeled as a multi-step flexural-shear plate with varying cross-section for buckling analysis. The governing differential equation of such a plate is established. Using appropriate transformations, the equation is reduced to analytically solvable equations by selecting suitable expressions of the distribution of stiffness. The exact solutions for buckling of such a one-step flexural-shear plate with variable stiffness are derived for several cases. A new exact approach that combines the transfer matrix method and closed from solution of one-step flexural-shear plate with continuously varying stiffness is presented for stability analysis of multi-step non-uniform flexural-shear plate. A numerical example shows that the present methods are easy to implement and efficient.

Free In-plane Vibration of a Clamped Circular Plate (고정된 원형 플레이트의 평면내 자유진동)

  • Park, Chan-Il
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.836-839
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    • 2005
  • The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

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