• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.439-445
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• 2003

In the recent years, functionally graded materials(FGM) have gained considerable attention in the high temperature environment applications. In the present work, study of the deflection and vibration of a functionally graded rectangular plate made of Ti-6Al-4V and Al$_2$O$_3$ is presented. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution Effects of volume fractions(power law exponent) on the deflection and natural frequency of FGM plate is studied. Also effects of temperature is studied. Wavier Solution is used to analyzed the FGM plate.

• Journal of the Korean Society for Railway
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• v.6 no.3
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• pp.163-168
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• 2003

This paper considers the sound radiation characteristics of a cracked rectangular vibrating plate, varying the orientation angle of a line crack. The vibration response of the cracked vibrating plate is obtained by using ANSYS, the acoustic theory based on the lumped parameter model is used to calculate radiated sound power. The radiated sound powers are computed with varying the orientation angle of the crack: i.e, 0$^{\circ}$, 45$^{\circ}$, and 90$^{\circ}$. It is found that characteristics of the radiated sound power are very closely related to the crack orientation, vibration mode and crack location.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.28 no.11
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• pp.93-99
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• 2014

The method of moments is applied to numerically compute the electrostatic capacitance of a parallel-plate rectangular capacitor of finite area. Each plate is discretized into 900 patches per unit area to ensure a high accuracy of computation. To further enhance computational results, the impedance matrix elements are additionally evaluated in the case that the observation patch is located above or below the source patch in the vertical direction. To examine the fringing effect at the edges of the capacitor, the normalized capacitances are computed as a function of separation distance. After these results have been verified by Palmer's formula, this method is extended to the computation of capacitances between two different size plates.

• Journal of the Korean Institute of Rural Architecture
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• v.16 no.4
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• pp.59-66
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• 2014

This paper deals with vibration of plates with concentrated mass on elastic foundation. The object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Free vibration analysis that tapered thick plate in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on pasternak foundation. The Winkler parameter is varied with 10, $10^2$, $10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0. And the Concentrated Mass is applied as P1, Pc, P2 respectively.

• Structural Engineering and Mechanics
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• v.21 no.6
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• pp.699-712
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• 2005

The response of a plate-column system having five-degree-of-freedom supported by an elastic foundation and subjected to static lateral load, harmonic ground motion and earthquake motion is studied. Two Winkler foundation models are assumed: a conventional model which supports compression and tension and a tensionless model which supports compression only. The governing equations of the problem are obtained, solved numerically and the results are presented in figures to demonstrate the behavior of the system for various values of the system parameters comparatively for the conventional and the tensionless Winkler foundation models.

• Steel and Composite Structures
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• v.28 no.6
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• pp.655-670
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• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• Journal of the Korean Society of Industry Convergence
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• v.5 no.1
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• pp.45-52
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• 2002

In this study, an exact solution of governing differential equation for the bending problem of partially loaded orthotropic rectangular plates is presented and also its computer program is developed. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could he subjected to uniform, partially uniform, and line loads. The solution for the deflection of rectangular plate is expressed as a Levy type single Fourier series and the loads arc expressed as a corresponding series. The advantage of the solution is that it overcomes the limitations of the previous Navier's and Levy's methods (limitation of boundary condition and loading conditions of plate), it is easy to program on a computer and it becomes fast to solve the bending problem with computer program. Calculations are presented for isotropic and orthotropic plates with different loading and boundary conditions. Comparisons are made for the isotropic plate with various boundary conditions between the result of this paper and the result of Navier, Levy and Szilard. The deflections were in excellent agreement.

• Steel and Composite Structures
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• v.20 no.3
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• pp.513-543
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• 2016

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

• Journal of the Korean Society of Visualization
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• v.17 no.2
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• pp.58-66
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• 2019

This study investigated heat transfer and flow characteristics of a sweeping jet issued from a rectangular nozzle with a thin plate. A thin vertical aluminum plate was attached on outlet of fluidic oscillator to increase velocity of central area with Coanda effect and enhance heat transfer performance. From visualization and PIV experiments, sweeping jet with a thin plate has larger velocity distribution in center region than that of the normal sweeping jet while oscillating frequency is similar as the normal one. Thermographic phosphor thermometry method was used to visualize the temperature field and Nu distribution of plate with impinging sweeping jet with thin plate. Four Reynolds numbers and three jet-to-wall distances were selected as parameters. It is found that heat transfer performance in the low jet-to-wall spacing was enhanced as the cooled area was expanded. However, when the jet-to-wall spacing became greater than 8dh, heat transfer performance became similar due to reduced impinging velocity.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.1
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• pp.56-63
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• 2004

Exact solutions are presented for the free vibration and buckling of rectangular plates haying two opposite edges ( x=0 and a) simply supported and the other two ( y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress $\sigma$$_{x}$=- $N_{0}$[1-a(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement ( w) to vary as sin(m$\pi$x/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients. for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and byields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters a= 0, 0.5, 1, 1.5. 2, for which a=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for a= 0, 1, 2 obtained by the method of integration of the differential equation (a=0) or the method of energy (a=1, 2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b =0.5, 1, 2 when a=2, with load intensities $N_{0}$ / $N_{cr}$ =0, 0.5, 0.8, 0.95, 1. where $N_{cr}$ is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes ate also shown.shown.