• 한국소음진동공학회논문집
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• 제15권12호
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• pp.1398-1407
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• 2005

This paper is concerned with the vibration analysis of a rectangular plate with a rectangular hole. Even though there have been many methods developed for the addressed problem, they suffer from computational time. In this paper, we developed a new methodology called Independent Coordinate Coupling Method which can couple two independent coordinate systems for the entire plate domain and the hole. By matching the deflection condition imposed on the expressions, the relationship between the global axes and the local axes is derived. This formula is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the proposed method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.593-599
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• 2005

This paper is concerned with the vibration analysis of a rectangular plate with a rectangular hole. Even though there have been many methods developed for the addressed problem, they suffer from computational time. In this paper, we developed a new methodology called Independent Coordinate Coupling Method which can couple two independent coordinate systems for the entire plate domain and the hole. By matching the deflection condition imposed on the expressions, the relationship between the global axes and the local axes is derived. This formula is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Steel and Composite Structures
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• 제17권1호
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• pp.69-81
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• 2014

The novelty of this paper is the use of trigonometric four variable plate theory for free vibration analysis of laminated rectangular plate supporting a localized patch mass. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The Hamilton's Principle, using trigonometric shear deformation theory, is applied to simply support rectangular plates. Numerical examples are presented to show the effects of geometrical parameters such as aspect ratio of the plate, size and location of the patch mass on natural frequencies of laminated composite plates. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of laminated rectangular plate supporting a localized patch mass.

• 한국소음진동공학회논문집
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• 제21권4호
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• pp.374-383
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• 2011

A numerical model based on a mode method coupling beams and a rectangular plate is proposed to estimate radiation characteristics of an edge-clamped rectangular plate. The radiation efficiency and radiation power in the audio frequency range including the critical frequency can be predicted. The proposed model is rather simple and straightforward and gives reliable results comparing to the previous studies. The estimated radiation characteristics are compared to those of the pinned condition plates and also to those based on the formulae proposed by Maidanik. The radiation efficiency of the clamped plate seems a little higher than that of the pinned plate in the frequency range of corner and edge modes. It is explicitly shown that the power as well as efficiency at high frequencies is not influenced by these edge boundary conditions.

• Structural Engineering and Mechanics
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• 제60권2호
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• pp.271-299
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• 2016

In this article, based on the higher-order shear deformation plate theory, buckling analysis of a rectangular plate made of functionally graded piezoelectric materials and its effective parameters are investigated. Assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for the buckling analysis of an FGP rectangular plate are established. In addition to the Maxwell equation, all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. Considering double sine solution (Navier solution) for displacement field and electric potential, an analytical solution is obtained for full simply supported boundary conditions. The accurate buckling load of FGP plate is presented for both open and closed circuit conditions. It is found that the critical buckling load for open circuit is more than that of closed circuit in all loading conditions. Furthermore, it is observed that the influence of dielectric constants on the critical buckling load is more than those of others.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 가을 학술발표회 논문집
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• pp.405-412
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• 1998

According to the relative stiffness between the half-space and plate or loading condition, some parts of the plate can be separated from the half-space. The finite element procedure to determine the contact area by considering the distribution of contact pressure between plate and the elastic half-space is developed. The vertical surface displacements of the elastic half-space can be obtained through the integrations of the Boussinesq's solution for a point load. The rectangular plate on the elastic half-space is modeled by the 8-node rectangular and 6-node triangular elements and the Mindlin plate theory is used in oder to consider the transverse shear effect. In this study, the contact area may be determined approximately by the analysis with rectangular elements. From this results, the mesh pattern is modified by using triangular and rectangular elements. The contact area can be determined by the new mesh pattern with a relatively sufficient accuracy.

• Structural Engineering and Mechanics
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• 제36권6호
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• pp.669-678
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• 2010

In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings.

• Steel and Composite Structures
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• 제6권4호
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• pp.319-333
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• 2006

A rectangular plate made of a porous material is the subject of the work. Its mechanical properties vary continuously on the thickness of a plate. A mathematical model of this plate, which bases on nonlinear displacement functions taking into account shearing deformations, is presented. The assumed displacement field, linear geometrical and physical relationships permit to describe the total potential energy of a plate. Using the principle of stationarity of the total potential energy the set of five equilibrium equations for transversely and in-plane loaded plates is obtained. The derived equations are used for solving a problem of a bending simply supported plate loaded with transverse pressure. Moreover, the critical load of a bi-axially in-plane compressed plate is found. In both cases influence of parameters on obtained solutions such as a porosity coefficient or thickness ratio is analysed. In order to compare analytical results a finite element model of a porous plate is built using system ANSYS. Obtained numerical results are in agreement with analytical ones.

• 한국소음진동공학회논문집
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• 제22권1호
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• pp.29-37
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• 2012

This paper is concerned with the natural vibration characteristics of a rectangular plate with a rectangular hole in contact with the water. The addressed problem was solved by using the Rayleigh-Ritz method combined with the Green function method. This study presents the numerical approach, numerical results and experimental results. In addition, the validity of the approximate formula which mainly depends on the so-called non-dimensionalized added virtual mass incremental factor and the natural mode shape change due to the presence of the water were investigated. Experiments were also carried out to validate theoretical results. The theoretical results are in good agreement with the experimental results. It was found that the effect of a square hole on the natural frequencies of the square plate in contact with water is different from the effect of a square hole on the natural frequencies of the square plate in air and the approximate formula can predict lower natural frequencies in water with a good accuracy.

• 대한기계학회논문집A
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• 제24권6호
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• pp.1419-1426
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• 2000

A dynamic analysis of rectangular Reissner-Mindlin plate was carried out using pseudospectral method. The pseudospectral method is superior to the finite element method because of more rapid conver gence speed of approximate solutions. Especially, the improvement in accuracy of the pseudospectral method is remarkable. Numerical examples demonstrate the excellent performance and robustness of the pseudospectral method with respect to thickness ratio of rectangular Reissner-Mindlin plate. The natural frequencies of rectangular Reissner-Mindlin plate calculated with the pseudospectral method are more reliable than those calculated with other numerical methods.