• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.691-703
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• 1997

This paper investigates the optimal locations of internal point supports in a symmetric crossply laminated rectangular plate for maximum fundamental frequency of vibration. The method used for solving this optimization problem involves the Rayleigh-Ritz method for the vibration analysis and the simplex method of Nelder and Mead for the iterative search of the optimum support locations. Being a continuum method, the Rayleigh-Ritz method allows easy handling of the changing point support locations during the optimization search. Rectangular plates of various boundary conditions, aspect ratios, composed of different numbers of layers, and with one, two and three internal point supports are analysed. The interesting results on the optimal locations of the point supports showed that (a) there are multiple solutions; (b) the locations are dependent on both the plate aspect ratios and the number of layers (c) the fundamental frequency may be raised significantly with appropriate positioning of the point supports.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.7
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• pp.1165-1171
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• 2004

The free vibration analyses of the isotropic and CFRP laminated composite rectangular plates with point supports at the fix edge is performed by FEM. We showed optimal position and mode shape of point supports that maximized fundamental natural frequency of the isotropic and CFRP laminated composite rectangular plates by each aspect ratio and the number of point supports.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.818-823
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• 2002

Addition of point supports results in increasing the fundamental frequency of a structure, generally. In this paper, searching more effective location of point supports is a major object to maximize a fundamental frequency of various cantilever plates. Results are presented by aspect ratio of the plate, by design domain within which point supports generate, and by mass location equipped on the plate. Optimization method is applied due to expand the ESO(Evolutionary Structural Optimization) method.

• Journal of KSNVE
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• v.8 no.4
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• pp.623-631
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• 1998

The free vibration analyses of the isotropic and composite(CFRP, GFRP) rectangular plates with point supports at the free edge and middle position are performed. The natural frequencies and nodal patterns of plates with point supports are experimentally determined by impact testing using an impact hammer. To compare and verify these experimental results, the finite element analysis is also carried out. The effect of the point support position, the number of point supports, and the anisotropic parameters on the natural frequencies and nodal patterns of cantilevered rectangular plates are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.414-419
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• 1997

The free vibration analysis of cantilever CFRP and GFRP composite rectangular plates with point supports at the free edge and interior position is performed. The natural frequencies and mode shapes of plates are experimentally determined by impact testing using an impact hammer. To compare and verify these experimental results, the finite element analysis is also carried out and the non-dimensional frequency parameters are compared with FE analysis results. The effects of the number and location of the point support on the frequencies are examined. In the experimental results, it is found that a significant increase in frequencies occurs when the point supports are added on certain parts of plates.

• Advances in concrete construction
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• v.9 no.6
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• pp.557-568
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• 2020

In this study, the impact of ring supports around the shell circumferential has been examined for their various positions along the shell axial length using Rayleigh-Ritz formulation. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the ring supports is investigated at various positions. These variations have been plotted against the locations of ring supports for three values of length-to-diameter ratios. Effect of ring supports with middle layer thickness is presented using the Rayleigh-Ritz procedure with three different conditions. The influence of the positions of ring supports for clamped-clamped is more visible than simply supported and clamped-free end conditions. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The Lagrangian functional is created by adding the energy expressions for the shell and rings. The axial modal deformations are approximated by making use of the beam functions. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported frequency curves are higher than that of clamped-simply curves. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.431-441
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• 2017

In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where possible, are verified upon comparison with available values in the literature, and excellent agreement is achieved.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.15 no.3
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• pp.32-38
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• 2006

During stereolithography processes, the shape errors such as curl distortion and distortion of side face are generated due to the shrinkage of liquid resins. In this study, the effects of dimension of part and structure of supports on the shape error are examined. Cubic specimens which have different thicknesses are manufactured and their deformations are measured with CMM. Thicker part generates smaller curl distortion of top face and larger of bottom face. Also thicker part generates larger distortion of side face until part thickness increases to about 20mm. Larger stiffness of supports which is obtained by shorter spacing of the supports and line type contact instead of point type contact generates smaller shape error of the part.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.333-347
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• 2014

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.

• Journal of Korea Multimedia Society
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• v.11 no.6
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• pp.816-827
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• 2008

In this paper, two-stage pipelined floating-point arithmetic unit (FP-AU) is designed. The FP-AU processor supports seventeen operations to apply 3D graphics processor and has area-efficient and low-latency architecture that makes use of modified dual-path computation scheme, new normalization circuit, and modified compound adder based on flagged prefix adder. The FP-AU has about 4-ns delay time at logic synthesis condition using $0.18{\mu}m$ CMOS standard cell library and consists of about 5,930 gates. Because it has 250 MFLOPS execution rate and supports saturated arithmetic including a number of graphics-oriented operations, it is applicable to mobile 3D graphics accelerator efficiently.