• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.716-720
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• 2006

In order to examine the effect of constant excitation on nonlinear interactions in vibrating modes of circular plates, we added a constant term to a harmonic excitation. A two-degree-of freedom system is derived by using the Galerkin's procedure. The system is shown to have quadratic and cubic nonlinearities subjected to a harmonic excitation.

• Journal of Electrical Engineering and Technology
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• v.4 no.2
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• pp.277-281
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• 2009

The complex resonant frequency problem of a superconductor patch is formulated in terms of an integral equation which is the kernel of a dyadic Green's function. To include the effect of the superconductivity of the microstrip patch, the surface complex impedance of the superconductor film is introduced using the two fluids model of Gorter and Casimir. The Galerkin procedure is used in the resolution of the electric field integral equation. Numerical results concerning the effect of the operating temperature of a superconductor patch on the characteristics of the antenna are presented.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.279-287
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• 2003

This paper deals with a comparative study on coupling of Element-free Galerkin(EFG) method and Infinite Element(IE) by IE's shape function. In this study, mapped infinite elements(mapped IE) and decay function infinite elements(decay IE) are coupled with the EFG method. A coupling procedure of EFG-Mapped IE is much easier to be integrated than a coupled EFG-Decay IE. A coupled EFG-IE method used well-defined functions to preserve the continuity and linear consistency on the interface of the EFG region and IE region. Several benchmark problems are solved to verify the effectiveness and accuracy of the coupling algorithms by IE's shape function. The numerical results show that the developed algorithms work well for the elastic problems with infinite boundaries.

• Journal of Advanced Navigation Technology
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• v.16 no.4
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• pp.635-640
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• 2012

In this paper, The TE (Transverse Electric) scattering problems by a perfectly conducting strip grating over a grounded two dielectric layers are analyzed by applying the conductive boundary condition and the FGMM (Fourier-Galerkin Moment Method) known as a numerical procedure, then the induced surface current density is expanded in a series of the multiplication of the unknown coefficient and the exponential function as a simple function. Generally, the reflected power gets increased according as the relative permittivity ${\epsilon}_{r2}$ and the thickness of dielectric layer $t_2$ of the region-2 in the presented structure gets increased, respectively. The sharp variations of the reflected power are due to resonance effects were previously called wood's anomaly, the numerical results show in good agreement with those of the existing papers.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.52-61
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• 2014

The present paper deals with the efficient computation of higher-order CFD methods for compressible flow using graphics processing units (GPU). The higher-order CFD methods, such as discontinuous Galerkin (DG) methods and correction procedure via reconstruction (CPR) methods, can realize arbitrary higher-order accuracy with compact stencil on unstructured mesh. However, they require much more computational costs compared to the widely used finite volume methods (FVM). Graphics processing unit, consisting of hundreds or thousands small cores, is apt to massive parallel computations of compressible flow based on the higher-order CFD methods and can reduce computational time greatly. Higher-order multi-dimensional limiting process (MLP) is applied for the robust control of numerical oscillations around shock discontinuity and implemented efficiently on GPU. The program is written and optimized in CUDA library offered from NVIDIA. The whole algorithms are implemented to guarantee accurate and efficient computations for parallel programming on shared-memory model of GPU. The extensive numerical experiments validates that the GPU successfully accelerates computing compressible flow using higher-order method.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.149-154
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• 1997

Based on the full Navier-Stokes solutions, the thermohydrodynamic performance of a long journal bearing is investigated. A numerical method based on Galerkin's procedure and B-spline test functions has been presented for solving two-dimensional problems involving fluid flow and heat transfer. For numerical stability the artificial compressibility is employed to the conservation of mass. The discretized algebraic equations are solved by Newton's method. Effects of varying the speed of an inner cylinder to load carrying capacity are investigated. The results indicated that the increase of the speed of an inner cylinder has a significant effect on the temperature profile and ultimately on the performance.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.504-514
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• 2003

We investigate global bifurcation in the subharmonic motion of a circular plate with one-to-one internal resonance. A system of autonomous equations are obtained from the partial differential equations governing the system by using Galerkin's procedure and the method of multiple scales. A perturbation method developed by Kovacic and Wiggins is used to find Silnikov type homoclinic orbits. The conditions under which the orbits occur are obtained.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.61-68
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• 1991

The system such as railway bridge can be modelled as the restrained beam with intermediate supports. This kind of structures are subject to the moving load, which has a great effect on dynamic stresses and can cause sever motions, especially at high velocities. Therefore, to analyze the dynamic characteristics of the system due to the moving load is very important. In this paper, the governing equation of motion of a restrained beam subjected to the moving load is derived by using the Hamilton's principle. The orthogonal polynomial functions, which are trial functions and satisfying the geometric and dynamic boundary conditions, are obtained through simple procedure. The dynamic response of the system subjected to the moving loads is obtained by using the Galerkin's method and the numerical time integration technique. The numerical tests for various constraint, velocity and boundary conditions were preformed. Furthermore, the effects of mass of the moving load are studied in detail.

• Advances in nano research
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• v.15 no.2
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• pp.113-128
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• 2023

The advancement of theoretical research has numerous challenges, particularly with regard to the modeling of structures, in contrast to experimental investigation of the mechanical behavior of complex systems. The main objective of this investigation is to provide an analytical analysis of the static problem of a new generation of composite structure, namely, functionally graded FG graphene reinforced composite GRC coated plates/shells. A complex power law function is used to define the material's graduation. Investigations are conducted on Hardcore and Softcore coated FG plates/shells. The virtual work approach is used to perform the equilibrium equations, which are then solved using the Galerkin technique to account for various boundary conditions. With reliable published articles, the presented solution is validated. The effects of hardcore and softcore distributions, gradation indexes, and boundary conditions on the buckling, bending deflection and stresses of FG GRC-coated shells are presented in detail. Obtained results and the developed procedure are supportive for design and manufacturing of FG-GRC coated plates/shells in several fields and industries e.g., aerospace, automotive, marine, and biomedical implants.

• Transactions of the Korean Society of Mechanical Engineers
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• v.1 no.3
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• pp.141-145
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• 1977

In this paper, approximate solutions of the von Karman equations for the free flexural vibration of a transversely isotropic thin rectangular plate with two simply supported edges and two clamped edges are obtained. Applying one term Ritz-Galerkin procedure, the spatial dependent part of the equation is separated and time dependent function is found to be the Duffing's equation. Then the relation between nonlinear period and amplitude of the vibration is obtained by using averaging method which is a method of the perturbation procedure. It can be seen that averaging method is easy and agrees well with prior results.