• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.702-707
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• 2005

The equations of motion of the structure, which is a small scale cantilever beam considering electrostatic force, squeeze film damping and van der Waals force are obtained employing Galerkin's method based on Euler beam theory. The influence of each force is investigated fur changing the size of a small scale cantilever beam which assumed uniform shape. Also the forces which are affected by the required size of a small scale cantilever beam for manufacturing are forecasted.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.465-468
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• 2005

The paper deals with the influences of external damping and tip mass on dynamic stability of a vertical cantilevered pipe conveying fluid. In general, real pipe systems may have some valves and attached parts, which can be regarded as attached lumped masses and support-dampers. The support-dampers can be assumed as viscous dampers. The equations of motion are derived by energy expressions using extended Hamilton's principle, and some numerical results using Galerkin's method are presented. Critical flow velocities and stability maps of the pipe with external dampers and tip mass are obtained for various tip mass ratios, external damping coefficients and positions of the viscous dampers.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.656-661
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• 2004

Static and dynamic responses of micro double cantilever beam structures interacted by electrostatic forces are obtained employing Galerkin's method based on Euler beam theory. Variations of static and dynamic responses as well as natural frequencies are estimated for several sets of beam properties and applied voltages. It is shown that the variations of beam properties resulted by manufacturing process influence the deflections and the modal characteristics significantly. Such information can be usefully employed for the design of MEMS structures.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.423-440
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• 2016

The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in [8]. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.470-474
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• 2016

Madsen et al. (2002)이 제안한 일차원 고차 Boussinesq 방정식에 대하여 불연속갤러킨 유한요소법(Discontinuous Galerkin Finite Element Method)을 적용하였다. 연속적인 Boussinesq 방정식에서 각 요소경계에 불연속을 허용할 수 있도록 공간차분하고, 시간방향으로 4차 Runge-Kutta 시간적분법, 각 요소사이에는 Lax-Friedrichs 수치흐름률을 사용하였다. 계산영역의 양쪽에 불필요한 파랑의 반사를 억제하도록 흡수층을 설치하였으며, 영역 내부에서 조파할 수 있도록 하였다. Luth et al.(1994)의 수중잠제 실험에 적용하여 관측값과 잘 일치함을 확인하였다.

• Structural Engineering and Mechanics
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• v.8 no.2
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• pp.151-164
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• 1999

The large deflection theory of the Mindlin plate and Galerkin's method are employed to examine the static responses of a plate produced by the weight of the plate, and the dynamic responses of the plate caused by the coupling effect of these static responses with a set of moving forces. Results obtained by the large deflection theory are compared with those by the small deflection theory. The results indicate that the effect of weight of the plate increases the modal frequencies of the structure. The deviations of dynamic transverse deflection and of dynamic bending moment produced by a moving concentrated force between the two theories are significant for a thin plate with a large area. Both dynamic transverse deflection and dynamic bending moment obtained by the Mindlin plate theory are greater than those by the classical plate.

• Steel and Composite Structures
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• v.10 no.2
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• pp.151-168
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• 2010

The subject of the paper is an isotropic metal foam rectangular plate. Mechanical properties of metal foam vary continuously through plate of the thickness. A nonlinear hypothesis of deformation of plane cross section is formulated. The system of partial differential equations of the plate motion is derived on the basis of the Hamilton's principle. The system of equations is analytically solved by the Bubnov-Galerkin method. Numerical investigations of dynamic stability for family rectangular plates with respect analytical solution are performed. Moreover, FEM analysis and theirs comparison with results of numerical-analytical calculations are presented in figures.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.05b
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• pp.503-508
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• 1997

The effect of rotary inertia of concentrated masses on the natural vibration of the simply supported-simply supported fluid conveying pipe has been studied. For the analysis Galerkin's method is used fer transformation of the governing equation to the eigenvalue problem and the natural frequencies and mode shapes for the system have been found. Introduction of rotary inertia results in lots of change on the natural frequencies and mode shapes and its effect is highly noticed at the higher natural frequencies and mode shapes. Consideration of rotary inertia results in much decrease on the natural frequencies and its neglect could lead to erroneous results.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.365-391
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• 2007

The vibration and stability analysis is investigated for composite cylindrical shells that composed of ceramic, FGM, and metal layers subjected to various loads. Material properties of FG layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations are obtained. Applying Galerkin's method analytic solutions are obtained for the critical parameters. The detailed parametric studies are carried out to study the influences of thickness variations of the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, material composition and material profile index on the critical parameters of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.

• Advances in nano research
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• v.5 no.4
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• pp.393-414
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• 2017

Forced vibration behavior of porous metal foam nanoplates on elastic medium is studied via a 4-variable plate theory. Different porosity distributions called uniform, symmetric and asymmetric are considered. Nonlocal strain gradient theory (NSGT) containing two scale parameters is employed for size-dependent modeling of porous nanoplates. The present plate theory satisfies the shear deformation effect and it has lower field variables compared with first order plate theory. Hamilton's principle is employed to derive the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, dynamic loading, porosity distributions and porosity coefficient on dynamic deflection and resonance frequencies of metal foam nanoscale plates are examined.