• Steel and Composite Structures
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• v.18 no.6
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• pp.1541-1555
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• 2015

In this paper mechanical behavior of the functional gradient materials (FGM) micro-gripper under thermal load and DC voltage is numerically investigated taking into account the effect of intermolecular forces. In contrary to the similar previous works, which have been conducted for homogenous material, here, the FGM material has been implemented. It is assumed that the FGM micro-gripper is made of metal and ceramic and that material properties are changed continuously along the beam thickness according to a given function. The nonlinear governing equations of the static and dynamic deflection of microbeams have been derived using the coupled stress theory. The equations have been solved using the Galerkin based step-by-step linearization method (SSLM). The solution procedure has been evaluated against available data of literature showing good agreement. A parametric study has been conducted, focusing on the combined effects of important parameters included DC voltage, temperature variation, geometrical dimensions and ceramic volume concentration on the dynamic response and stability of the FGM micro-gripper.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.40 no.5
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• pp.187-196
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• 2003

Effects of Airgap and anisotropy substrate on input impedance and radiation pattern of rectangular microstrip patch antenna are studied in terms of an integral equation formulation. The input impedance and radiation pattern of microstrip patch antenna is investigated by using Galerkin's moment method in solving the integral equation. Sinusoidal functions are selected as basis functions, which resemble in the actual standing wave on the Patch. From the numerical results, the variation of input impedance and radiation patterns in the variation of air gap thickness, anisotropy ratio of substrate, and relative permittivity of anisotropy substrate are presented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.11B
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• pp.1600-1606
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• 2001

Resonant frequency in rectangular microstrip patch antenna on anisotropic substrates with airgap and superstrate are analyzed. Dyadic Green function is derived for selected anisotropic material by constitutive relation. From these results, integral equations of electric fields are formulated using Fourier transform in space region. The electric field integral equations are discretized into the matrix form by applying Galerkin\`s moment method. Sinusoidal functions are selected as basis functions because they resemble in the actual standing wave on the patch. To verify the validity of numerical result, we compare our result with existing one and get a good agreement between them. From the numerical results, the resonant frequency in the variation of air gap, patch length and anisotropy ratio are presented and analysed.

• Advances in nano research
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• v.9 no.4
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• pp.221-235
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• 2020

The following composition establishes a nonlocal strain gradient plate model that is essentially related to mass sensors laying on Winkler-Pasternak medium for the vibrational analysis from graphene sheets. To achieve a seemingly accurate study of graphene sheets, the posited theorem actually accommodates two parameters of scale in relation to the gradient of the strain as well as non-local results. Model graphene sheets are known to have double variant shear deformation plate theory without factors from shear correction. By using the principle of Hamilton, to acquire the governing equations of a non-local strain gradient graphene layer on an elastic substrate, Galerkin's method is therefore used to explicate the equations that govern various partition conditions. The influence of diverse factors like the magnetic field as well as the elastic foundation on graphene sheet's vibration characteristics, the number of nanoparticles, nonlocal parameter, nanoparticle mass as well as the length scale parameter had been evaluated.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.38 no.9
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• pp.29-39
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• 2001

Dielectric cover effect of rectangular microstrip patch antenna on uniaxial substrates with airgap are studied. First, we derive Dyadic Green function for selected anisotropic material by constitutive relation and then formulate integral equations of electric fields using Fourier transform in space region. Using Galerkin's moment method, we discretize the electric field integral equations into the matrix form and select sinusoidal functions as basis functions. We verify the validity of numerical results and compare the results with existing ones in showing a good agreement between them. When the dielectric cover thickness is varied, the resonant frequencies and input impedances in the variation of air gap, patch length and thickness and permittivity of superstrate are presented and analyzed.

• Journal of Ocean Engineering and Technology
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• v.32 no.4
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• pp.228-236
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• 2018

The performance of a porous swash bulkhead for the reduction of the resonant liquid motion in a swaying rectangular tank was investigated based on the assumption of linear potential theory. The Galerkin method (Porter and Evans, 1995) was used to solve the potential flow model by adding a viscous frictional damping term to the free-surface condition. By comparing the experimental results and the analytical solutions, we verified that the frictional damping coefficient was 0.4. Darcy's law was used to consider the energy dissipation at a porous bulkhead. The tool that was developed with a built-in frictional damping coefficient of 0.4 was confirmed by small-scale experiments. Using this tool, the free-surface elevation, hydrodynamic force (added mass, damping coefficient) on a wall, and the horizontal load on a bulkhead were assessed for various combinations of porosity and submergence depth. It was found that the vertical porous bulkhead can suppress sloshing motions significantly when properly designed and by selecting the appropriate porosity(${\approx}0.1$) and submergence depth.

• Steel and Composite Structures
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• v.22 no.1
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• pp.91-112
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• 2016

In this paper, post-buckling behavior of sandwich plates with functionally graded (FG) face sheets under uniform temperature rise loading is examined based on both sinusoidal shear deformation theory and stress function. It is supposed that the sandwich plate is in contact with an elastic foundation during deformation, which acts in both compression and tension. Thermo-elastic non-homogeneous properties of FG layers change smoothly by the variation of power law within the thickness, and temperature dependency of material constituents is considered in the formulation. In the present development, Von Karman nonlinearity and initial geometrical imperfection of sandwich plate are also taken into account. By employing Galerkin method, analytical solutions of thermal buckling and post-buckling equilibrium paths for simply supported plates are determined. Numerical examples presented in the present study discuss the effects of gradient index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation parameters.

• Computers and Concrete
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• v.25 no.5
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• pp.411-425
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• 2020

In this paper, the shell material has been taken as functionally graded material and their material quantity is located by the exponential volume fraction law. Moreover, the impact of ring supports around the shell circumference has been examined for their various positions along the shell axial length. These rings support restraints the radial displacement in the transverse direction. While the axial modal deformation functions have been estimated by characteristic beam functions and nature of materials used for construction of cylindrical shells. The fundamental natural frequency of cylindrical shell of parameter versus ratios of length- and height-to-radius for a wide range has been reported and investigated through the study. In addition, by increasing height-to-radius ratio resulting frequencies also increase and frequencies decrease on ratio of length-to-radius. Though the trends of frequency values of both ratios are converse to each other with three different boundary conditions. Also it is examined the position of ring supports with length-to radius ratio, height-to-radius ratio and varying the exponent of volume fraction. MATLAB software package has been utilized for extracting shell frequency spectra. The obtained results are confirmed by comparing with available literature.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.387-394
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• 2000

Theoretical and experimental study is conducted on the contact pressure distribution of a radial tire in motion under various camber angles. Tire construction is modelled by a spring bedded elastic ring, consisted of sidewall springs and a composite belt ring. The contact area is assumed to be a trapezoidal shape varying with camber angles and weighted load. The basic equation in a quasi-static form is derived for the deformation of a running belt with a constant velocity by the aid of Lagrange-Euler transformation. Galerkin's method and stepwise calculation are applied for solving the basic equation and the mechanical boundary condition along both sides of the contact belt part subjected to shearing forces transmitted from the sidewall spring. Experimental results on the contact pressure, measured by pressure sensors embedded in the surface of the drum tester, correspond well with the calculated ones for the test tire under various camber angles, running velocities and weighted loads. These results indicate that a buckling phenomenon of the contact belt in the widthwise direction occurs due to the effect of camber angle.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.7
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• pp.510-517
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• 2015

The free vibration and stability analysis of a spinning composite shaft modelled as a thin-walled closed beam is performed for several design parameters, such as ply angle, aspect ratio, and spin speed. The governing equations of spinning shafts based on the Timoshenko beam theory are derived via Hamilton's variational principle. Coriolis acceleration and anisotropy of constituent materials are incorporated in the derivation. The equations of motion are then transformed to the standard form of an eigenvalue problem for free vibration and stability analysis. Analytical results both for uniform circular cylindrical shaft and rectangular cross-section shaft are obtained by using extended Galerkin method, and the results are compared with those from FEM ANSYS analysis for a verification.