• 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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.23 no.3
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• pp.215-224
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• 1990

Finite element model capable of solving coupled deformation-fluid diffusion equations for the fully saturated porous medium was developed using Galerkin's residual method. This model was used to study the mechanical and hydraulic behaviors of unconsolidated sediment near South Harbor, Pusan. The vertical displacement of top surface clay sediment, when subjected to the external load, is significantly affected by the excessive pore pres- sure buildup and its decay due to the pore fluid diffusion. The sand deposit overlain by the much less permeable clay layer serves as a flow channel. Consequently, the fluid diffusion due to pore pressure difference is significantly facilitated, which also affects the diffusion-dependent sediment deformation.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.525-534
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• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.140-147
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• 2001

In this paper, the dynamic response of non-uniform beams subjected to a travelling mass is investigated. Dynamic behaviors of flexible beam structures under a moving mass have been a concern in the design of bridges, ceiling crain in industry, as well as gun barrel fields. Most of studies for moving mass problems have been related to the theoretical dynamic responses of a simple beam model with uniform cross-sections. In some experimental studies, only a few transverse inertia effects due to travelling mass have been studied so far. The intended aim of the present Paper is to investigate the dynamic response of non-uniform beams taking into account of inertia force. centrifugal force, Coriollis force and self weight due to travelling mass. Galerkin's mode summation method is applied for the discretized equations of motion. Numerical results for the dynamic response of non-uniform beams under a travelling mass are demonstrated for various magnitudes and velocities of the travelling mass. In order to verify propriety of numerical solutions, experiments were conducted. Experimental resu1ts have a good agreement wish theoretical Predictions.

• Smart Structures and Systems
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• v.22 no.1
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• 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.14 no.4
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• pp.303-312
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• 2023

In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin's method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type-I and Type-II functionally graded cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type-I and -II clamped simply supported FG cylindrical shell with different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.2
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• pp.176-197
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• 1995

Two-dimensional and three-dimensional structures of tidal currents on southeastern waters of Korea off Kyungnam coast were investigated via a series of numerical models based on dynamic principles. With a two-dimensional tidal model, tidal regimes of major eight tidal constituents (M$_2$, S$_2$, K$_1$, O$_1$, N$_2$, K$_2$, P$_1$, Q$_1$) were computed. Model results showed that the computed results were in good agreement with coastal observations. On the basis of these results the model was further improved to compute three-dimensional structure of tidal current in inner Jinhai and Masan Bay regions of the model area where severe pollutions occur due to red tide by combination of the previous two-dimensional model and inner three-dimensional model. For this work, three-dimensional Galerkin-Spectral model and two-dimensional depth-integrated model are dynamically combined by the method presented by Davies (1980). In addition to the previous work by Davies, the advective term and quadratic bottom friction term are included in present Three-dimensional numerical model. The computed results of M$_2$ tidal current ellipses with respect to depth showed general agreements with those of current observations by KORDI (1990).

• 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.

• 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.