• Journal of the Korean Society for Precision Engineering
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• v.16 no.8
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• pp.162-169
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• 1999

Fourier heat conduction law becomes invalid for the situations involving extremely short time heating, very low temperatures and fast moving heat source(or crack), since the wave nature of heat propagation becomes dominant. For these conditions, the modified heat conduction equation with the finite propagation speed of heat in the medium could be applied to predict heat flux and temperature distributions. In this study, temperature distributions at the vicinity of a very fast moving heat source are investigated numerically. Thermal fields are characterized by thermal Mach numbers(M) defined as the ratio of moving heat source speed to heat propagation speed in the solid. In the transonic and supersonic ranges($M{\ge}1$), thermal shocks are shown, which separate the heat affected zone from the thermally undisturbed zone.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.396-403
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• 1991

A solution is presented for the computation of the elastic-creep stresses in a hollow cylinder subjected to nonaxisymmetric temperature distribution. The creep problem is treated by the Maxwell creep model. Laplace transformation is used for reformation of the governing equation of elastic problem and Hooke's law in a function of .gamma. , .theta. , and creep constant. The governing equation is set up using the Airy stress function which leads to the biharmonic equation. The solution is obtained by using Fourer series method and Laplace inverse method used to obtain the stress components which include the variation of time. This solution shows excellent agreement with Lamkin's and Boley & Weiner's solution. The viscoelastic stresses are also obtained for the fuel rob tube subjecting nonaxisymmetric thermal load.

• Journal of Energy Engineering
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• v.8 no.4
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• pp.540-545
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• 1999

The classical Fourier heat conduction equation is invalid at temperatures near absolute zero or at very early times in highly transient heat transfer processes. In such situations, a hyperbolic equation model for heat conduction based on the modified Fourier law is introduced because the wave nature of heat propagation becomes dominant. The Fourier model and the hyperbolic model for heat conduction are analyzed by using the Green's function technique together with the integral transform. Analytical expressions for the heat flux and temperature distributions in a finite slab subjected to a periodic surface heating at one of its surfaces are presented and the results obtained from each model are compared with each other. The thermal wave implied b the hyperbolic model is shown to travel through a medium and to reflect back toward the origin at the other insulated surface. On the other hand, the heat by the Fourier model propagates at an infinite speed instantaneously after a thermal disturbance is felt throughout the medium.

• Magazine of the Korean Society of Agricultural Engineers
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• v.9 no.2
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• pp.1301-1305
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• 1967

Ground water flow can be studied with model test. Model test of ground water works are necessary for economic and safe design of the works. Also influence of the ground water flow to the durability and safety of hydraulic structures can be studied with this model. a. Sand model ; Water flow through porous media is the principle of sand model. Darcy's formula is the basic equation, $q=k{\frac{dh}{ds}}^{\circ}. The effect of the ground water flow on the grain system itself is represented with this model only. b. Hele-Shaw model ; In this model use is made of the viscous flow analogy. Viscous fluid such as glycerine flowing through two parallel plates depends on Poiseuille law, $q=-c{\frac{dh}{ds}}$. The analogue can be used vertically and horizontally. c. Heat model ; This is based on the analogy of the Fourier's law for heat conduction and Darcy's law for ground water flow. Especially unsteady problem can be studied with this model. A difficulty of the construction of this model is the isolation, which has to prevent losses of the heat. d. Electirc model ; Ohm's law for electric current is analogous to Darcy's law. Resistance material such as metal foil, graphite block, water with salt added, gelatine with salt added, ete. is connected to electric sources and resistor, and equi-voltage line is detected with galvanometer, $N_aCl$, $CuSo_4$, etc. are used as salt in the model. e. Membrane model ; This model is based on the facts that the deflection of a thin membrane obeys Laplace's equation if there is no load in the direction perpendicular to the membrane, and if the dellection is small.

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.390-396
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• 1993

When a one-dimensional telecentric paraxial holographic kinoform is used as a Fourier transform lens, we analyzed three surface-relief structures, i.e., plano-convex, convex-plano and biconvex shapes, employing exact raytracing method based on Snell's law. For the kinoform of E/8 and focal length of 15 mm, the number of zones, the thickness, and the slope of parabolic surfaces are varied by changing the refractive indicies of kinoform material and surrounding medium. It is found that biconvex shape gives the best results in general, although off-axis performance degrades in all cases as the slope of parabolic surfaces increases.

• Journal of the Korean Vacuum Society
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• v.17 no.4
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• pp.302-310
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• 2008

Heat transfer between substrate and substrate-heater in low vacuum was investigated. The convection related with gas flow and pressure, the heat conduction considering surface roughness and contact pressure, and the heat loss by radiation depending on the surface emissivity were considered. The coefficient of heat conduction $h_c$ in the Fourier's law were determined experimentally from the temperature difference between the substrate and the substrate-heater in the range of substrate-heater temperature $100\;-\;500^{\circ}C$, in the pressures of 300 mTorr - 1 Torr. The temperature difference was then calculated in the reverse way for the purpose of verification, using the heat flow and the experimentally determined coefficients. The verified temperature differences were thus obtained within 0.33 % error.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.163-177
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• 2012

This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented.

• Earthquakes and Structures
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• v.9 no.1
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• pp.173-194
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• 2015

Site response analysis is an important topic in earthquake engineering. A time-domain numerical method called as one-dimensional (1D) finite element artificial boundary method is proposed to simulate the homogeneous plane elastic wave propagation in a layered half space subjected to the obliquely incident plane body wave. In this method, an exact artificial boundary condition combining the absorbing boundary condition with the inputting boundary condition is developed to model the wave absorption and input effects of the truncated half space under layer system. The spatially two-dimensional (2D) problem consisting of the layer system with the artificial boundary condition is transformed equivalently into a 1D one along the vertical direction according to Snell's law. The resulting 1D problem is solved by the finite element method with a new explicit time integration algorithm. The 1D finite element artificial boundary method is verified by analyzing two engineering sites in time domain and by comparing with the frequency-domain transfer matrix method with fast Fourier transform.

• Coupled systems mechanics
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• v.9 no.2
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• pp.125-145
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• 2020

In this paper, we present a 3D thermo-hydro-mechanical coupled discrete beam lattice model of structure built of the nonisothermal saturated poro-plastic medium subjected to mechanical loads and nonstationary heat transfer conditions. The proposed model is based on Voronoi cell representation of the domain with cohesive links represented as inelastic Timoshenko beam finite elements enhanced with additional kinematics in terms of embedded strong discontinuities in axial and both transverse directions. The enhanced Timoshenko beam finite element is capable of modeling crack formation in mode I, mode II and mode III. Mode I relates to crack opening, mode II relates to in-plane crack sliding, and mode III relates to the out-of-plane shear sliding. The pore fluid flow and heat flow in the proposed model are governed by Darcy's law and Fourier's law for heat conduction, respectively. The pore pressure field and temperature field are approximated with linear tetrahedral finite elements. By exploiting nodal point quadrature rule for numerical integration on tetrahedral finite elements and duality property between Voronoi diagram and Delaunay tetrahedralization, the numerical implementation of the coupling results with additional pore pressure and temperature degrees of freedom placed at each node of a Timoshenko beam finite element. The results of several numerical simulations are presented and discussed.

• Journal of the Korean Wood Science and Technology
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• v.22 no.2
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• pp.61-70
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• 1994

This study was executed to find the applicability of press drying of tree disk by investigating the shrinkage and drying defect and to form appropriate model by comparing the actual moisture content(MC) and internal temperature in respect of drying time with calculated values based computer simulation to which was applied finite difference method. In press drying disk, heating period, constant drying rate period maintained plateau temperature at 100$^{\circ}C$ and falling drying rate period were significantly distinguished. Actual MC and internal temperature were analogous to those calculated at comparing points. Heat transfer model formed by Fourier's law using specific heat of moist wood and conduction coefficient considering fractional volume of each element of wood cell wall, bound water, free water and air showed applicability as basic data to developing heat expansion, shrinkage and drying stress during press drying. Also mass transfer model formed by Fick's diffusion law using water vapor diffusion coefficient showed applicability. Longitudinal shrinkage was developed by pressure of hot press and tangential shrinkage was restrained by hygrothermal recovery. The heart check, surface check and ring failure were occurred differently in species, but V-shaped crack didn't develop.