• Advances in nano research
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• v.12 no.5
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• pp.467-482
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• 2022

In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.

• Korea-Australia Rheology Journal
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• v.18 no.2
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• pp.51-65
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• 2006

Of concern in the present theoretical investigation is the study of blood flow and convection-dominated diffusion processes in a model bifurcated artery under stenotic conditions. The geometry of the bifurcated arterial segment having constrictions in both the parent and its daughter arterial lumen frequently appearing in the diseased arteries causing malfunction of the cardiovascular system, is constructed mathematically with the introduction of suitable curvatures at the lateral junction and the flow divider. The streaming blood contained in the bifurcated artery is treated to be Newtonian. The flow dynamical analysis applies the two-dimensional unsteady incompressible nonlinear Wavier-Stokes equations for Newtonian fluid while the mass transport phenomenon is governed by the convection diffusion equation. The motion of the arterial wall and its effect on local fluid mechanics is, however, not ruled out from the present model. The main objective of this study is to demonstrate the effects of constricted flow characteristics and the wall motion on the wall shear stress, the concentration profile and on the mass transfer. The ultimate numerical solutions of the coupled flow and diffusion processes following a radial coordinate transformation are based on an appropriate finite difference technique which attain appreciable stability in both the flow phenomena and the convection-dominated diffusion processes.

• Journal of computational fluids engineering
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• v.5 no.1
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• pp.1-7
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• 2000

In general, FDM(finite difference method) and FVM(finite volume method) are used for analyzing the fluid flow numerically. However it is difficult to apply them to problems involving complex geometries, multi-connected domains, and complex boundary conditions. On the contrary, FEM(finite element method) with coordinates transformation for the unstructured grid is effective for the complex geometries. Most of previous studies have used commercial codes such as KIVA or STAR-CD for the flow analyses in the engine cylinder, and these codes are mostly based on the FVM. In the present study, using the FEM for three-dimensional, unsteady, and incompressible Navier-Stokes equation, the velocity and pressure fields in the engine cylinder have been numerically analyzed. As a numerical algorithm, 4-step time-splitting method is used and ALE(arbitrary Lagrangian Eulerian) method is adopted for moving grids. In the Piston-Cylinder, the calculated results show good agreement in comparison with those by the FVM and the experimental results by the LDA.

• Korea-Australia Rheology Journal
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• v.17 no.2
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• pp.47-62
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• 2005

The present study deals with a mathematical model describing the dynamic response of heat and mass transfer in blood flow through bifurcated arteries under stenotic condition. The geometry of the bifurcated arterial segment possessing constrictions in both the parent and the daughter arterial lumen frequently appearing in the diseased arteries causing malfunction of the cardiovascular system, is formulated mathematically with the introduction of the suitable curvatures at the lateral junction and the flow divider. The blood flowing through the artery is treated to be Newtonian. The nonlinear unsteady flow phenomena is governed by the Navier-Stokes equations while those of heat and mass transfer are controlled by the heat conduction and the convection-diffusion equations respectively. All these equations together with the appropriate boundary conditions describing the present biomechanical problem following the radial coordinate transformation are solved numerically by adopting finite difference technique. The respective profiles of the flow field, the temperature and the concentration and their distributions as well are obtained. The influences of the stenosis, the arterial wall motion and the unsteady behaviour of the system in terms of the heat and mass transfer on the blood stream in the entire arterial segment are high­lighted through several plots presented at the end of the paper in order to illustrate the applicability of the present model under study.

• Journal of KSNVE
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• v.4 no.2
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• pp.163-175
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• 1994

An analytical method for nautral frequencies of a partially liquid- filled circular cylindrical shell with various boundary conditions is developed by means of the Stokes's transformation and Fourier series expansion on the basis of Sanders' shell equation. The liquid-shell coupled system is divided into two regions for convenient formulation. One is the empty shell region in which the Sanders' shell equations are formulated without the lipuid effect, the other is wetted shell region in which the shell equations are formulated with consideration of the liquid dynamic effect. The shell equations for each regions are combined by the geometry and the force continuities at the junction of the two regions. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in axial direction. The unknown parameters are selected to satisfy the boundary condition along the wetted shell surface. The natural frequencies of the liquid filled cylindraical shells with the clamped- free and the clamped-clamped boundary conditions examined in the previous works, are obtained by this analytical method. The results are compared with the previous works, and excllent agreement is found for the natural frequencies of the shells.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.2
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• pp.77-89
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• 1991

Based on Boussinesq equation, the parabolic approximation equation is used to analyse the propagation of shallow water waves with currents over slowly varying depth. Rip currents (jet-like) occur mainly in shallow waters where the Ursell parameter significatly exceeds the range of application of Stokes wave theory. We employ the nonlinear parabolic approximation equation which is valid for waves of large Ursell parameters and small scale currents. Two types of currents are considered; relatively strong and relatively weak currents. The wave propagating over rip currents on a sloping bottom experiences a shoaling due to the variations of depth and current velocity as well as refraction and diffraction due to the vorticity of currents. Numerical analyses for a nonlinear theory are valid before the breaking point.

• Coupled systems mechanics
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• v.9 no.3
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• pp.289-309
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• 2020

The paper studies the fluid flow profile contained between the orthotropic plate and rigid wall under the action of the moving load on the plate and main attention is focused on the fluid velocity profile in the load moving direction. It is assumed that the plate material is orthotropic one and the fluid is viscous and barotropic compressible. The plane-strain state in the plate and the plane flow of the fluid is considered. The motion of the plate is described by utilizing the exact equations of elastodynamics for anisotropic bodies, however, the flow of the fluid by utilizing the linearized Navier-Stokes equations. For the solution of the corresponding boundary value problem, the moving coordinate system associated with the moving load is introduced, after which the exponential Fourier transformation is employed with respect to the coordinate which indicates the distance of the material points from the moving load. The exact analytical expressions for the Fourier transforms of the sought values are obtained, the originals of which are determined numerically. Presented numerical results and their analyses are focused on the question of how the moving load acting on the face plane of the plate which is not in the contact with the fluid can cause the fluid flow and what type profile has this flow along the thickness direction of the strip filled by the fluid and, finally, how this profile changes ahead and behind with the distance of the moving load.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.28 no.6
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• pp.332-349
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• 2016

OLAFOAM is the powerful CFD code and is an expanded version of $OpenFOAM^{(R)}$, for wave mechanics simulation. The $OpenFOAM^{(R)}$ does provide many solvers to correspond to each object of the numerical calculation in a variety of fields. OLAFOAM's governing equation bases on VARANS (Volume-Averaged Reynolds-Averaged Navier-Stokes) equation, and the finite volume method is applied to numerical techniques. The program is coded in C++ and run on the Linux operating system. First of all, in this study, OLAFOAM was validated for 1) wave transformation inside porous structure under bore and regular wave conditions, 2) wave transformation by submerged breakwater under regular wave condition, and 3) regular wave transformation and resultant vertical velocity distribution under current by comparison with existing laboratory measurements. Hereafter, this study, which is almost no examination carried out until now, analyzed closely variation characteristics of water surface level, wave height, frequency spectrum, breaking waves, averaged velocity and turbulent kinetic energy around porous submerged breakwater in the wave and current coexisting field for the case of permeable or impermeable rear beach. It was revealed that the wave height fluctuation according to current direction(following or opposing) was closely related to the turbulent kinetic energy, and others.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.4
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• pp.401-412
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• 2008

Simulations of three-dimensional numerical wave tank are performed to investigate wave force acting on a large cylindrical structure and consequent wave deformation, which are induced by bore after breaking waves. The numerical model is based on the three-dimensional Navier-Stokes equations with a finite-difference method combined with a volume of fluid(VOF) method, which is capable of tracking the complex free surface, including wave breaking. In order to promote wave breaking of the incident wave, the approach slope was built seaward of the structure with a constant slope and a large cylindrical structure was installed on a flat bed. The incident waves were broken on the approach slope or flat bed by its wave height. In the present study, all waves acting on the large cylindrical structure were limited to breaking bore after wave breaking. The effects of the position of the structure and the incident wave height on the wave force and wave transformations were mainly investigated with the concern of wave breaking. Further, the relations between the variation of wave energy by wave propagation after wave breaking and wave force acting on the structure were discussed to give the understanding of the full-linear wave-structure interactions in three-dimensional wave fields.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.3B
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• pp.323-334
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• 2008

Present study examined the functionality of the solitary wave (tsunami) control of the two-rowed porous submerged breakwater by numerical experiments, using a numerical wave tank which is based on the Navier-Stokes equation to explain fluid fields and uses a Volume of Fluid (VOF) method to capture the free water surface. Solitary wave was generated by the internal wave source installed within the computational zone in the numerical wave tank and its wave transformations by structure were compared with those in the previous study. Comparisons with the precious numerical results showed a good agreement. Based on these results, several tow-dimensional numerical modeling investigations of the water fields, including wave transformations, reflection, transmission and energy flux, by the one- and two-rowed permeable submerged breakwater under solitary waves were performed. Even if, it is a research of the limited scope, in case of two-rowed permeable submerged breakwater with $h_0/h=0.925$ ($h_0$ is height of submerged breakwater and h is water depth), the wave height damping in range of $l/L_{eff}>0.4$($L_{eff}$ is effective distance of solitary wave) can reach nearly 60% of the incident wave height. In addition, it is found that reflection coefficient increases nearly 47% and transmission coefficient decreases nearly 18% than one-rowed one. The numerical results revealed that the tow-rowed submerged breakwater can control the incident solitary wave economically and more efficiently than the one-rowed one.