• International Journal of Naval Architecture and Ocean Engineering
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• 제8권1호
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• pp.53-65
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• 2016

The interaction between incident waves and a floating rectangular breakwater with the vertical porous side plates has been investigated in the context of the two-dimensional linear potential theory. The matched eigenfunction expansion method(MEEM) for multiple domains is applied to obtain the analytic solutions. The dependence of the transmitted coefficients and motion responses on the design parameters, such as porosity and protruding depth of side plates, is systematically analyzed. It is found that the non-dimensional wavelength where the sudden drop of transmission coefficients occurs, corresponds to the heave resonant frequency obtained from Ruol et al. (2013) for $\pi$-type floating breakwater. It is concluded that both properly selected porosity and deeper protruding depth of side plates are helpful in reducing the transmission coefficients and also extending the wider applicable extent of incident wavelength for performance enhancement.

• 호남수학학술지
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• 제30권1호
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• 충청수학회지
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• 제20권3호
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• pp.261-267
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• 2007

We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions $$u_{tt}-u_{xx}+av^+=s{\phi}_{00}+f$$, $$v_{tt}-v_{xx}+bu^+=t{\phi}_{00}+g$$, $$u({\pm}\frac{\pi}{2},t)=v({\pm}\frac{\pi}{2},t)=0$$, where $u_+=max\{u,0\}$, s, $t{\in}R$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}=1$ of the eigenvalue problem $u_{tt}-u_{xx}={\lambda}_{mn}u$ with $u({\pm}\frac{\pi}{2},t)=0$, $u(x,t+{\pi})=u(x,t)=u(-x,t)=u(x,-t)$ and f, g are ${\pi}$-periodic, even in x and t and bounded functions in $[-\frac{\pi}{2},\frac{\pi}{2}]{\times}[-\frac{\pi}{2},\frac{\pi}{2}]$ with $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f{\phi}_{00}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g{\phi}_{00}=0$.

• Structural Engineering and Mechanics
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• 제20권3호
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• pp.335-346
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• 2005

The T-stress of cracks in elastic sheets is solved by using the fractal finite element method (FFEM). The FFEM, which had been developed to determine the stress intensity factors of cracks, is re-applied to evaluate the T-stress which is one of the important fracture parameters. The FFEM combines an exterior finite element model with a localized inner model near the crack tip. The mesh geometry of the latter is self-similar in radial layers around the tip. The higher order Williams series is used to condense the large numbers of nodal displacements at the inner model near the crack tip to a small set of unknown coefficients. Numerical examples revealed that the present approach is simple and accurate for calculating the T-stresses and the stress intensity factors. Some errors of the T-stress solutions shown in the previous literature are identified and the new solutions for the T-stress calculations are presented.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2000년도 춘계학술대회 논문집
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• pp.140-145
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• 2000

The spectral method which is composed of an eigenfunction expansion of free modes in the wave number domain is used to produce two dimensional unsteady inviscid wave simulation such as progressive waves in a numerical pneumatic wave tank. A spatial and time dependent free surface elevation and the potential are calculated by integrating ODE derived from fully nonlinear kinematic and dynamic free surface boundary condition at each time step. The nonlinear characteristics in the waves by this method were notable as increasing wave steepness. This method is very useful and powerful in terms of saving computational time caused by rapid convergence exponentially with increasing number of nodes, even preserving accurate numerical results. Moreover, it will given us many possibilities to apply to naval and ocean engineering fields.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• 제6권1호
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• pp.7-14
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• 2003

The interaction of monochromatic incident waves with a submerged horizontal porous membrane is investigated in the context of two-dimensional linear hydro-elastic theory. It is assumed that the membrane is made of material with very fine pores so that the normal velocity of the fluid passing through the porous membrane is linearly proportional to the pressure difference between two sides of the membrane (e.g. Darcy's law). Using the Eigen-function expansion method, the wave-blocking performance of a submerged horizontal porous membrane is tested with various membrane tensions, porosities, lengths, and submerged depths. It is found that an optimal combination of design parameters exists for given water depth and wave characteristics.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.63-65
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• 2003

General classes of boundary-pressure-driven flows of incompressible Newtonian fluids in three­dimensional (3D) channels and in 3D pipes with known steady laminar realizations are investigated respectively. The characteristic physical and geometrical quantities of the flows are subsumed in the kinetic Reynolds number Re and a parameter $\psi$, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form $\underline{u}=u_{L}+U,\;where\;u_{L}$ is the scaled laminar velocity and periodical conditions are prescribed for U in the unbounded directions. The objects of our numerical investigations are autonomous systems (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction, where these systems (S) were received by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.233-238
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• 2010

A two-dimensional laminar flow past a vertical plate in a microchannel is investigated. At far upstream and downstream from the plate in the microchannel, the plane Poiseuille flow exists. The Stokes flow for this microchannel is investigated analytically and then the laminar flow by numerical method. For the Stokes flow analysis, the method of eigenfunction expansion is used. From the results, the streamline pattern and the pressure distribution are plotted, and the additional pressure drop induced by the plate and the force exerted on the plate are calculated as functions of the length of the plate. For the laminar flow, finite difference method (FDM) is used to obtain the vorticity and the stream function. When the Reynolds number exceeds a critical value, a pair of viscous eddies appears behind the plate.

• 대한기계학회논문집A
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• 제25권11호
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• pp.1835-1843
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• 2001

The energy release rate for an interface crack in anisotropic dissimilar materials was obtained by the eigenfunction expansion method and also was analyzed numerically by the reciprocal work contour integral method. It was shown that the results for orthotropic dissimilar materials are consistent with the other worker's results.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.27-47
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• 2012

It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.