• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-412
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• 2011

In this paper, the equation of the transient Stokes flow of an incompressible viscous fluid is studied. Growth and decay estimates are established associating some appropriate cross sectional line and area integral measures. The method of the proof is based on a first-order differential inequality leading to an alternative of Phragm$\'{e}$n-Lindell$\"{o} $f type in terms of an area measure of the amplitude in question. In the case of decay, we also indicate how to bound the total energy.

• Tribology and Lubricants
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• v.18 no.6
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• pp.411-417
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• 2002

Two dimensional slow viscous flow between a rotating cylinder and a translating plate is investigated using Stokes' approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns are shown and the pressure distribution in the flow field is determined. By integrating the stress distributions on the cylinder, the farce and the moment exerted on the cylinder are calculated. The flow rate through the gap between the cylinder and the plate is also determined as a function of the distance between the cylinder and the plate. Special attention is directed to the case of very small distance between the cylinder and the plate concerned with the lubrication theory and the minimum pressure is calculated to explain a possible cavitation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.537-547
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• 1995

Numerical study on the chaotic stirring of viscous flow in an alternately driven cavity has been performed. Even under the Stokes-flow assumption, the inherent singularity at the corners made the problem not so easily accessible. With some special treatments to the region near the corners, the biharmonic equation was solved numerically by using the fully implicit method. The velocity field was then used in obtaining the trajectories of passive particles for studying the stirring effect. The three tools developed in the field of the nonlinear dynamics and chaos, that are the Poincare sections, the unstable manifolds, and the Lyapunov exponents, were used in analysing the stirring effect. It was shown that the unstable manifolds obtained in this study well fit the experimental results given by the previous investigators. It is predicted that the best stirring can be obtained when the aspect ratio a is near 0.8 and the dimensionless period T is in the range 4.3 - 4.7.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.633-644
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• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• Geomechanics and Engineering
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• v.6 no.3
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• pp.213-233
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• 2014

The present paper is dealing with the investigation of the stress field around the infinitely long cylindrical cavity, of a circular cross section, contained in the transversally isotropic elastic continuum. Investigation is based upon the determination of the stress function that satisfies the biharmonic equation, for the given boundary conditions and for rotationaly symmetric loading. The solution of the partial differential equation of the problem is given in the form of infinite series of Bessel's functions. Determination of the stress-strain field around cavities is a common requirement for estimation of safety of underground rock excavations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.121-128
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• 1997

The Boundary Element Method(BEM) has many advantages. Nevertheless the applicability of BEM to structural analysis is seemed to be behind the other methods. This study presents the application of the BEM for analysis of assembled plate structures which is light weight and has a great loading capacity. Firstly, we formulate the boundary integral equation of the single plate, using the biharmonic fundamental solution for plate bending and internal force problems. Nextly, each plates are assembled on 3-dimensional space. In this process, the boundary conditions on assemble line are used. To verify the objectivity and universal validity of analysis by BEM, the results of BEM was compared to that of SAP90 by using FEM.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.3
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• pp.423-431
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• 2002

An experimental study is conducted to investigate the effect of two-frequency forcing on turbulent flow behind a backward-facing step at the Reynolds number of 27000 based on the step height. The forcing is provided from a thin slit located at the edge of the backward-facing step to increase mixing behind the backward-facing step and consequently to reduce the reattachment length. With single frequency forcing, the minimum reattachment length is obtained at the non-dimensional forcing frequency (F) of St$\_$h/ = 0.29. With two-frequency forcing, a subharmonic frequency (F/2) or biharmonic frequency (2F) is combined with the fundamental frequency (F), i.e. (F, F/2) or (F, 2F) forcing is applied. In the case of (F, F/2) forcing, the reattachment length is not much sensitive to the phase difference between F and F/2. However, the reattachment length significantly depends on the phase difference between F and 2F in the case of (F, 2F) forcing. At a certain range of the phase difference, the reattachment length becomes smaller than that of the single frequency forcing.