• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.453-459
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• 2019

In this paper, we analyze the behaviour of flows near closed sets with compact boundary which contains no semi-orbits. Also, we give a condition that a closed invariant set is to be asymptotically stable.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.465-477
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• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.55-67
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• 2004

In this paper, an active vibration control of a translating steel strip in a zinc galvanizing line is investigated. The control objectives in the galvanizing line are to improve the uniformity of the zinc deposit on the strip surfaces and to reduce the zinc consumption. The translating steel strip is modeled as a moving belt equation by using Hamilton’s principle for systems with moving mass. The total mechanical energy of the strip is considered to be a Lyapunov function candidate. A nonlinear boundary control law that assures the exponential stability of the closed loop system is derived. The existence of a closed-loop solution is shown by proving that the closed-loop dynamics is dissipative. Simulation results are provided.

• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.271-299
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• 2016

In this article, based on the higher-order shear deformation plate theory, buckling analysis of a rectangular plate made of functionally graded piezoelectric materials and its effective parameters are investigated. Assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for the buckling analysis of an FGP rectangular plate are established. In addition to the Maxwell equation, all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. Considering double sine solution (Navier solution) for displacement field and electric potential, an analytical solution is obtained for full simply supported boundary conditions. The accurate buckling load of FGP plate is presented for both open and closed circuit conditions. It is found that the critical buckling load for open circuit is more than that of closed circuit in all loading conditions. Furthermore, it is observed that the influence of dielectric constants on the critical buckling load is more than those of others.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1747-1751
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• 2000

It is well known that acoustic signals, even measured in an anechoic chamber, can be contaminated due to the wall interference. Therefore, it is necessary to reconstruct the original signal from the measured data, which is very critical for the case of measurement of source signal in a water tunnel. In this thesis, new methods for the reconstruction of sound sources are proposed and validated by using Boundary Element Method from measured data in a closed space. The inverse Helmholtz integral equation and its normal derivative are used for the reconstruction of sound sources in a closed space. An arbitrary Kirchhoff surface over the sources is proposed to solve the surface information instead of direct solution for the source. Although sound sources are not directly known by the inverse Helmholtz equation, the original sound source of pressure-field outside of the wall can be indirectly obtained by using this new method.

• Korean Journal of Head & Neck Oncology
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• v.26 no.2
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• pp.204-211
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• 2010

Background and Objectives : Boundary detection and drawing are essential in 3D reconstruction of neck mass. Manual tracing methods are popular for drawing head and neck tumor. To improve manual tracing, circular boundaries overlapping was tried. Materials and Methods : Twenty patients with neck tumors were recruited for study. Representative frames were examined for shapes of outline. They were all single closed curves. Circular boundaries were added to fill the outlines of the tumors. Inserted circles were merged to form single closed curves(Circular boundary overlapping, CBO). After surface rendering, 3 dimensional images with volumes and area data were made. Same procedures were performed with manual tracing from same cases. 3D images were compared with surgical photographs of tumors for shape similarity by 2 doctors. All data were evaluated with Mann-Whitney test(p<0.05). Results : Shapes of boundaries from CBO were similar with boundaries from manual tracing. Tumor outlines could be filled with multiple circular boundaries., While both boundary tracing gave same results in small tumors, the bigger tumors showed different data. Two raters gave the similar high scores for both manual and CBO methods. Conclusion : Circular boundary overlapping is time saver in 3 dimensional reconstruction of CT images.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.83-90
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• 2000

We establish a sufficient condition for a simple closed curve in the Euclidean plain $\mathbb{R}^2$, the unit sphere $S^2$ or the hyperbolic plane $H^2$ to be the boundary of a metric ball.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.535-549
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• 2019

This study aimed to develop a high-order shear deformation theory to predict the free vibration of hybrid cross-ply laminated plates under different boundary conditions. The equations of motion for laminated hybrid rectangular plates are derived and obtained by using Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle-ply laminates are obtained by using Navier's solution. To assess the validity of our method, we used the finite element method. Firstly, the analytical and the numerical implementations were validated for an antisymmetric cross-ply square laminated with available results in the literature. Then, the effects of side-to-thickness ratio, aspect ratio, lamination schemes, and material properties on the fundamental frequencies for different combinations of boundary conditions of hybrid composite plates are investigated. The comparison of the analytical solutions with the corresponding finite element simulations shows the good accuracy of the proposed analytical closed form solution in predicting the fundamental frequencies of hybrid cross-ply laminated plates under different boundary conditions.