• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.9
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• pp.881-887
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple rectangular holes. Even though there have been many methods developed for the addressed problem, they suffer from computational time. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a rectangular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

• Bulletin of the Korean Chemical Society
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• v.35 no.12
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• pp.3459-3464
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• 2014

Synthesis and structural characterization of mercury(II) halides and perchlorate complexes (1-4) of bis-$OS_2$-macrocycle (L) are reported. L reacts with mercury(II) chloride and bromide to yield an isostructural 2D coordination polymers with type $[Hg(L)X_2]_n$ (1: X = Cl and 2: X = Br). In 1, each Hg atom which lies outside the cavity is six-coordinate with a distorted octahedral geometry, being bound to four adjacent ligands via monodentate Hg-S bonds and two remaining sites are occupied by two terminal chlorido ligands to form a fishnet-like 2D structure. When reacting with mercury(II) iodide, L afforded a 1D coordination polymer $\{[Hg_2(L)I_4]{\cdot}CHCl_3\}_n$ (3) in which each exocyclic Hg atom is four-coordinate, being bound to two sulfur donors from different ligands doubly bridging the ligand molecules in a head-to-tail mode. The coordination sphere in 3 is completed by two iodo terminal ligands, adopting a distorted tetrahedral geometry. On reacting with mercury(II) perchlorate, L forms solvent-coordinated 1D coordination polymer $\{[Hg_2(L)(DMF)_6](ClO_4)_4{\cdot}2DMF\}_n$ (4) instead of the anion-coordination. In 4, the Hg atom is five-coordinate, being bound to two sulfur donors from two different ligands doubly bridging the ligand molecules in a side-by-side mode to form a ribbon-like 1D structure. The three remaining coordination sites in 4 are completed by three DMF molecules in a monodentate manner. Consequently, the different structures and connectivity patterns for the observed exocyclic coordination polymers depending on the anions used are influenced not only by the coordination ability of the anions but also by anion sizes.

• Atmosphere
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• v.26 no.3
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• pp.473-482
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• 2016

An accurate determination of turbulent fluxes over an urban area is a challenging task due to its morphological diversity and associated flow complexity. In this study, an eddy covariance (EC) method is applied over a highly heterogeneous urban area in a small city (Gongju), South Korea to investigate the quantitative influence of 'coordinate tilt' in determining the turbulent fluxes of sensible heat, latent heat, momentum, and carbon dioxide mass. Two widely-used coordinate transform methods are adopted and applied to eight directional sections centered on the site to analyze a 1-year period EC measurement obtained from the urban site: double rotation (DR) and planar fit (PF) transform. The results show that mean streamline planes determined by the PF method are distinguished from the sections, representing morphological heterogeneity of the site. The sectional pitch angles determined by the DR method also compare well with those in the PF method. Both the PF and DR methods show large variabilities in the determined streamline planes at each directional section, implying that flow patterns may form in a complicate way due to the surface heterogeneity. Resulting relative differences of the turbulent fluxes, defined by $(F_{DR}-F_{PF})/F_{DR}$, are found on average +13% in sensible heat flux, +21% in latent heat flux, +37% in momentum flux, and +26% in carbon dioxide mass flux, which are larger values than those reported previously for fairly homogeneous natural sites. The fractional differences depend significantly on wind direction, showing larger differences in northerly winds at the measurement site. It is also found that the relative fractional differences are negatively correlated with the mean wind speed at both stable/unstable atmospheric conditions. These results imply that EC turbulent fluxes determined over heterogeneous urban areas should be carefully interpreted with considering the uncertainty due to 'coordinate tilt' effect in their applications.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.2079-2087
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• 1993

The effects of subcooling and natural convection are studied numerically on the melting process of an initially subcooled phase-change medium filled inside a horizontal circular cylinder. It is postulated that melting continues with the tube wall kept at a constant temperature and with the unmelted solid core fixed. Primary emphasis is placed on the evolution of interface morphology, the local/overall heat transfer rate at the tube wall and at the interface, and the structure of natural convection. The numerical results are mainly presented in terms of the Rayleigh and subcooling numbers. As the degree of subcooling intensifies, the melting rate and the movement of the interface are impeded but the interfaces are of similar shape with the passage of time. The heat transfer characteristics are found to be mostly governed by the formation pattern of natural convection in the liquid phase. Good agreement with available experimental data is found.

• Structural Engineering and Mechanics
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• v.28 no.1
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• pp.53-67
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• 2008

Anisotropic materials are increasingly required in modern technological applications. Certainly, civil, mechanical and naval engineers frequently deal with the situation of analyzing the dynamical behaviour of structural elements being composed of such materials. For example, panels of anisotropic materials must sometimes support electromechanical engines, and besides, holes are performed in them for operational reasons e.g., conduits, ducts or electrical connections. This study is concerned with the natural frequencies and normal modes of vibration of rectangular anisotropic plates supported by different combinations of the classical boundary conditions: clamped, simply - supported and free, and with additional complexities such holes of free boundaries and attached concentrated masses. A variational approach (the well known Ritz method) is used, where the displacement amplitude is approximated by a set of beam functions in each coordinate direction corresponding to the sides of the rectangular plate. Consequently each coordinate function satisfies the essential boundary conditions at the outer edge of the plate. The influence of the position and magnitude of both hole and mass, on the natural frequencies and modal shapes of vibration are studied for a generic anisotropic material. The classical Ritz method with beam functions as spatial approximation proved to be a suitable procedure to solve a problem of such analytical complexity.

• Journal of Korean Society of Steel Construction
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• v.19 no.6
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• pp.599-610
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• 2007

In this paper, we described a co-rotational formulation for the geometrical nonlinear analysis of three-dimensional frames. We suggested a new concept called the Zero-Twist-Section Condition (ZTSC) to decide the element coordinate system consistently. According to the ZTSC procedure, it is possible to obtain an element coordinate system and natural deformations consistently when finite displacements and rotations are induced in an element. Based on the developed procedure, numerical examples are investigated to calculate natural rotations while finite displacements are imposed on an element. Also, the developed co-rotational procedure gives accurate results in the analysis of post-buckling problems with finite rotations.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1043-1052
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• 2014

This paper deals with in-plane free vibrations of the horseshoe circular arch. Simultaneous ordinary differential equations governing free vibration of the arch are derived with respect to the radial and tangential deformations. Particularly, differential equations are obtained under the arc length coordinate rather than the angular one in order to extend the horseshoe arch whose subtended angle is greater than ${\pi}$ radians. The differential equations are numerically solved for calculating the natural frequencies accompanying with the corresponding mode shapes. In parametric studies, effects of the rotatory inertia, slenderness ratio and circumferential arc length ratio on frequency parameters are extensively discussed.

• Journal of Mechanical Science and Technology
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• v.19 no.12
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• pp.2187-2196
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• 2005

In this paper, the stiffness and the mass matrices for the in-plane motion of a thin circular beam element are derived respectively from the strain energy and the kinetic energy by using the natural shape functions of the exact in-plane displacements which are obtained from an integration of the differential equations of a thin circular beam element in static equilibrium. The matrices are formulated in the local polar coordinate system and in the global Cartesian coordinate system with the effects of shear deformation and rotary inertia. Some numerical examples are performed to verify the element formulation and its analysis capability. The comparison of the FEM results with the theoretical ones shows that the element can describe quite efficiently and accurately the in-plane motion of thin circular beams. The stiffness and the mass matrices with respect to the coefficient vector of shape functions are presented in appendix to be utilized directly in applications without any numerical integration for their formulation.

• 한국신재생에너지학회:학술대회논문집
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• 2005.06a
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• pp.534-537
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• 2005

Free Vibration Analysis using Non-dimensional Dynamic Influence Function (NDIF) is extended to arbitrarily shaped plates including polygonal plates. Since the corners of polygonal plates have indefinite normal directions and additional boundary conditions related to a twisting moment at a corner along with moment and shear force zero conditions, it is not easy to apply the NDIF method to polygonal plates wi th the free boundary condition. Moreover, owing to the fact that the local polar coordinate system, which has been introduced for free plates with smoothly varying edges, cannot be employed for the straight edges of the polygonal plates, a new coordinate system is required for the polygonal plates. These problems are solved by developing the new method of modifying a corner into a circular arc and setting the normal direction at the corner to an average value of normal direct ions of two edges adjacent to the corner. Some case studies for plates with various shapes show that the proposed method gives credible natural frequencies and mode shapes for various polygons that agree well with those by an exact method or FEM (ANSYS).

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.455-462
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• 1991

This paper present an analysis method of crankshaft of four cylinder internal combustion engine for studying dynamic characteristics of the shaft. For simple analysis, uniform sections of journal, pin and arm parts were assumed. Transfer Matrix Method was used, considering branched part and coordinate transformation part. Natural frequencies, natural modes and transfer functions of crank shaft were investigated based upon the Timosenko beam theory: It was shown that the calculated natural frequencies, modeshapes agree well with the experimental results.