• Kyungpook Mathematical Journal
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• 제27권1호
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• pp.35-41
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• 1987

Consider the system (i) x'=Ax. Let ${\Phi}$ be its fundamental matrix solution. If there is w>0 such that A(t+w)-A(t) commutes with ${\Phi}$ for all t, then we call this system a "generalized" Floquet system or a "G. F. system". We show that $A(t+w)-A(t)=B_1$=constant if and only if $A(t)=C+B_1t/w+Q(t)$, Q is periodic of period w>0. For this A(t) We prove that if all eigenvalues of $B_1$ have negative real parts, then the origin is asumptotically stable. We find a growth condition for a continuous D(t) which guarantees that all solutions of z'=[A(t)+D(t)]z are bounded if all solutions of the G. F. system (i) are bounded. Combining the foregoing results yield a class of perturbed G. F. operators all of whose solutions are bounded.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.513-532
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• 2022

This paper deals with the stability of solutions to 𝜓-Hilfer fractional differential systems. We derive the fundamental solution for the system by using the generalized Laplace transform and the Mittag-Leffler function with two parameters. In addition, we obtained some necessary conditions on the stability of the solutions to linear fractional differential systems for homogeneous, non-homogeneous and non-autonomous cases. Numerical examples are also given to illustrate the behavior of solutions.

• 한국전산구조공학회논문집
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• 제20권4호
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• pp.417-425
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• 2007

곡선보(curved beam)의 회전관성(rotatory inertia) 및 전단변형(shear deformation)을 고려한 면외(out-of-plane) 자유진동을 해석하는데 미분구적법(DQM)을 이용하여 고정-고정 경계조건(boundary conditions)과 다양한 굽힘각(opening angles)에 따른 진동수(frequencies)를 계산하였다. DQM의 결과는 엄밀해(efact solution) 또는 다른 수치해석 결과와 비교하였으며, DQM은 적은 요소(grid points)를 사용하여 정확한 해석결과를 보여주었다.

• 한국물환경학회지
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• 제22권1호
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• pp.122-127
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• 2006

Fundamental studies were carried out for an effective removal and recovery of silver from waste photo-developing solution by solvent extraction. The organic solvents examined for silver-extraction were ALIQUAT 336, D2EHPA, KELEX 100, and TBP. ALIQUAT 336, which is an anionic exchanger, was found to be efficient for the extraction of silver and the reason for this was considered to be due to the chloride ion contained in its structure. The extent of silver extraction was examined to increase with the concentration of ALIQUAT 336 until it reached 0.6 M and no more extraction was observed above this concentration. The extraction of silver by ALIQUAT 336 was found to reach its pseudo-equilibrium within a few minutes after the reaction started and additional slight increase in silver extraction was observed until 30 minutes of reaction time. The observed differences in silver extraction for artificial and actual waste solutions were considered to be based upon the different ionic form of silver-containing species in these solutions.

• Structural Engineering and Mechanics
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• 제70권5호
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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.

• Ocean Systems Engineering
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• 제13권2호
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• pp.123-146
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• 2023

In this paper, Moore-Gibson-Thompson theory of thermoelasticity is considered to investigate the fundamental solution and vibration of plane wave in an isotropic photothermoelastic solid. The governing equations are made dimensionless for further investigation. The dimensionless equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature distribution and carrier density distribution). Fundamental solutions are constructed for the system of equations for steady oscillation. Also some preliminary properties of the solution are explored. In the second part, the vibration of plane waves are examined by expressing the governing equation for two dimensional case. It is found that for the non-trivial solution of the equation yield that there exist three longitudinal waves which advance with the distinct speed, and one transverse wave which is free from thermal and carrier density response. The impact of various models (i)Moore-Gibson-Thomson thermoelastic (MGTE)(2019), (ii) Lord and Shulman's (LS)(1967) , (iii) Green and Naghdi type-II(GN-II)(1993) and (iv) Green and Naghdi type-III(GN-III)(1992) on the attributes of waves i.e., phase velocity, attenuation coefficient, specific loss and penetration depth are elaborated by plotting various figures of physical quantities. Various particular cases of interest are also deduced from the present investigations. The results obtained can be used to delineate various semiconductor elements during the coupled thermal, plasma and elastic wave and also find the application in the material and engineering sciences.

• 한국지진공학회논문집
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• 제1권4호
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• pp.59-68
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• 1997

터널 등과 같은 지하구조계를 유한요소법 등의 수치적 방법으로 해석할 경우 인위적인 경제에서 파의 반사가 발생하게 되어 실제 결과의 큰 차이를 발생시킨다. 따라서 동역학적 하중을 받는 지하구조계는 실질적인 반무한 구조계로 고려되어야 한다. 특히 지하구조계는 실제 다층구조로 구성되어 있으므로 이러한 다층문제를 고려할 수 있어야 한다. 이를 위해 본 연구에서는 외부영역 경제적문제로 해석하기 위한 동적 수치기본해를 개발하였다. 주파수영역의 정적인 경우에 대한 엄밀 적분해와 Bessel 함수의 점근식을 이용한 적분을 통해 축대치문제를 2차원 문제로 보다 쉽게 적용할 수 있도록 하였다. 이와 같이 개발된 동적 수치기본해를 경제 적분 방정식에 적용하여 해석한 결과와 기존 해석결과와의 비교를 통해 그 효율성을 입증하였다. 또한 다층지반내 지하구조물에 대해 지반매체의 각 물성 및 공동의 깊이에 따른 민감도분석을 수해하여 지하구조계의 동적 거동특성 파악의 적용성을 다루었다.

• 전산구조공학
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• 제8권4호
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• pp.129-136
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• 1995

본 연구에서는 Biot의 선형압밀이론에 근거한 2차원 압밀문제의 근사해를 구하기 위한 경계요소법을 제시한다. 먼저 선형 압밀문제의 기초미분방정식의 시간의존성을 제거하기 위하여 시간에 대한 Laplace변환을 적용시키고, 변환공간에서의 미분방정식을 대상으로 정식화를 한다. 변환공간에서의 변위와 간극수압에 대한 경계적분방정식계를 유도하고, 변환공간에서의 연성문제에 대한 기본해를 구체적으로 보인다. 변환공간에서의 해를 실공간의 해로 변환하기 위하여 Hosono의 수직 Laplace역변환법을 적용하였으며, 해석예로서 2차원 반무한 지반의 국소재하에 의한 압밀문제를 해석예로 선택하였고, 암밀해와 비교하여 제안해법의 적용성 및 타당성을 보였다.

• 드라이브 ㆍ 컨트롤
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• 제19권1호
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• pp.69-75
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• 2022

This study aimed to develop solutions for the intermittent performance deterioration of self-propelled spinach harvesters through analysis model. The study was conducted in the following manner. First, changes in performance deterioration and surplus flow, which result from oil temperature changes, were analyzed by simulating actual sequential harvesting movements, which involve driving with actuators operated simultaneously, by analysis model developed in a previous study. Second, fundamental solutions for surplus flow problems were presented. Third, the solutions were applied to a virtual environment to present their practicality and quantitative effects. The two solutions based on the study results were as follows. First, a closed center-type directional control valve was applied to the hydraulic circuit. Second, an unloading system was set up through an on-off solenoid valve.