• Coupled systems mechanics
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• v.11 no.6
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• pp.485-504
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• 2022

This paper presents nonlinear oscillations of a carbon nanotube reinforced composite beam subjected to lateral harmonic load with damping effect based on the modified couple stress theory. As reinforcing phase, three different types of single walled carbon nanotubes distribution are considered through the thickness in polymeric matrix. The non-linear strain-displacement relationship is considered in the von Kármán nonlinearity. The governing nonlinear dynamic equation is derived with using of Hamilton's principle.The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The frequency response equation and the forced vibration response of the system are obtained. Effects of patterns of reinforcement, volume fraction, excitation force and the length scale parameter on the nonlinear responses of the carbon nanotube reinforced composite beam are investigated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.5 no.3
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• pp.183-192
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• 1981

The present study gives an apprximate equation of circular cylindrical shell on the basis of Flugges's exact theory. The longitudinal bending moment .MU.$\_$x/ and circumferential strain .epsilon.$\_$.theta. are assumed to be small to be small and have been neglected. The governing equation of the cylindrical shell, which is generaly presented as 8th order partial differential equation, is reduced into a 4th order partial differential equation for axial coordinate. To verify the validity and accuracy of this approximate theory, the cantilever cylindrical shell subjected to a concentrated load is analyzed. The maximum errors of longitudinal stress and deflection are about 10 percent compared with the analysis by flugge's theory and are about 15 percent with experimental results.

• Journal of the Korean Applied Science and Technology
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• v.23 no.3
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• pp.185-191
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• 2006

It is desirable to have an accurate expression on the temperature dependence of surface(or interfacial) tension ${\sigma}$, because most of the interfacial thermodynamic functions can be derived from it. There have been proposed several equations on the temperature dependence of the surface tension, ${\sigma}(T)$. Among them $E{\ddot{o}}tv{\ddot{o}}s$ equation and the one modified by Katayama, which is called Katayama equation, for improving accuracies of $E{\ddot{o}}tv{\ddot{o}}s$ equation close to critical points, have been most well-known. In this article Katayama equation is interpreted on the basis of the cell model to understand the nature of the equation. The cell model results in an expression very similar to Katayama equation. This implies that, although $E{\ddot{o}}tv{\ddot{o}}s$ and Katayama equations were obtained on the basis of experimental results, they have a sound theoretical background. The Katayama equation is also modified with the phase volume replaced with a critical scaling expression. The modified Katayama equation becomes a power-law equation with the exponent slightly different from the value obtained by critical-scaling theory. This implies that Katayama equation can be replaced by a critical-scaling equation which is proven to be accurate.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2017.11a
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• pp.27-29
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• 2017

Container terminals in Northern Vietnam have recorded an impressive development in recent years. This development, however, also raises a fierce competition among local container terminals to attract customers. Beside the handling charges, the vessels' waiting cost is also an important factor that drive the opinion of users in choosing appropriate terminal. This research plans to estimate the waiting cost in different container terminals in Northern Vietnam by building regression equation that describe the relationship between the rate of throughput/capacity and waiting cost/TEU. Queuing theory with the application of Poisson distibution is used to estimate the waiting time of arrival vessels and uncertainty theory is applied to estimate the vessel's daily expenses. Previous studies suggested two different formation of the equation and according to the research results, cubic equation is more suitable in the given case. The research results are also useful for further research which require calculation of waiting cost per TEU in each container terminal in Northern Vietnam.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.195-204
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• 2014

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.267-276
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• 2019

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

• Journal of Korean Society of Water and Wastewater
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• v.21 no.2
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• pp.253-258
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• 2007

The adsorption capacity of bone char for lead, cadmium and zinc was studied in both single and binary multiple component systems. Equilibrium experimental studies have been performed to determine the sorption capacity of bone char for each metal ion. These have been analysed using single and multi-component equilibrum models. The results show that the sorption of metal ions for multi-component systems can be predicted reasonably well from the IAS theory with the Langmuir equation, the Freundlich and the Slip equation for metal ions.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay equations and general boundary conditions. The basic new idea of this paper is to Introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.