• Journal of KSNVE
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• v.8 no.6
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• pp.1144-1149
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• 1998

A two degree-of-freedom model of suspended cables is studied for forced resonant response. The method of averaging is used to obtain first-order approximations to the response of the system. A bifurcation analysis of the averaged system is performed in the case of 2-to-1 internal resonance. Nonlinear coupled-mode motions are found to bifurcate from single-mode responses and further bifurcate to limit cycle motions via Hopf bifurcations. The limit cycle solutions undergo period doubling bifurcations to chaos.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.241-252
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• 2008

By means of a Riccati transform and averaging technique some oscillation criteria are established for perturbed nonlinear differential equations of second order $(P_1)\;(p(t)x'(t))'+q(t)|x({\phi}(t)|^{{\alpha}+1}sgnx({\phi}(t))+g(t,\;x(t))=0$ $(P_2)$ and $(P_3)$ satisfying the condition (H). A comparison theorem and examples are given.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2835-2838
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• 2003

We study the characteristics of oscillating in non-autonomous condition and the conducted noise generation in a RL-photocoupler circuit. This circuit may be shown a period-doubling and a chaos dynamics under any specific conditions of input circuit. But, the relationship between input signals and output signals is different according to the amplitude of driving input voltage. Then, the oscillation noise was analyzed with respect to both the frequency and the amplitude of an external ac signal and do values. The results show that the noise-induced oscillations for falling and rising cycles induced by kick-back effect in an inductor, nonlinear capacitance, nonlinear resistance and charge storage time in a diode and an LED. We also compared the simulation with the experimental results.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.2
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• pp.140-147
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• 2008

This paper describes a Neural Network based PD control scheme for motion control of pneumatic servo cylinder. Pneumatic systems have inherent nonlinearities such as compressibility of air and nonlinear frictions present in cylinder. The conventional linear controller is limited in some applications where the affection of nonlinear factor is dominant. A self-excited oscillation method is applied to derive the dynamic design parameters of linear model. Based on the parameters thus identified, a PD feedback compensator is designed first and then a neural network is incorporated. The experiments of a trajectory tracking control using the proposed control scheme are performed and a significant reduction in tracking error is achieved by comparing with those of a PD control.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.659-674
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• 2010

This paper is concerned with the asymptotic behavior of solutions of the second-order nonlinear perturbed dynamic equation $$(r(t)x^{\Delta}(t))^{\Delta}\;+\;F(t,\;x^{\sigma}))=G(t,\;x^{\sigma},\;(x^{\Delta})^{\sigma})$$ on a time scale $\mathbb{T}$. By using a new technique we establish some sufficient conditions which ensure that every solution oscillates or converges to zero. Our results improve the known oscillation results on the literature for the perturbed dynamic equations on time scales. Some examples illustrating our main results are given.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.593-611
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• 2008

Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.12
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• pp.1880-1885
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• 2012

Nonlinear dynamical behaviors in thermionic low pressure discharge are investigated using a particle-in-cell(PIC) simulation. An electrostatic PIC code is developed to model the plasma discharge system including the kinetic effects. The elastic collision, excitation collision, ionization collision, and electron-ion recombination collision are considered in this code. The generated electrons and ions are traced to analyze physical characteristics of the plasma. The simulation results show that the nonlinear oscillation structures are observed for cold plasma in the system and the similar structures are observed for warm plasma with a shift in values of the bifurcation parameter. The detailed oscillation process can be subdivided into three distinct mode; anode-glow, temperature-limited, and double-layer modes.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.6 s.249
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• pp.523-530
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• 2006

One of the fascinating prospects is the possibility of new hydrodynamics technology on micro-scale system since oscillations of micro-droplets are of practical and scientific importance. It has been widely conceived that the lowest oscillation mode of a pendant droplet is the longitudinal vibration, i.e. periodic elongation and contraction along the longitudinal direction. Nonlinear and forced oscillations of supported viscous droplet were focused in the present study. The droplet has a free contact line with solid plate and inviscid fluid. Natural frequencies of a pendant droplet have been investigated experimentally by imposing the acoustic wave while the frequency is being increased at a fixed amplitude. It is found that a pendant droplet shows the resonant behaviors at each mode similar to the theoretical analysis. The rotation of the droplet about the longitudinal axis is the oscillation mode of the lowest resonance frequency. This rotational mode can be invoked by periodic acoustic forcing and is analogous to the pendulum rotation. It is also found that the natural frequency of a pendant droplet is independent of the drop density and surface tension but inversely proportional to the square root of the droplet size.

• Wind and Structures
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• v.19 no.3
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• pp.233-247
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• 2014

Vortex-induced oscillation is a type of aeroelastic phenomenon, to which extended structures such as long-span bridges are most susceptible. The vortex-induced vibration (VIV) behaviors of a concerned bridge were investigated conventionally in virtue of wind tunnel tests on string-mounted sectional models. This necessitates the building of a linkage between the response of the sectional model and that of the prototype structure. Although many released literatures have related to this issue and provided suggestions, there is a lack of consistency among them. In this study, some theoretical models describing the vortex-induced structural motion, including the linear empirical model, the nonlinear empirical model and the modified (or generalized) nonlinear empirical model, are firstly reviewed. Then, the concept of equivalent mass density is introduced based on the principle that an equal input of energy should result in identical structural amplitudes. Based on these, the theoretical linkages between the amplitude of a section model and that corresponding to the prototype bridge are discussed with different analytical models. Theoretical derivation indicates that such connections are dependent mainly on two factors, one is the presupposed shape of deformation, and the other is the theoretical VIV model employed. The theoretical analysis in this study shows that, in comparison to the nonlinear empirical models, the linear one can result in obvious larger estimations of the full bridges' responses, especially in cases of cable-stayed bridges.