• Korean Journal of Mathematics
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• v.15 no.2
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• pp.149-165
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• 2007

We investigate the existence of multiple nontrivial solutions $u(x,t)$ for a perturbation $b[({\xi}-{\eta}+2)^+-2]$ of the hyperbolic system with Dirichlet boundary condition $$(0.1)\;L{\xi}={\mu}[({\xi}-{\eta}+2)^+-2]\;in\;({-{\frac{{\pi}}{2}}},{\frac{{\pi}}{2}}){\times}\mathbb{R},\\L{\eta}={\nu}[({\xi}-{\eta}+2)^+-2]\;in\;({-{\frac{{\pi}}{2}}},{\frac{{\pi}}{2}}){\times}\mathbb{R},$$, where $u^+$=max{u,o}, ${\mu}$, ${\nu}$ are nonzero constants. Here L is the wave operator in $\mathbb{R}^2$ and the nonlinearity $({\mu}-{\nu})[({\xi}-{\eta}+2)^+-2]$ crosses the eigenvalues of the wave operator.

• Smart Structures and Systems
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• v.21 no.1
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• pp.113-122
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• 2018

In this article, an exact analytical solution for mechanical buckling analysis of magnetoelectroelastic plate resting on pasternak foundation is investigated based on the third-order shear deformation plate theory. The in-plane electric and magnetic fields can be ignored for plates. According to Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. The von Karman model is exploited to capture the effect of nonlinearity. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical results reveal the effects of (i) lateral load, (ii) electric load, (iii) magnetic load and (iv) higher order shear deformation theory on the critical buckling load have been investigated. These results must be the analysis of intelligent structures constructed from magnetoelectroelastic materials.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.723-732
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• 2007

We investigate the existence of solutions u(x, t) for a perturbation b[$(\xi+\eta+1)^+-1$] of the hyperbolic system with Dirichlet boundary condition (0.1) = $L\xi-{\mu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$, $L\eta={\nu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$ where $u^+$ = max{u,0}, ${\mu},\nu$ are nonzero constants. Here $\xi,\eta$ are periodic functions.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.6
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• pp.138-144
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• 2003

A crack in a ferroelectric ceramic subjected to an electric field is analyzed. The boundary of the electrical saturation zone is estimated based on the finite-width saturation zone model, which is analogous to a finite-width Dugdale zone model for mode III. It is shown that the shape and size of the switching zone depends strongly on the boundary of the electrical saturation zone and the ratio of the coercive electric field to the yield electric field. The crack tip stress intensity factor under small scale conditions is evaluated by employing the model of electric nonlinear domain switching. It is found that fracture toughness of the ferroelectric material may be increased or decreased depending on the material property of electrical nonlinearity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.605-609
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• 1996

Continuous sliding mode control is applied to turning process for cutting force regulation. The highest feedrate compatible with the allowable cutting force is applied in rough cutting process such that maximum productivity is ensured and tool breakage is avoided. The programmed feedrate is overridden after the control algorithm is carried out. However, most CNC lathe manufacturers offer limited number of data bits far feedrate override, thus resulting in nonlinear behavior of the machine tools. Such nonlinearity brings “quantized” effect, and the optimal faedrate is rounded off before being fed into the CNC system. To compensate for this problem, continuous sliding mode control is applied. Conventional switching control law at a sliding surface is replaced by a smooth control interpolation in a selected boundary layer to avoid the excitation of high-frequency dynamics. Simulation results are presented in comparison with those obtained by applying adaptive control.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.11
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• pp.1075-1080
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• 2010

For the aeroelastic analysis of a wing with friction damping, coupled time integration method was used to obtain time responses in the subsonic and transonic regions. To take into account aerodynamic nonlinearity induced by shock wave on the lifting surface, transonic small disturbance equation with in-phase periodic boundary condition was used for unsteady aerodynamic calculation. For 2-DOF airfoil system with displace-dependent friction dampers, the effects of normal load slope and Mach number on flutter boundary were investigated.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.1-6
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• 2007

Two impedance imaging systems of multi-frequency electrical impedance tomography (MFEIT) and magnetic resonance electrical impedance tomography (MREIT) are described. MFEIT utilizes boundary measurements of current-voltage data at multiple frequencies to reconstruct cross-sectional images of a complex conductivity distribution (${\sigma}+i{\omega}{\varepsilon}$) inside the human body. The inverse problem in MFEIT is ill-posed due to the nonlinearity and low sensitivity between the boundary measurement and the complex conductivity. In MFEIT, we therefore focus on time- and frequency-difference imaging with a low spatial resolution and high temporal resolution. Multi-frequency time- and frequency-difference images in the frequency range of 10 Hz to 500 kHz are presented. In MREIT, we use an MRI scanner to measure an internal distribution of induced magnetic flux density subject to an injection current. This internal information enables us to reconstruct cross-sectional images of an internal conductivity distribution with a high spatial resolution. Conductivity image of a postmortem canine brain is presented and it shows a clear contrast between gray and white matters. Clinical applications for imaging the brain, breast, thorax, abdomen, and others are briefly discussed.