• Steel and Composite Structures
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• v.41 no.6
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• pp.821-829
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• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• Current Optics and Photonics
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• v.2 no.6
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• pp.525-531
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• 2018

The effect of eccentricity on dispersion and nonlinear properties of a photonic crystal fiber having elliptical air holes is investigated using a fully vectorial effective index method. It is found that the effective refractive index increases with increase of eccentricity. The dependence of dispersion and nonlinear properties of the PCF on the eccentricity of the air hole is investigated. It is revealed that eccentricity of the air hole affects the zero dispersion wavelength. Further, the nonlinear properties such as mode field area, nonlinear coefficient and self phase modulation of the Photonic crystal fibers are analyzed. The mode field area increases and the nonlinear coefficient decreases with increase in eccentricity. The variation of the self phase modulation with elliptical air hole is also discussed.

• Current Optics and Photonics
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• v.5 no.2
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• pp.191-197
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• 2021

The anomalous propagation characteristics of a single Airy beam in nonlocal nonlinear medium are investigated by utilizing the split-step Fourier-transform method. We show that besides the normal straight propagation trajectory, the breathing solitons formed by the interaction between Airy beam and nonlocal nonlinear medium can propagate along the sinusoidal trajectory, and the anomalous trajectory can be modulated arbitrarily by altering the initial amplitude and the nonlocal nonlinear coefficient. In addition, the initial amplitude and the nonlocal nonlinear coefficient can have inverse impacts on the formation and transformation of the equilibrium state of spatial solitons, when the two parameters are larger than certain values. Therefore, the reversible transformation of the evolution dynamics of two soliton states can be realized by adjusting those two parameters properly. Finally, it is shown that the propagation properties of the solitons formed by the interaction between Airy beam and nonlocal nonlinear medium can be controlled arbitrarily, by adjusting the distribution factor and nonlocal coefficient.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.277-288
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• 2010

We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.11 no.11
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• pp.969-974
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• 1998

The effects of $La_2O_3$on the microstructure and electrical characteristics of Pr-based ZnO varistors were investigated. The average grain size increased in the range of 21.9~56.3$\mu$ m with increasing $La_2O_3$additive content(0.0~2.0 mol%). La was, of course grain boundary, largely segregated at the nodal point. As $La_2O_3$additive content increases, threshold voltage and nonlinear coefficient decreased and leakage current increased. In particular, 2.0 mol% $La_2O_3$-added varistor exhibited low threshold voltage 17.0V/mm and nonlinear coefficient of about 6. Based on these results, this varistor can be said to be used as low-voltage varistor, if nonlinear coefficient is somewhat improved forward.

• Proceedings of the KIEE Conference
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• 1999.07d
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• pp.1692-1695
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• 1999

The nonohmic characteristics of ZnO-$Pr_6O_{11}$-CoO-based ceramic varistor doped with $Dy_2O_3$ in the range $0.0\sim2.0mol%$ sintered at $1300^{\circ}C$ and $1350^{\circ}C$ were investigated. 98.5 ZnO-$0.5Pr_6O_{11}$-1.0CoO varistor sintered at $130^{\circ}C$ exhibited higher nonlinear coefficient of 36 than the established Pr-based varistor. The four-component-system varistor such as 96.5 ZnO-$0.5Pr_6O_{11}$-1.0CoO-$2.0Dy_2O_3$ exhibited very highly nonohmic characteristics, which has nonlinear coefficient of 53.9. 98.5ZnO-$0.5Pr_6O_{11}$-1.0CoO varistor sintered at $1350^{\circ}C$, in contrast with that of $1300^{\circ}C$, exhibited approximately ohmic characteristics but nonlinear coefficient of varistor doped with 0.5mol% $Dy_2O_3$ showed higher nonlinear coefficient of probably 35. Consequently, it can be confirmed that $Dy_2O_3$ acted as additive of improvement on nonlinear coefficient. It is estimated that $Dy_2O_3$ will be used as additive of improvement on nonlinear coefficient to develop a goof ZnO varistor.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.379-391
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• 2015

We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

• Proceedings of the KIEE Conference
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• 2000.07c
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• pp.1617-1619
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• 2000

In this study the nonlinear dielectric properties of amorphous copolymers were analyzed by the related nonlinear dielectric theory. The theory is related to the cooperated dipoles and the number of the dipoles. The relation between the polarization coefficient $R_p$ and the nonlinear coefficient $R_s$ was deduced under the assumption of isotropic media.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.65-75
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• 2011

We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the Leray-Schauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.

• Journal of the Korean Vacuum Society
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• v.7 no.s1
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• pp.149-155
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• 1998

The linear electro-optic (EO) effect is one of the second-order nonlinear optical effects existing in a noncentrosymmetric macroscopic system. In a polymer thin film, the noncentrosymmetry is achieved by electric field poling. The magnitude of the linear EO response is determined through the orientational distribution function of hyperpolarizable molecular dipoles. The relation between the linear EO coefficient and the second-order nonlinear optical susceptibility is explained. Three different methods of measuring the linear EO coefficient of a poled nonliner optical polymer thin film are introduced and discussed. All of them make use of the interferometric technique, the difference being in the optical parameters which are interfering.