• Current Optics and Photonics
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• 제5권2호
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.83-102
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• 2015

The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge-Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.

• Steel and Composite Structures
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• 제33권2호
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• pp.307-318
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• 2019

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

• 한국광학회지
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• 제13권5호
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• pp.400-407
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• 2002

2차원 공간 고립파는 비선형 굴절률이 빛의 세기에 따라 일정한 값에 수렴하는 포화 매질에서 안정적으로 전파될 수 있다. 그러나 빛의 세기가 크지 않은 경우, 5차 비선형 굴절률이 음수인 매질은 포화 매질의 특성을 가지므로 2차원 공간 고립파가 전파될 수 있다. 2차원 비선형 슈뢰딩거 방정식의 전산 시늉을 통하여 빛의 세기가 크지 않은 경우 가우시안 빛살이 5차 비선형 매질을 전파하는 과정을 조사하였다. 그 결과 자체 포획 일률로 입사시킬 때 가장 안정적으로 2차원 공간 고립파가 전파한다는 것을 알 수 있었다. 또한 위상차가 180$^{\circ}$인 두 공간 고립파를 0.05$^{\circ}$의 충돌각으로 충돌시키면서 한 쪽 고립파의 입사 일률을 조절한다면 출력단에서 두 공간 고립파의 완전 광 스위칭이 가능함을 확인하였다.

• 한국광학회:학술대회논문집
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• 한국광학회 2002년도 하계학술발표회
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• pp.94-95
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• 2002

Photonic crystal (PC) has special interests for their promising applications in three-dimensional photon control and integrated devices. In a nonlinear photonic crystal (NPC), optical intensity in a defect layer is greatly increased due to the location function of NPC and nonlinearity. The nonliearity of the defect layer is very much enhanced because the group velocity is reduced and the interaction time between light and nonlinear medium in the defect layer is enlarged. (omitted)

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 춘계학술대회 논문집
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• pp.348-352
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• 1995

In the conventional linear elasticity, ultrasonic velocity is determined by elastic modulus and density of te medium which ultrasonic wave propagates through. But, practical ultrsonic wave depends on the stress acting in the medium, and as the stress increases such dependency becomes nonlinear. This nonlinear dependencyof ultrasonic velocity on stress can be identified by using nonlinear elastic modulus up to 4th order. In thid paper, with the above background relationships between nonlinear elastic modulus and the internalstatus of materials, normal, plastic deformed or heat stressed, are discussed. For this purpose, a new type of measuring system extended from the general nondestructive UT(ultrasonic test) equipment is constructed.

• Structural Engineering and Mechanics
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• 제53권3호
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• pp.497-517
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• 2015

In this study, nonlocal nonlinear buckling analysis of embedded polymeric temperature-dependent microplates resting on an elastic matrix as orthotropic temperature-dependent elastomeric medium is investigated. The microplate is reinforced by single-walled carbon nanotubes (SWCNTs) in which the equivalent material properties nanocomposite are estimated based on the rule of mixture. For the carbon-nanotube reinforced composite (CNTRC) plate, both cases of uniform distribution (UD) and functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. The small size effects of microplate are considered based on Eringen's nonlocal theory. Based on orthotropic Mindlin plate theory along with von K$\acute{a}$rm$\acute{a}$n geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the buckling load of system. The effects of different parameters such as nonlocal parameters, volume fractions of SWCNTs, distribution type of SWCNTs in polymer, elastomeric medium, aspect ratio, boundary condition, orientation of foundation orthtotropy direction and temperature are considered on the nonlinear buckling of the microplate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the buckling load.

• Structural Engineering and Mechanics
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• 제59권1호
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• pp.153-186
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• 2016

This paper addresses temperature-dependent nonlinear vibration and instability of embedded functionally graded (FG) pipes conveying viscous fluid-nanoparticle mixture. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Reddy third-order shear deformation theory (RSDT) of cylindrical shells are developed using the strain-displacement relations of Donnell theory. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on energy method and Hamilton's principal, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as mode numbers, nonlinearity, fluid velocity, volume percent of nanoparticle in fluid, gradient index, elastic medium, boundary condition and temperature gradient are discussed. Numerical results indicate that with increasing the stiffness of elastic medium and decreasing volume percent of nanoparticle in fluid, the frequency and critical fluid velocity increase. The presented results indicate that the material in-homogeneity has a significant influence on the vibration and instability behaviors of the FG pipes and should therefore be considered in its optimum design. In addition, fluid velocity leads to divergence and flutter instabilities.

• Structural Engineering and Mechanics
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• 제78권1호
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• pp.103-116
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• 2021

In this work, a model of a functionally graded (FG) nanotube conveying fluid embedded in an elastic medium is developed based on the nonlocal strain gradient theory (NSGT) in conjunction with Euler-Bernoulli beam theory (EBT). The main objective of this research is to investigate the nonlinear vibration and stability analysis of fluid-conveying nanotubes. The governing equations of motion are derived by means of Hamiltonian principle. The analytical expressions of nonlinear frequencies and critical flow velocities for two different types of boundary conditions including pinned-pinned (P-P) and clamped-clamped (C-C) conditions are obtained by employing Galerkin method as well as Hamiltonian Approach (HA). Comparison of the obtained results with the published works show the acceptable accuracy of the current solutions. The effects of the power-law index, the nonlocal and material length scale parameters and the elastic medium on the stability and nonlinear responses of FG nanotubes are thoroughly investigated and discussed.

• Structural Engineering and Mechanics
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• 제68권1호
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• pp.103-119
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• 2018

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.