材料非线性对复合材料层合板热自由边界效应的影响

本文用准三维有限元法研究了材料非线性对复合材料层合板热自山边界效应的影响,给出了修正型Hahn-Tsai非线性应力-应变关系的三维形式。由本文非线性分析方法得到的层间应力与以往由线性分析方法得到的层间应力做了比较,结果表明:材料非线性能显著降低层间剪应力的集中程度,但对层间正应力影响不太明显。     

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

In this paper, we study multiplicity of positive solutions for a class of Kirchhoff type of equations with the nonlinearity containing both singularity and critical exponents. We obtain two positive solutions via the variational and perturbation methods.     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

Tunneling-induced enhancement of self-Kerr nonlinearity in asymmetric quantum wells

We propose an asymmetric AlGaAs/GaAs double quantum wells (QWs) structure for realizing the enhancement of self-Kerr nonlinearity. It is found, with resonant tunneling, that the self-Kerr nonlinearity can be clearly enhanced, while the absorption of probe field is very small and can be safely neglected. We attribute the enhancement of self-Kerr nonlinearity mainly to the constructive interference induced by resonant tunneling.     

Atomistic–continuum coupled model for nonlinear analysis of single layer graphene sheets

In this paper, atomistic–continuum coupled model for nonlinear flexural response of single layer graphene sheet is presented considering von-Karman geometric nonlinearity and material nonlinearity due to atomic interactions. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that of at atomic level through Cauchy–Born rule. Strain and curvature dependent tangent in-plane extensional, bending–extension coupling, bending stiffness matrices are derived from strain energy density function constructed through Tersoff–Brenner potential. The finite element method is used to discretize the graphene sheet at continuum level and nonlinear bending response with and without material nonlinearity is studied. The present results are also compared with Kirchhoff plate model and significant differences at higher load are observed. The effects of other parameters like number of atoms in the graphene sheet, boundary conditions on the central/maximum deflection of graphene sheet are investigated. It is also brought out that the occurrence of bond length exceeding cutoff distance initiates at corners for CFCC, CFCF, SFSS, SFSF graphene sheets and near center for SSSS and CCCC graphene sheets.     

Features of nonlinear deformation and critical states of shell systems with geometrical imperfections

Results from theoretical and experimental investigations into the nonlinear deformation (geometrical nonlinearity, plastic deformation, creep) and critical states (limit loads, buckling) of shell-frame systems with geometric imperfections are analyzed. The presence of prestresses is allowed. Diverse effects of various geometrical imperfections and plastic deformation for different load histories are studied. New qualitative effects of the mutual influence of these factors are established. Relevant experimental results are outlined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 3–47, December 2006.     

基于行波管螺旋导电面模型的空间电荷场研究

通过分析行波管螺旋导电面模型中的电磁场，给出了色散和耦合阻抗计算公式，并深入研究了非线性理论中的空间电荷降低因子.结果表明，螺旋导电面模型相对理想导电圆筒中的空间电荷降低因子在较高频段变化不大.空间电荷降低因子的变化反映了螺旋线外电磁场对电子注的作用，同样的慢波结构，较高频率的电磁场应有较大的影响.因此，使用螺旋导电面模型在较高频段计算空间电荷降低因子是不合适的. 关键词： 行波管 非线性 螺旋导电面 空间电荷降低因子 色散 耦合阻抗     

Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

A semi-discrete dynamic model has been developed for the formation of the spatial structure of wave fields in a medium with cubic nonlinearity. The characteristic features of self-focusing and conical modulation of intense Bessel-Gaussian light beams of different orders have been studied in different stages of their evolution during propagation. It has been shown that as a result of nonlinear refraction, in the far zone wave structures are formed consisting of three spatially separated conical beams. Increasing the cone angle of the wave vectors leads to a decrease in the effect of conical modulation of the radiation, and improves the structural stability of the beam. The considered self-modulation effects can be used for passive limiting of the laser radiation power. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 626–630, September–October, 2006.     

非线性演化方程的孤立波解

用齐次平衡原则和辅助微分方程方法得到了6个重要的n次非线性演化方程的孤立波解.辅助微分方程方法的主要思想是借助简单的可解微分方程的解去构造复杂的非线性演化方程的行进波解.这里简单的可解微分方程称为辅助微分方程.本文使用的辅助方程有双曲正割幂型解或双曲正切幂型解.     

Propagation of optical beams in strongly nonlocal nonlinear media

The propagation of arbitrary laser beams in strongly nonlocal nonlinear media is investigated based on the ABCD matrix. The second-order moment beam width and the mean curvature radius are derived under the off-waist incident condition.