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Inverse method for the reconstruction of refractive index profile and power management in gradient index optical waveguides


Secondary bistable solitons have been calculated for a nonlinear optical inhomogeneous medium with parabolic gradient index and quadratic intensitydependent refractive index change.


Secondary bistable solitons in nonlinear gradient index media


The new possibilities of controlled nonlinear evaluation of short pulses in gradient index optical fibres, connected with the fundamental and higher modes of the fibre geometry and with the pulse envelope are analysed.


The nonlinear dynamical stabilization of pspulses in gradient index optical fibres

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 By introducing displacement functions as well as stress functions, this paper establishes two independent state equations with variable coefficients from the threedimensional dynamic equations of a radially inhomogeneous spherically isotropic elastic medium. Using the laminated approximation theory, one can transfer the state equations to the ones with constant variables in each divided sublayers, of which the solutions can be easily obtained using available matrix theory. The continuity conditions at each... By introducing displacement functions as well as stress functions, this paper establishes two independent state equations with variable coefficients from the threedimensional dynamic equations of a radially inhomogeneous spherically isotropic elastic medium. Using the laminated approximation theory, one can transfer the state equations to the ones with constant variables in each divided sublayers, of which the solutions can be easily obtained using available matrix theory. The continuity conditions at each interface then lead to linear algebraic equations about the state variables only at the inner and outer spherical surfaces. It is found that there exist two independent classes of vibrations. Considering the free conditions at the boundaries, frequency equations are then derived. No matter how many sublayers there are, it is shown that for the first class of vibration, the frequency equation is a firstorder determinant, while for the second class, it is firstorder when n = 0 and secondorder when n > 0 . Numerical calculations are finally presented and discussion on the effect of the material gradient index is also given. Obviously, it is rather straightforward to apply the present method to analyze spherically isotropic laminated spheres. It may be useful in the geodynamic study because the latest geophysical results have shown that the Earth in fact should be modelled as a laminated hollow sphere with spherical isotropy. Since the present method is completely based on the threedimensional elasticity without introducing any assumptions on deformation, the solution could be accurate enough when the shell is divided into a certain number of sublayers. Therefore, the solution can be a benchmark to verify any twodimensional shell theories and/or numerical methods.  通过引入位移函数和应力函数，针对沿径向为非均匀的球面各向同性弹性动力学的基本方程建立了两个解耦的变系数状态方程．利用层合近似理论，将变系数状态方程转化为常系数状态方程，并给出了相应的解．进而利用层间连续条件，得到关于内外球壳表面边界量的相应线性方程．由自由表面条件导出对应两类独立振动的频率方程．最后给出了算例，并讨论了材料梯度指标对球壳两类固有频率的影响．在地球动力学分析中有一定的应用前景．  Based on the threedimensional equations for thermoelasticity and by the introduction of two displacement functions and two stress functions, a secondorder homogeneous state equation and a fourthorder inhomogeneous state equation were derived. A laminate approximation model, for which the plate is divided into a certain number of sufficiently thin layers, was employed. Thus the material constants in any layer can be approximately taken as constant. The thermoelastic analysis of a simply supported transversely... Based on the threedimensional equations for thermoelasticity and by the introduction of two displacement functions and two stress functions, a secondorder homogeneous state equation and a fourthorder inhomogeneous state equation were derived. A laminate approximation model, for which the plate is divided into a certain number of sufficiently thin layers, was employed. Thus the material constants in any layer can be approximately taken as constant. The thermoelastic analysis of a simply supported transversely isotropic functionally graded rectangular plate of arbitrary thickness was analyzed. For a thin plate, compared with the thin plate theory, the good agreement is acquired. The effect of material gradient index on the thermoelastic field was finally discussed. It is found that the effect is different in different intervals of the material gradient index, and the effect on thermal stress is also different from that on displacement even in the same interval of the material gradient index.  直接从三维热弹性力学基本方程出发,通过引入两个位移函数和两个应力函数,导出了一个二阶的齐次状态方程和一个四阶的非齐次状态方程。分析中采用了层合近似模型,即将板划分成厚度足够小的若干薄层,从而可将每一层内的材料常数近似为常数。给出了任意厚度的四边简支横观各向同性功能梯度矩形板的热弹性分析,特别当板较薄时,与薄板理论进行了数值对比,发现两者结果吻合得很好。最后研究了材料梯度指标对热弹性场的影响,结果显示梯度指标对热应力和位移都有着显著的作用:在不同的区间,梯度指标对它们有不同的影响;并且在同一区间,梯度指标对两者的影响程度也有所不同。  For a hybrid rectangular plate comprised of a functionally graded materials substrate and piezoelectric patches perfectly bonded on its top and bottom surfaces as actuators,the equivalent actions were obtained by considering the inverse piezoelectric effect.Based on the classical theory of plate,the equilibrium differential equation was derived for the buckling analysis of thin elastic plate with functionally graded structure considering small deflection.The functionally graded material properties obeyed a power... For a hybrid rectangular plate comprised of a functionally graded materials substrate and piezoelectric patches perfectly bonded on its top and bottom surfaces as actuators,the equivalent actions were obtained by considering the inverse piezoelectric effect.Based on the classical theory of plate,the equilibrium differential equation was derived for the buckling analysis of thin elastic plate with functionally graded structure considering small deflection.The functionally graded material properties obeyed a power law across the thickness.The critical buckling loads were presented for a simply supported rectangular plate made of functionally graded material bonded piezoelectric patches by using bitriangle series expansion method.The numerical examples were given and the influences of the plate aspect ratio and functionally gradient index on the buckling voltage were discussed.These results show that the stability can be controlled effectively by means of regulating the magnitude and direction of voltage applied on actuators.  考虑功能梯度薄板,其上下表面嵌有压电执行元件。根据逆压电效应将电压转换成作用于板上的等效电载荷。假设梯度材料的弹性参数为板厚度方向坐标的幂函数,基于经典板理论,导出了功能梯度弹性薄板小挠度屈曲平衡微分方程。利用双三角级数展开法,得到了四边简支具有压电元件的功能梯度矩形板的临界屈曲载荷,在此基础上通过数值例子讨论了弹性板的几何尺寸、材料梯度指数的变化对临界电压(载荷)的影响。研究结果表明,材料的梯度指数对临界电压有重要影响,并且通过调整作用于执行元件上的电压的大小和方向,可实现对结构稳定性的有效控制。   << 更多相关文摘 
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