Nonlinear natural frequency of shallow conical shells with variable thickness

IntroductionTheplatesandtheshellswithvariablethicknessarewidelyusedinengineering .Theproblemaboutstaticshasbeenstudiedbymanyscholars;therearemanyRefs .[1 -4 ]inthisfield .Papersaboutnonlineardynamicsaremuchless[5 ,6 ].Inthispaper,selectingthemaximumamplitudeinthecenterofshallowconicalshellswithvariablethicknessasperturbationparameter,thenonlinearnaturalfrequencyofshallowconicalshellswithvariablethicknessisobtainedbymethodgiveninRef.[7] .Thenonlinearnaturalfrequencyisnotonlyconnectedwiththeva…     

金属疲劳剩余寿命预测模型的一种探索

利用基于热力学的非线性连续疲劳损伤理论，考虑应力幅带来的非线性累积效应，理论上探索了金属电阻变化率与疲劳寿命的关系。提出了用电阻变化率进行疲劳损伤剩余寿命分析的模型。并通过电阻变化测定实验，验证了理论模型。为金属疲劳剩余寿命的预测提出一种理论模型和新的实践方法。     

Mutual Interdependence of Partitions Functions in Vicinity T g of Transition

The solid—liquid transition is described by use of the model incorporating the non-linear interactive oscillators. The individual non-linear oscillators are formed from the mechanical units of about the monomer size and produce the vibrations on the lower amplitude level, for the solid phase, either in amorphous or in crystal-like form. As the temperature starts to overpass the Vogel's temperature, the vibrations of individual units are big enough to cause the permanent displacements of the individual vibrating particles; the material starts to flow and the process of diffusion begins as well. As the temperature is passing through T _g vicinity, the large mechanical heterogeneity's start to appear as the small percentage of oscillators enlarge their amplitude of vibrations enormously and act as the local stress perturbations centers. These centers are responsible for the destruction of original matrixes and the sharp onset of fluidity and diffusion takes place. The upper amplitude of vibration motion is the basic property of a liquid state. The whole system of vibrations in matrix is described by use of techniques of deterministic chaos theories. It is shown as well, how the mutual interplay of the partition functions (vibration and cohesive), plays the important role in transition from liquid to solid states.This revised version was published online in November 2005 with corrections to the Cover Date.     

Transversality and separation of zeros in second order differential equations

Sufficient conditions on the non-linearity are given which ensure that non-trivial solutions of second order differential equations of the form have a finite number of transverse zeros in a given finite time interval. We also obtain a priori lower bounds on the separation of zeros of solutions. In particular our results apply to non-Lipschitz non-linearities. Applications to non-linear porous medium equations are considered, yielding information on the existence and strict positivity of equilibrium solutions in some important classes of equations.

     

条纹相机扫速非线性的标定和修正

研究了条纹相机扫速非线性、动态范围等测试用标准具的精确设计方法。通过选用合适的标准具,实验标定了C1587条纹相机的扫速非线性,并采用逐点对强度修正的方法,完成了条纹相机的扫速非线性的计算机自动修正。     

Efficient analysis of large-scale structural problems with geometrical non-linearity

The paper presents an efficient methodology for the analysis of large-scale structural problems with geometrical non-linearity. A finite element based tool is developed, taking advantage of the analytical formulation of the stiffness matrix of a beam element, which is explicitly separated in linear and non-linear terms. The methodology proposes the substitution of the typical Newton-type non-linear analysis procedure, by a series of incremental linear analyses and a set of ‘fictitious’ forces, replacing the non-linear effect. The proposed technique is demonstrated in several structural problems that exhibit geometrical non-linear behaviour, with satisfactory results. The method’s advantages on the analysis of large-scale non-linear problems are discussed, as well as the limitations and the further development that is required.     

色散和非线性效应对高斯脉冲综合影响的理论分析

从光孤子传输所满足的非线性薛定谔方程出发,采用单独分析和综合分析对比,分析了影响高斯脉冲传输的色散、非线性等因素,结果表明：二阶色散参量只会影响脉冲的幅值,对脉冲形状影响不大,而输入脉冲的啁啾则是使脉冲发生形变的主要原因|在啁啾、三阶色散和五阶非线性的共同作用下,它们对脉冲都会产生较大的影响,且存在相互影响和制约作用,在某一临界值,对脉冲存在着较高的压缩增益效应和“整形”作用.从理论上提出了改善高斯光脉冲在光纤中传输特性的解决方案,这对光纤孤子通信的实践过程具有一定的理论借鉴意义.     

Sharp transition between extinction and propagation of reaction

We consider the reaction-diffusion equation

on with and . In 1964 Kanel proved that if is an ignition non-linearity, then as when , and when L_1$">. We answer the open question of the relation of and by showing that . We also determine the large time limit of in the critical case , thus providing the phase portrait for the above PDE with respect to a 1-parameter family of initial data. Analogous results for combustion and bistable non-linearities are proved as well.

     

On the controllability for the Khokhlov–Zabolotskaya–Kuznetsov-like equation

Recalling the proprieties of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, we prove the controllability of moments result for the linear part of the KZK equation and its non-linear perturbation.