非线性

Based on the basic theoryof non linear finite element, the author of the paper set up the double non linearfinite element equation based on the updated Lagrangefor mutations forthe 8-node degenerate shell element and considering the nonlinear of geometryand the nonlinear of materials.

本文根据非线性有限元的基本理论，采用基于修正的拉格朗日法描述的八节点超参数壳体单元，考虑几何非线性和材料非线性，推导建立了双重非线性有限元方程，结合混合强化本构关系，编制了非线性有限元计算程序。

Firstly, the author establish the functions of stability on the basis of the spline function method ,according to the theory of geometrical nonlinear and the theory of stability, educe the stability equation of structure based on variational principle, then carry through the flexuosity analysis of CFST arch.The big distortion geometrical nonlinear was considered by the stability equation,the author simplified the problem of geometrical nonlinear through ignored quadratic term and reserve the simple term, at last boiled down to solve the linear stability equation of eigenvalue .

利用样条函数方法、根据几何非线性变形理论和结构稳定性理论，先建立起结构稳定的泛函，再由变分原理导出结构的稳定方程，进行钢管混凝土拱屈曲分析；本文所建立的稳定方程考虑了几何非线性的大变形效应，通过忽略几何非线性的二次项，保留一次项，将几何非线性问题简化，最后归结为求解线性稳定问题的特征值稳定方程，建立了结构非线性静力稳定性问题的新算法及失稳类型判别准则。

Then steady forced vibration of the nonlinear Disk spring-mass system under base excitation and force excitation is obtained individually by using the Fourier series analysis and harmonic balance method.

详细探讨了考虑静力载荷影响的、具有弹性非线性和Coulomb摩擦阻尼非线性的碟簧元件的建模和动力学特性，首先利用Fourier级数分析技巧和平均法研究了非线性碟簧-质量系统的自由振动，讨论了影响自由振动的振幅和频率的各种因素，然后利用Fourier级数分析技巧和谐波平衡法研究了地基激励和力激励下非线性碟簧-质量系统的强迫振动，通过详细的参数研究考察了非线性碟簧元件的减振性能特征，最后采用修正的稳定性分析方法研究了两种激励下稳态响应的稳定性。

Optimal algorithm of combined nonlinear Hopfield network appears powerful validity in solving nonlinear planning, which includes nonlinear objective function, linear constrains and high-demension of decision-making variants, for its ability of nonlinear parallel computation. It is prominent among optimal algorithms because of its function of simply implement with electrocircuit hardware. Genetic algorithm is expressly suitable for optimal calculation regarding the planning of massive, highly nonlinear, inconsecutively differentiable and multiobjective function as well as objective function without analytical expression. However, it inclines to prematurity, as well as its limitation in ability of partial optimal search. Introducing the optimal algorithm of niche genetic simulated annealing to standard Genetic algorithm, can therefore improve the full-scale or partial search ability of Genetic algorithm effectively. It has a far-flung perspective in the field of systemic planning of water pollution control.

组合式非线性Hopfield网络优化算法所具有的非线性大规模并行计算能力在求解具有非线性目标函数、线性约束条件及高维决策变量的非线性规划问题方面显示出了强大的生命力，它易于电路硬件实现的功能更是在优化算法中独树一帜；遗传算法采用概率搜索技术，不受目标函数与约束条件的限制，特别适合大规模、高度非线性的不连续可微的多峰目标函数及无解析表达式的目标函数的规划问题的优化计算，但其存在容易早熟、局部寻优能力较差等缺点，本文在标准遗传算法中引入小生境技术及模拟退火算法有效地改善遗传算法的全局和局部搜索性能，提高了全局最优解的寻优质量，小生境遗传退火模拟优化算法在水污染控制系统规划中的应用前景极为广阔。

The methods are as follows: the first is for Hammerstein-type nonlinear system model with known upper value of its order; the second is for the nonlinear system model based on the nonlinear Laguerre model derived from the Volterra series input-output presentation, and the third is for the Wiener-type nonlinear system model based on the combination of Laguerre function with neural networks.

给出了三类非线性系统的即时线性化自适应预测控制策略，即(1)已知非线性子系统阶次上限值的Hammerstein型非线性系统；(2)基于Volterra-Laguerre函数模型的非线性系统；(3)基于Laguerre函数与神经网络的组合模型的Wiener型非线性系统。

The fluid film bearing-flexible rotor nonlinear system with squeeze film damper is modeled practically using the finite element method and the Hamilton principle.(3) The film forces produced by fluid film bearing and squeeze film damper are determined by finite element method at any moment, and the Jacobian matrix is also determined.(4) A method for analyzing the dynamics of a large system with local nonlinearities is presented. The stability and bifurcation of the equilibrium position and the unbalance responce of a fluid film bearing-flexible rotor system with squeeze film damper are investigated based on the assumption of an incompressible lubricant together with the long bearing approximation for fluid film bearing, short bearing approximation for squeeze film damper and the"π"film cavitation model.

主要研究内容包括下面几个方面：（1）对挤压油膜阻尼器-滑动轴承-转子非线性动力系统中的非线性现象进行了机理方面的研究；（2）应用有限元方法及Hamilton原理对复杂的挤压油膜阻尼器-滑动轴承-转子非线性动力系统进行了建模分析；（3）对滑动轴承及挤压油膜阻尼器中任一时刻的油膜力及相应的Ja-cobi矩阵的确定进行了分析；（4）对一类具有局部非线性的多自由度动力系统，提出了一种可以有效地分析其动力特性的方法；（5）采用实验与理论分析相结合的方法，对挤压油膜阻尼器-滑动轴承-转子非线性动力系统的动力特性进行了分析。

The emulation result shows that the error of polarizer rotation angle almost does not influence nonlinearity when elliptic polarization of laser beams exists; when the error of rotation angle of polarizing beam splitter exists, the second-harmonic nonlinearity caused by the error of polarizer rotation angle will not increase, but the first-harmonic nonlinearity will increase greatly.

仿真结果表明，当存在激光束椭圆偏振时，检偏器旋转误差对非线性误差的影响很小；当存在偏振分光镜旋转误差时，检偏器旋转误差引起的非线性误差不增加二次谐波分量，但增大了非线性误差一次谐波分量，严重影响非线性误差的大小，当偏振分光镜旋转误差为3°时，检偏器旋转误差从0°增加到5°，非线性误差从0.14 nm增大到0.97 nm。

In airplane design, structural nonlinearities cannot be avoided. The structuralnonlinearities arise from worn hinges of control surfaces, loose control linkages,material behavior and various other sources. In the flighting, the aerodynamicnonlinearities also cannot be avoided. The aerodynamic nonlinearities can benegligible when the speed of the plan is not very high;but when the speed of the planis supersonic or highly supersonic, it cannot be negligible.

在飞机设计中，结构非线性是不可避免的，结构非线性源于控制其表面的旧铰链，松散的控制器联动装置，材料性能和其它的来源；在飞机的飞行中，气动的非线性也是不可避免的，对于飞行速度不是很高的情况，气动的非线性是可以忽略的，而对于超音速以及超高音速的飞机来说，气动的非线性是不可以忽略的。

Operations are given and testified in this paper. The research methods of intrinsical linear nonholonomic dynamics are similar to those of holonomic dynamics.The rationality and equivalence of Chetaev model and Vacco model in the intrinsical linear nonholonomic system are testified from the mathematic and mechanical aspects. The essential reason is the nonlinear property of intrinsical nonlinear nonholonomic constrain that bring on Chetaev model and Vacco model inequivalent. Chetaev model is a linear approximate method in intrinsical nonlinear nonholonomic system. Vacco dynamical equations are not satisfied to the ideal constraint force conditions, but it gives a significative ponderation on the realizations of intrinsical nonlinear nonholonomic constrain.

本文比较研究了一般非完整系统的Chetaev模型和Vacco模型，首次从力学和数学的角度论证了这两种模型在完整系统和本质线性非完整系统中的合理性和等价性；同时给出了在本质非线性非完整系统中，Chetaev模型和Vacco模型不等价的根本原因，是由本质非线性非完整约束的不确定性非线性本质所导致的；指出在本质非线性非完整系统中，Chetaev模型是一种线性近似的结果，Vacco动力学方程虽然不满足约束力的理想性质，但是为我们研究本质非线性非完整约束的物理实现提供了有益的思考。

The electronic structures and the non-linear optical properties of bis schiff base and their derivatives have been studied using FF/HF method.The effects of electron donor/acceptor on nonlinear optical property were examined at the molecular level.As a result,the NLO coefficients of the substituted compounds are all larger than the unsubstituted compound.Among them, the β value of compound 4 is the largest one.

自1961年激光发现以来，非线性光学和非线性光学材料迅速发展起来[1～4]，随着光通讯、光电子学和光信息处理等在实际中的应用，对非线性光学材料的理论与实验研究进一步展开，寻找和设计具有较大非线性光学系数，超快光学响应，较低的光学损伤阈值，良好的化学稳定性和热稳定性的非线性光学材料成为这一领域的主题[5～12]。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。