结构方程

Based on a series of shear creep tests of discontinuous plane with regular dentation,the relationship between shear creep and different normal stress,shear stress,and slope ratio is obtained.

文章在规则齿形结构面剪切蠕变试验的基础上，分析了剪切蠕变随不同的爬坡角、正应力和剪应力的影响，拟合了剪切蠕变曲线，并将拟合的方程与Burgers模型的本构方程进行了比较分析，讨论了Burgers模型中剪切模量、粘滞系数的变化规律及其影响因素，取得了较为理想的结论，为结构面剪切蠕变本构方程的建立提出了较为合理简便的方法。

The main contents of this course include: the elementary solution of first order differential equations, the theory of existence, uniqueness and continuity dependency of initial value problem of first order differential equations, the structure theory of higher order linear differential equation and the solution of constant coefficient equations, the structure theory of system of linear equations, basic solution matrix and the solution of system of constant coefficient equations.

本课程内容有：一阶微分方程初等解法，一阶微分方程初值问题的存在性、唯一性、连续依赖性理论，高阶线性微分方程解的结构理论和常系数方程解法，线性方程组的结构理论、基解矩阵和常系数方程组的解法。

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。

This paper mainly consists of three parts:(1) Based on the Reddy's higher-order shear deformation plate theory and general von Kármán-type equations, put forward the governing equations of pre- and post-buckled vibration of several hybrid FGM plate forms which have not been studied adequately, triumphantly applying the perturbation technique combined with Galerkin method into equations solving, and get the comparatively simple result forms with complicated deduction at last;(2) As a new type of materials, piezoelectric fiber reinforced composite actuators were applied to optimal vibration control, interrelated informatons be depicted in this paper;(3) During the investigative cource, some factors not been considered adequently in other researches were discussed fully in the postbuckled vibration analysis, such as the temperature-dependent material coefficients, heat conduction and nonlinear vibration characteristic etc.

本文的研究工作主要包括：(1)基于Reddy高阶剪切变形板理论和广义Kármán型方程，给出了几类现有研究成果较少或没有彻底解决的FGM混合板结构的屈曲前和屈曲后振动特性研究的控制方程，成功将摄动-Galerkin混合法应用于求解过程，并给出了各控制方程相对直观且易于计算的解析解形式；(2)单向压电纤维增强复合材料(Piezoelectric Fiber Reinforced Composite，简称PFRC)是一种新型压电材料，本文将其应用到了结构振动控制研究当中，发现通过压电纤维体积含量的选择可以实现混合板结构的优化振动控制；(3)围绕几种有代表性的FGM混合板结构，讨论其屈曲后的振动特性，在分析中同时考虑热传导，材料物性参数的温度相关性，以及机/热/电荷载耦合效应对非线性振动特性的影响，最后给出了大量数值计算结果。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated.

因此，本文基于FPK方程和伊藤随机微分方程，研究了滞后结构物的随机地震反应和随机滤波问题的基本方法，并利用等效线性化法和矩方程法，研究了非线性结构随机地震反应分析和随机滤波分析的近似解法及它们的工程应用。

Variational identity play a important role to prove nonexistence and get prior estimate of solution, In this thesis, we study following parts on the relationship of symmetry group of partial differential equations with variational structure and the variational identity.

变分恒等式在证明具有变分结构偏微分方程解的不存在性以及得到方程解的先验估计时有着非常重要的作用，本文研究了一些具有变分结构偏微分方程的对称群与其变分恒等式的关系。

To overcome the difficulties and the draw backs in modeling dynamic systems by traditional methods, a hybrid evolutionary modeling algorithm was proposed to model the Dynamic system with a system of ordinary differential equations whose main idea was to embed string coded idea and evolution algorithm optimize system.

针对传统方法解决动态系统微分方程建模问题所遇到的困难和存在的不足，设计将方程进行串结构编码并用进化方法进行演化建模的算法，以串形结构表示结构，用进化算法优化结构和参数，成功地实现了动态系统的常微分方程组建模过程的自动化。

The kinematic analysis of the planar four-bar linkage and dimensional six-bar linkage can be done by building up the structural equations.

平面四杆机构和空间六杆机构的运动学分析可以通过建立闭链的结构方程来实现。

Methods: A total of 350 questionnaires was sent to 18 medical centers; 181 valid responses were received. The main respondents were radiographers. The collected data were analyzed by the utilization of Structural Equation Modeling to validate the research model.

针对18家医学中心之放射科技师进行问卷调查，共发出350份问卷，回收181份有效问卷，所搜集资料透过结构方程模式进行研究模式之验证。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。