解析法

By using Lee\'s matching law, the excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained for one-dimensional consolidation in unsaturated soils, under the large-area uniform instantaneous loading. A computer program using the method by Crump and Durbin is developed to obtain the semi-analytical solution of the excess pore-air pressure, excess pore-water pressure and settlement under the boundary conditions of the top surface permeable to water and air and the bottom impermeable to water and air.

8采用李氏比拟法，应用Merchant粘弹性模型，得到了Laplace变换域内粘弹性非饱和土地基一维固结时超孔隙水压力，超孔隙气压力以及土层沉降的解；采用Crump及Durbin方法实现Laplace逆变换，获得大面积均布瞬时加荷，在顶面排气排水，底面不排气不排水情况下粘弹性非饱和土地基一维固结时的半解析解。

Based on the domain superposition method and the differential cubature method as well as the Levy s general solution technique, a new semi-analytical solution has been developed in this paper, for free vibration analysis of moderately thick plates with abrupt thickness.

采用Mindlin中厚板理论，基于Levy解法和微分容积法，给出一种求解轴向受压的阶梯式变厚度板的自由振动问题的半解析解，板的边界条件为两对边简支、另两边任意。

Starting with properties of cubic parabola, it is demonstrated elementarily that solving elliptic equations using Jacobian elliptic functions, analytic solutions for a class of nonlinear wave equations and properties of nonlinear waves can be obtained, especially for solitary waves.

从立方抛物线的特性谈起，用较初浅的方法，借助于雅可比椭圆函数求椭圆方程的解，说明一类非线性波方程可用行波法求解析解。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

The far-field analytical expressions for the electromagnetic fields of a cylindrically polarized vector beam propagating in free space are obtained based on the vector angular spectrum and the method of stationary phase.

基于矢量角光谱法与静态位相方法，推导出了矢量圆柱偏振光束在自由空间传输的电磁场的远场解析表达式。

The governing equation of in-plane vibration of cable-restraint system is derived by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations by Garlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is made to prove that this vibration control has obvious damping effects and then the influence of cable tension, support mass, natural frequency and spring stiffness on the damping are discussed. Eventually, the approximate analytic solution of the optimum damping parameter is obtained to provide a simple and effective reference and design method for the engineers.

通过D'Alembert原理建立拉索－弹性约束系统振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格－库塔积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼参数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。

Firstly, based on the wave equation, determining reasonably its initial boundary condition, the paper establishes a computer diagnostic model of oil pumping mechanical well, the damping factor in the model has been reasonably determined, the implicit difference solutionis conducted to the model by changing of step width expression difference solves, and the half analytical solution is explored to the model - fine integral method; and realizes the transformation from dot indicator diagram to indicator diagram of any section.

首先从抽油机井计算机诊断技术的理论基础入手，考虑多级抽油杆连续性，建立了粘滞阻尼波动方程，合理确定模型中的阻尼系数，采用无条件稳定的隐式差分法及半解析方法求解方程，获得抽油杆柱任意断面和抽油泵处的示功图。

Based on Reddy higher-order shear deformation plate theory and general von Kármán-type equations, the analytical solutions for free vibration and dynamic response of simply supported functionally graded plates with piezoelectric layers in thermal environments are described with double Fourier series, where temperature-dependent material properties are taken into account.

基于Reddy高阶剪切变形理论和广义Kármán 型方程，用双重Fourier级数展开法求得了热环境下带压电层的功能梯度复合材料混合层合板的自由振动及动力响应的解析解，分析中考虑了材料热物参数对温度变化的依赖性，讨论了环境温度和控制电压对固有频率及动力响应的影响。

Even … many kneel at her feet for … 323,to be known for …因…而著称 Freud is known for his psychoanalysis and his Dream Analysis and he is one of the greatest psychologists the world has ever known.

弗洛伊德以他的精神分析法理论和他的《梦的解析》著称于世，而且他是全世界已知的最伟大的心理学家之一。必备得分佳句

These kinds of analytical elements can describe the crack tip fields for the Dugdale model and can also be combined with the ordinate finite elements to form the semi-analytical finite element method.

该类超级单元能够准确地描述基于Dugdale模型的裂纹尖端场，可与普通有限单元相结合，构成半解析有限元法。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。