解析式

Eular -Bernonulli beam model and Tomosimko beam model were adapted to study the inherence vibration properties of the pipelines under dynamical loads, and the analytical answers of the chanmical results were brought out in the fifth chapter. And gave priority to the Eular -Bernonulli beam model, the simply and convenient analytical resolution for the response of the pipelines under dynamical traffic loads through the impulse function and the congruence method of the vibration form and so on.

本文采用Eular-Bernonulli梁模型和Tomosimko梁模型对动力下Kelvin粘弹性地基中管道固有振动性状进行了分析，提出了各力学结果描述的解析式；并以Eular-Bernonulli梁模型为主，基于脉冲函数、振型迭加法等对管道在动力交通荷载作用下的管道响应问题提出简单便捷的解析算法；在管道受力结果的分析中，考虑管道响应输出的随机性，将管道响应用随机过程来描述其概率特征，使得结果描述更加真实准确。

New ideas and methods in the paper:1 The formulas on perforated casing collapse strength were deducted, which offereda convenient method to analyze the relationship between casing collapse strength and perforation;2 The stress and displacement formulas on the system of casing, cement anddeformation under the non-uniform load were deducted, which offered the theoretical found for designing optimally casing string;3 The relationship between structure in-situ field of whole oil field and casing failurewere studied, which offered the scheme for the prediction of casing failure. The process of study in the paper:1 For simulating the relationship between the structure in-situ field and the casingfailure in the oil-deformation, the tests of the uniaxial tensile, compress, tnaxial compress and dilatability were made on the samples of the drill cores from deformation of casing failure position in Yuejing II oil field.

本文的主要创新： 1推导出了射孔套管抗挤强度的解析式，为分析射孔与套管强度的变化关系提供了简便的方法； 2推导出了非均匀地层载荷作用下套管、水泥环和地层组合体的应力和位移解析式，并非均匀作用下套管柱优化设计提供了理论依据； 3研究整个油田区块构造应力场与套管损坏关系，为预测套管损坏提供了可行方案；本文的研究过程如下： 1为模拟构造应力场与油层段套管损坏关系，做了大量的岩石单轴抗拉、单轴抗压、三轴试验以及岩石遇水膨胀试验，获得了研究区块岩石的弹性模量、泊松比、内聚力、内摩擦角以及岩石的线膨胀系数，这此数据为本文研究油层段套管损坏机理研究的理论分析和有限元法提供了实验数据。

This paper discusses such problems which are easily solved incorrectly in limitedteaching as, segment function is uncertain not to be elementary function, elementary function is un-certain to be continuous in its field of definition, unlimited variable is uncertain to be infinity, theinfinitely many infinitesimal is uncertain to be infinitesimal, the multiplication of two non- infinitesi-mal is uncertain not to be infinitesimal.

1分段函数不一定不是初等函数我们知道初等函数的定义是：常数和基本初等函数经过有限次的四则运算或复合，用一个解析式表示的函数叫初等函数。教材中的定义强调的"有限次"和"一个解析式"，使很多同学产生"非有限次"和"非一个解析式"的函数就不是初等函数的误解。例1f=ceox，s xx！0为分段函数，但也可以表示为f=e12(x-x2")+cos12(x+x2#"$)-1，故为初等函数。

For different parameters, the diffraction patterns of the expression of the Fraunhofer diffraction are identical, indicating the correctness of the expression.

在各种参量条件下，近似解析式所表示的衍射图样与严格的夫琅和费衍射积分的衍射图样完全一致，这表明用此解析式表征远场衍射是正确的。

Based on the method that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, the propagation characteristics of a Gaussian beam passing through apertured spatial filter systems are analysed and the corresponding analytical formulae are obtained respectively.

根据矩形函数可以展开为有限复高斯函数之和的方法，从柯林斯衍射积分公式出发，对高斯光束通过受限空间滤波器传输特性进行分析，得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟，得出一组直观的结果。

The residual gas pressure in an electron tube can be measured when the tube itself is operated as a hot cathode ionization gauge.Usually,its sensitivity K is determined by the method of gauge calibration.In this paper,author try to determine the sensitivity K by ca- lculation.The formulae for this purpose have be found out,and are used for both plate and cylindrical electrode systems.

把电子管接成热阴极电离计的工作形式，用来测量管内残气压强时，其灵敏度如何计算的问题在本文中作了讨论，给出了平板形电极系统和圆柱形电极系统的灵敏度解析式，对式中各量的计算作了详细介绍；并指出四极管中电子在电离区的平均渡越次数的表示式与三极管中的完全不同。

Based on the Rayleigh-Sommerfeld diffraction integral and complex analytical signal representation,the free-space propagation equation and its Fourier spectrum for ultrashort chirped pulsed Gaussian beams are derived,and the far-field analytical electric field and spatial intensity are presented.

基于瑞利-索末菲衍射积分，使用复解析信号法推导出了啁啾脉冲高斯光束在自由空间中的传输方程及其傅里叶谱，给出了远场的光场和空间光强的解析式，研究了啁啾参数C对脉冲光束传输的影响。

The calibrated curve of prism monochromator is traced out, and its function is obtained with the Origin software based on the normal Cauchy chromatic dispersion.

给出了棱镜单色仪定标曲线及其解析式确定的方法，并用 Origin软件算出定标曲线解析式。

This paper presents analytical solutions of internal forces of a solid three hinged arch subjected to complex loadings by a singular function method.

用奇异函数法导出了实体三铰拱在复杂载荷作用下内力的解析解，与传统的数解法相比，由于用统一的解析式表达内力，便于编程计算，也便于根据已知外载情况合理地设计拱轴

According to this exact analytical expression,the effect of every part of a beam pumping unit on crank axle torque can be quantitatively studied. This method can be used to analyze all types of beam pumping units.

利用该解析式可以定量地分析游梁式抽油机各部件对曲柄输出轴扭矩的影响，准确地进行游梁式抽油机的平衡分析和设计计算。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失