查询词典 Bessel

In this report, by applying Fourier Bessel series, we study the solution of the fluid inertia wave motion equation in a rotating and precessing cylinder.

本文用Fourier Bessel级数表示出了充液不满的自旋进动圆筒内部流体运动方程的一个解。

According to Bessel function and Fourier series theory, generation, magnitude and distribution of voltage harmonic generated by single-phase two-level SPWM inverter and three-phase SPWM inverter are analyzed and calculated particularity and concretely in allusion to inverter-motor system.

然后针对逆变器-电动机系统，利用贝塞尔函数和傅里叶级数理论，分别对单相二阶SPWM逆变器和三相SPWM逆变器的输出电压谐波的产生、大小和分布进行了细致而具体的分析和计算。

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

First, the physical models associated with dislocations and cracks are respectively converted to mixed boundary value problems in mathematics. Secondly, by using the Fourier transform, a dual integral equation for a crack and an algebraic equation for a dislocation can be derived from the boundary conditions relating with a crack and a dislocation, respectively. Solving these equations, exact analytical solutions can be obtained in terms of Bessel functions in close-form.

先把位错和裂纹的物理模型写成与它们相关的边值问题，然后，利用Fourier变换将这些边值问题化成一个对偶积分方程(对位错而言，得到一个代数方程)，求解此对偶积分方程，可以获得以Bessel函数给出的封闭形式的分析解。

All the most commonly used special functions are included: Bessel functions, Fresnel integrals, etc.

所有最常用的特殊功能包括：贝塞尔函数，菲涅耳积分等

Hankel inversion is calculated by Gauss integration in integral region, which are plotted at the zero points of Bessel function.

Hankel逆变换依据Bessel函数零点划分积分段，采用高斯积分计算。

In order to study the propagation of partially coherent modified Bessel-Gaussian beams passing through a paraxial ABCD optical system with hard-edge aperture,the approximate analytical propagation equation was derived with the hard-edged aperture function expanded into a finite sum of complex Gaussian functions.

为了对部分相干修正贝塞尔－高斯光束通过有硬边光阑近轴4BCD光学系统的传输进行研究，采用将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，得到了近似的解析传输公式。

As an application example,numerical calculation was performed for partially coherent modified Bessel-Gaussian beams propagating in free space with hard-edge aperture,and the computation errors and application ranges of those analytical equations were discussed.

以部分相干修正贝塞尔－高斯光束在有光阑情况下自由空间的传输为例作了数值计算，对所得解析公式的计算误差和适用范围进行了讨论。

Furthermore, the problem of coupled piezothermoelastic response of a piezoelectric cylinder of crystal class 6mm is investigated. Analytical solutions for this problem are successfully obtained by using Bessel-Fourier series expansion and Laplace transform. These solutions are helpful for study of the influence of coupling on the distribution of stresses, displacements, electric potential and other quantities as well as the role of inertia term.

研究了热电材料圆柱的瞬态压电热弹性响应问题，应用Bessel-Fourier级数展开和拉氏变换方法成功地求得了该问题的解析解，此解有助于研究瞬态响应问题中耦合效应对应力、位移和电势等物理量分布的影响以及惯性项的作用等问题。

The general analytical expression of the deformed high-order Bessel beam and its propagation properties of in self-focusing lens self-imaging process in free space wer.

从产生高阶贝塞尔光束的典型光路着手，通过将高阶贝塞尔光束分解为高阶贝塞尔余弦光束和高阶贝塞尔正弦光束，利用柱坐标下的Collins公式，分析了变形高阶贝塞尔光束的解析表达式和在自聚焦透镜中的传播。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。