查询词典 harmonic differential equation

The stress was the study of the new methods of calculation the harmonic voltage and the harmonic current, and a new concept of filter ratio to evaluate the actual effect of single harmonic filter was raised considering the background harmonics. As well, the calculation mode of the single harmonic filter was also given based on the concept of filter ratio; it can offer effect data to evaluate the actual filter ratio of the single harmonic filter. At the same time, a method of designing the single harmonic filter was given, too, considering the background harmonics of the power system. In this paper, both the computer analysis and the proven had been done. And the result was shown to be that the voltage aberration and the harmonic current were decreased, and that the actual filter ratio of single harmonic filter was raised. The reason that we must consider the background harmonics when designing a single harmonic filter was also expatiated in this paper.

重点研究了考虑电网背景谐波下谐波电压、电流的计算方法，提出了用滤波率来评价单调谐滤波器安装容量利用率的概念，基于滤波率，分别给出了不考虑、考虑电网背景谐波时，单调谐滤波器的计算模型，为定量分析和评价单调谐滤波器的实际补偿效果提供了依据：并以此提出了考虑电网背景谐波的单调谐滤波器计算机辅助优化设计方法，并经计算机仿真分析、论证，减少了负载母线谐波电压畸变率和注入系统的谐波电流，有效地提高了单调谐滤波器的滤波效果，阐述了单调谐滤波器的设计过程中要考虑电网背景谐波的理论和实际意义。

Harmonic Drive Technical Dynamic League Group Co., Ltd. is consisted of Beijing Feida CTKM Harmonic Drive Technology Innovation Co., Ltd., Beijing CTKM Harmonic Drive Co., Ltd. and other units. The group company is home to many experts, professors and researchers, who have been in the field of harmonic drive for years, and have had a number of key results of harmonic drive technology, including series harmonic drive products with 8 different structures. The group has the strongest capability in harmonic drive technology innovation, and has made important contributions to the development of China's harmonic drive technology.

由北京飞达克美谐波传动技术创新有限公司和北京中技克美谐波传动有限责任公司等单位组成的动态联盟集团公司集中了我国多年来从事谐波传动技术研究的专家，教授及科技人员，曾主持完成我国多项谐波传动技术成果，开发出八个不同结构的谐波传动系列产品，具有最强的谐波传动技术创新能力，为我国的谐波传动技术的发展做出了重大贡献。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

Content: By learning this course, students should grasp the elementary solution of first order differential equation, the structure theory of linear differential equation or system of linear differential equations and the solution of constant coefficient differential equation or system of constant coefficient differential equations.

主要内容：通过对本课程学习，使学生掌握一阶微分方程的初等解法、线性微分方程的结构理论和常系数方程的解法，对微分方程初值问题的一些基础理论有一定的了解，对

Differential equation model is classified as ordinary differential equation, partial differential equation and stochastic differential equation.

微分方程模型的形式包括常微分方程，偏微分方程和随机微分方程。

However, harmonic analysis lays the foundation for power harmonic treatment. The paper discusses the development of a power harmonic analyzer hosed on DSP and LabVIEW, which is used to analyze and measure harmonic on real-time. The analyzer's hardware, harmonic analysis algorithm, LabVIEW software design and the implementation are alt brought forward in detail.

为了有效地检测电力谐波，并对其进行治理，本文将DSP与LabVIEW虚拟仪器技术相结合，提出了一个谐波实时测量分析仪的设计方案，同时给出了系统的硬件构成和谐波分析算法，以及LabVIEW子程序的详细设计及实现。

Derives the formulae for calculating the distortion and stress on the acting surface of flexspline load in the drive process of the harmonic gear drive with three-wave wavegenerator;(2) analyzes and compares the performance of plastic and steel products under light load drive and calculates the probably reached limit of drive ratio for both types of flexsplines under the same load;(3) applies the harmonic gear drive with three-wave wavegenerator to the small-sized multiple-revolution electric device of valves by taking into consideration of the low limit of the drive ratio for the harmonic gear drive with three-wave wavegenerator made of plastics, improves the design on the main drive mechanism of the traditional small-sized multiple-revolution electric device of valves, and validates through examples the feasibility for the harmonic gear drive with three-wave wavegenerator made of plastics to be applied to the small-sized multiple-revolution electric device of valves. Finally the author performs calculations on the two types of the flexsplines of the harmonic gear with three-wave wavegenerator by using the finite element method and analyzes the causes for the errors.

本文根据三波谐波齿轮传动的运动变形特点，采用弹性薄壳的力矩理论，推导了三波谐波齿轮传动柔轮载荷作用面上的变形及应力计算公式；分析比较了轻载传动情况下塑料和钢材的性能，计算了塑料制谐波柔轮和钢制谐波柔轮在相同载荷情况下可能达到的传动比极限；对塑料制及钢制三波谐波齿轮柔轮进行了有限元计算，分析了产生误差的原因；针对三波塑料谐波齿轮传动比极限低的特点，将之运用于小转矩多回转阀门电动装置中，对传统的小型多回转阀门电动装置的主传动机构进行了改良设计，并通过实例验证了三波塑料谐波齿轮传动在小转矩多回转阀门电动装置中应用的可行性。

In this paper, the current states of research about the basic theory of harmonic oscillator and hydrogen atom in quantum mechanics are firstly reviewed. On base of it, and the relationships between harmonic oscillator and hydrogen atom in quantum mechanics are studied. By use of the relationships between the hermite polynomial and the laguerre polynomial, the eigenequations of one-dimensional harmonic oscillator and hydrogen atom are conversed into the same equations in form. Therefore the relationships between energy levels and wave functions of one-dimensional harmonic oscillator and hydrogen atom are found. Through the coordinates transform, the relationships between energy levels and wave functions of two-dimensional harmonic oscillator and hydrogen atom are found.

首先综述了谐振子与氢原子的基本理论的研究现状，并在此基础上对谐振子与氢原子的关系展开了研究，通过厄密特方程与拉盖尔方程的相互转化，将一维谐振子与一维氢原子的本征值方程转化为相同形式的方程，从而比较得出它们能量及波函数间的关系，并通过坐标变换将直角坐标系下二维氢原子的本征值方程转化成与曲线坐标系下二维谐振子的本征值方程相同的形式，从而得出二维氢原子与二维谐振子的能量及波函数的关系。

We are forbidden from giving money to these shoeless, skinny children, as this will perpetuate begging.

向光着脚，骨瘦如柴的孩子施舍是不可以的，因为要招来无休无止的乞讨。

It would be hard not to fall victim to some sharpeyed policeman.

要想不被某个目光锐利的警察抓到，谈何容易。