abel equation

abel equation的基本解释

-

阿贝耳方程

与abel equation相关的网络例句 [注：此内容来源于网络，仅供参考]

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。

These results show that:(1) the results retrieved from the Abel integral and absolute TEC inversion are consistent on the whole at higher orbits altitude (~800 km), and in good agreement with those measured by ionosondes; the results retrieved from absolute TEC inversion are in better agreement with those obtained from ionosondes than that by the Abel integral inversion at lower orbits attitude (~500 km);(2) the maximal electron density N m from absolute TEC inversion is closer to N mF2 from ionosondes than that from Abel integral inversion, and the method of the former is more rigorous and effective than that of the latter;(3) absolute TEC is more sensitive to cycle slip than Abel integral, but for the two ways significant loss of inversion precision due to cycle slip always exists.

结果表明：（1）在较高轨道高度（约800 km），Abel积分与绝对TEC方法的反演结果基本一致，都与电离层测高仪反演结果符合良好；在较低轨道高度（约500 km），绝对TEC反演精度优于Abel积分反演精度；（2）绝对TEC反演的最大电子密度 N m较Abel积分法获得的结果更接近于电离层测高获得的峰值电子密度 N mF2，绝对TEC反演法更加严密和有效；（3）周跳对绝对TEC反演结果的影响较Abel积分反演结果的影响更为敏感，但无论哪种方法，周跳对反演精度都造成严重损失。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

与abel equation相关的网络解释 [注：此内容来源于网络，仅供参考]

abel equation：阿贝耳方程

abbreviation 简化 | abel equation 阿贝耳方程 | abel identity 阿贝耳恒等式

Abel integral equation：阿贝尔积分方程

阿贝尔积分|Abelian integral | 阿贝尔积分方程|Abel integral equation | 阿贝尔晶体|Abelian crystal

Abel integral equation：阿贝耳积分方程式

zone of silence 宁静区 | Abel integral equation 阿贝耳积分方程式 | Abel transform 阿贝耳转换

abel's integral equation：阿贝尔积分方程

abbreviation 简写,缩写词,略语 | abel's integral equation 阿贝尔积分方程 | abend 任务异常结束