adjoint differential equation

adjoint differential equation的基本解释

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伴随微分方程

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

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

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。

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

adjoint differential equation：伴随微分方程

adjacent side 邻边 | adjoint differential equation 伴随微分方程 | adjoint operator 伴随算符

adjoint differential equation：相关微分方程式

附属频带指定 adjectival band designation | 相关微分方程式 adjoint differential equation | 相关运算子 adjoint operator

self adjoint differential equation：自伴微分方程

self adjoint boundary value problem 自伴边值问题 | self adjoint differential equation 自伴微分方程 | self adjoint eigenvalue problem 自伴特盏问题

adjoint partial differential equation：伴随偏微分方程

伴随正交系;共轭转置正交系 adjoint orthogonal systems | 伴随偏微分方程 adjoint partial differential equation | 伴随多项式 adjoint polynomial

adjoint linear differential equation：伴随线性微分方程

196,"adjoint kernel","伴随核" | 197,"adjoint linear differential equation","伴随线性微分方程" | 198,"adjoint linear transformation","伴随线性变换"