导出

Based on the variational principle of virtual voltage and virtual displacement derived in this thesis and the classical theory of linear laminated plates, and by using the constitutive equations of elastic piezoelectric materials, and the DKQ quadrilateral plate bending element, the finite element modeling for the fabric reinforced laminated plates with nonlinear voltage-electric strain relationship of piezoelectric actuators has been established for the first time in this thesis. And the expressions for the electric loadings with obvious mechanical meaning and convenient for computation are established, which can be used to the deformation analysis of laminated plates with piezoelectric actuators under specified voltages.

以本文直接导出的压电结构的虚电势—虚位移变分原理为基础，依据经典线性层合板理论和压电弹性体的本构方程，采用基于离散法线假设的DKQ四结点任意四边形薄板弯曲单元，首次建立了考虑非线性电压—电应变关系的含压电致动器的纤维增强型层合板的有限元分析模型，并推导建立了力学意义明确、便于计算的电荷载表达式，可用于指定电压条件下纤维增强型叠层合成板的变形分析。

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。

This affects the print preview, export, and printing of your spreadsheet.

这会影响到打印预览、导出、和您的电子表格的打印。

This choice affects the print preview, export, and printing of your spreadsheet.

这会影响到打印预览、导出、和您的电子表格的打印。

This paper presents a novel multiple object segmentation algorithm based on a Bayesian framework. According to the characteristic of the intra-frame and inter-frame information, a representation of Maximization of the A posteriori Probability of spatio-temporal label field is proposed. So a minimization of energy function is obtained.

摘要该文提出了一种基于贝叶斯框架的时空标记场最大后验概率的多视频对象分割算法，根据视频序列帧间和帧内信息的不同特点，建立基于多个对象分割标记场的最大后验概率公式，并导出其最小能量函数，通过求解最小能量使其分割标记的后验概率达到最大。

The paper introduces a differential equation derived from Markov theory and probability generating function.

文章介绍用Markov理论与母函数方法建立相关微分方程，并导出近似解析解，着重对常数源在系统中的涨落作了数学描述，给出了数值例子。

If the program finds a Bad item, you can choose to deactivate it immediately, and also export the results as report.

如果该软件发现了一个坏的项目，你可以选择将其立即封存，还可以将结果导出为报告。

LogExport is a small program to Export the Call Register data to a CSV file.

LogExport是可以将电话中存储的数据以CSV格式导出的小巧程序。

In this paper,according to the characteristic that the scale exhibits progressional variety, anti-symmetric lifting wavelet filter is deduced from Gaussian function.

从Gaussian函数出发，根据尺度呈级数变化的特点，导出了反对称提升小波滤波器。

Based on the cross-ratio of five coplanar points, a group of projective invariants is derived for recognition planar polygons.

论文利用具有射影不变性的共面五点交比，导出一组用于识别平面多边形的射影不变量，并给出了相应的识别算法。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。