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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。

Should define target market together with client as far as possible, locate the other target that be alluded from inside psychograph or demography standard and does not have designation actually.

应该尽可能与委托人一起确定目标市场，找出从心理描绘图或人口统计学标准中暗示而实际上没有指名的其他目标。

With the advice and unanimous consent of our brothers, cardinals of the holy Roman church, by means of this our constitution which will have permanent validity, we establish, ordain, decree and define, by apostolic authority and the fulness of our power, that if it happens (which may God avert in his mercy and goodness towards all), after God has released us or our successors from the government of the universal church, that by the efforts of the enemy of the human race and following the urge of ambition or greed, the election of the Roman pontiff is made or effected by the person who is elected, or by one or several members of the college of cardinals, giving their votes in a manner that in any way involves simony being committed -- by the gift, promise or receipt of money, goods of any sort, castles, offices, benefices, promises or obligations -- by the person elected or by one or several other persons, in any manner or form whatsoever, even if the election resulted in a majority of two-thirds or in the unanimous choice of all the cardinals, or even in a spontaneous agreement on the part of all, without a scrutiny being made, then not only is this election or choice itself null, and does not bestow on the person elected or chosen in this fashion any right of either spiritual or temporal administration, but also there can be alleged and presented, against the person elected or chosen in this manner, by any one of the cardinals who has taken part in the election, the charge of simony, as a true and unquestionable heresy, so that the one elected is not regarded by anyone as the Roman pontiff.

的意见，并一致同意，我们的兄弟，红雀的罗马教会，通过我们的宪法，这将永远有效，我们建立，注定，法令和确定，由使徒权威和丰富我们的权力，如果发生（可能避免上帝在他的仁慈和善良对所有），上帝已发布后我们或我们的继任政府的普世教会，这所作出的努力的敌人，人类的欲望和以下的目标或贪婪，选举是罗马教皇或影响的人谁当选，或由一个或几个成员的枢机主教，使他们的选票的方式，以任何方式涉及西摩尼正在致力於-的礼物，许诺或收到的资金，货物的任何类型，城堡，办事处， benefices ，承诺或义务-选出的人或由一个或几个其他人，以任何方式或形式，即使选举产生了多数三分之二或一致选择所有红雀，甚至在一种自发的协议的一部分，所有，未经审核作出，那麼不仅是本次选举或选择本身无效，并没有赋予人选举或选择以这种方式的任何权利或者精神或时间管理，而且还可以有指控，并提出，对当选者，或选择以这种方式，任何一个红雀谁参加了选举，充电的西摩尼，作为一个真正的和不容置疑的邪说，使选举是一个任何人都不会认为是罗马教皇。

I shall define him as an individual who has elected as his primary duty and pleasure in life the activity of thinking in Socratic way about moral problems.

我将把他定义为一个体，他已经选择以苏格拉底的方式思考道德问题的活动为他的在生活中最重要的责任和愿望。

I shall define him as an individual who has elected as his primary duty and pleasure in life the activity of thinking in a Socratic way about moral problems.

我会把"知识分子"定义为这样的人，他们把以苏格拉底的方式来思考道德问题的活动作为人生的主要任务和乐趣。

I shall define him as an individual who has elected as his primary duty and pleasure in life the activity of thinking in Socratic way about moral problem.

我将把他定义为这样的人，他把以苏格拉底的方式去思考道德问题作为人生首要的责任和乐趣。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

In his works like the Terrazzo series, Wang did not offer any definitive meaning or even content to the viewers, instead, the objects in these paintings are represented as the form itself, making it hard to define the works as "abstract" or "figurative".

但是王光乐的绘画却从另一个角度出发，像"水磨石"系列并没有明确的意义、内容的指向，而是仅仅将对象赋予一种形式，很难从具象或是抽象的角度来定义。

Yet Wang Guangle has his own approach to painting. In his works like the Terrazzo series, Wang did not offer any definitive meaning or even content to the viewers, instead, the objects in these paintings are represented as the form itself, making it hard to define the works as "abstract" or "figurative".

但是王光乐的绘画却从另一个角度出发，像"水磨石"系列并没有明确的意义、内容的指向，而是仅仅将对象赋予一种形式，很难从具象或是抽象的角度来定义。

To define the relationship between ultra vires act of enterprise as legal person and that of legal representative can help to decide inside responsibility of enterprise as legal person.

对企业法人越权行为与法定代表人越权行为的关系作出界定，有利于正确划分法人的内部责任，但我国现行立法并未对此作出规定。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。