虚位移

Bernoulli (Swiss, 1667~1748) found the principle of virtual displacements.

瑞士的伯努利(1667~1748)虚位移原理。

Besides this, the calculation of magnetic energy and electromagnetic torque of SCLRM is deduced by virtual displacement principle, and the physical essence of the electromagnetic torque is also analyzed in detail.

利用虚位移原理推导出了SCLRM中的磁场能量和电磁转矩的计算方法，并详细分析了电磁转矩产生的物理本质。

It introduced fundamental functions of elastic mechnics, elastic FEM, principle of virtual displacement and the creation of structure equilibrum equation.

第二章 有限单元法原理部分，在该部分中概要介绍了弹性连续体的有限元方法，虚位移原理和结构平衡方程的建立。

Virtual displacement principle of the analysis statics was used to establish static-equilibrium equations, which was used in calculating driving forces and torques when the mechanism was at some static-equilibrium state.

采用分析静力学的虚位移原理建立静力平衡方程，并用该方程计算了机构处于某种静力平衡状态下的平衡驱动力及力矩。

Based on the virtual displacement principle of finite element method, a weak variation of GAO-YONG turbulence equations is put forward. The subroutine of the element and the integrated finite element code are generated by the finite element program generator successfully.

基于有限元方法中的虚位移原理，写出了不可压流Gao-Yong湍流方程组弱形式的微分方程表达式，利用有限元程序自动生成系统得到了全部有限元计算程序。

The mathematical model of coal-bed methane seepage is established considering slipped effect, giving the weak form of the differential equation based on the principle of virtual displacement, hereby writing FEPG program. Using FEPG system's all the source program of the finite element which considers the mathematical model of coal-bed methane seepage of slip effect the numerical solution is sought.

建立考虑滑脱效应的煤层气渗流数学模型，给出了基于虚位移原理的微分方程的弱形式，据此编写了FEPG程序，利用FEPG系统生成了考虑滑脱效应的煤层气渗流数学模型有限元问题的全部Fortran源程序，并进行了数值求解。

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。

First, the inertia map in the work space is estimated by the use of virtual work principle and matrix singular value theory.

针对这类机构的结构特点，利用虚位移原理和矩阵奇异值理论，估算出主动关节负载惯量随位形变化的规律。

Let the junction of the three fracture lines have a virtual displacement.

令三条折断线的相交处有一虚位移。

The study is based on the Reddy s high order shear deformation theory .

首先用虚位移原理推导出以位移形式表达的Reddy型高阶剪切变形理论复合材料层板的非线性控制方程及相应的边界条件。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。