模态的

For analysis of traditional experimental modal, hammer and shaker are often used to force the structure as the clamped-clamped beam to raise the vibration of the structure, meanwhile accelerometer is placed on the structure as a sensor, then the modal parameter could be found.

传统实验模态分析大多使用冲击鎚或激振器施加点力於结构例如固定梁，做为驱动器激发结构的振动，利用加速度计做为感测器置於结构上，以求取结构之模态参数，但传统之模态实验设备都有实验操作不易以及价格昂贵的缺点。

When the residual modes are high frequency modes, it will be suitable to use a filter to prevent the spillover by filtering the measuring signals. The closed loop poles would excurse if the measuring signals were filtered directly.

对于剩余模态和控制模态分离得较好的受控对象，可采用对测量信号进行滤波去除信号中剩余模态分量的方法防止溢出问题。

The project proposed and established the strict unique mathematical model of instantaneous frequency aiming at the currently existed problems in Hilbert Huang Transform form the viewpoint of physical connotative meaning; proposed and established the strict mathematical model of general intrinsic mode signal based on the concept of general continuous intrinsic mode signal and the compositive principle of practical general intrinsic mode signal; researched and proposed the fitting method of envelope lines in HHT from the viewpoint of theory, conquered the blindness and random in quondam EMD envelope line fitting and boundary treatment; developed a virtual time-frequency analyzer based on general intrinsic mode signal decomposition to open out the local time-frequency characteristics of nonlinear and nonstationary signal more deeply and accurately.

本项目针对希尔伯特-黄变换现阶段存在问题，从物理内涵的角度提出并建立了瞬时频率严格的唯一的数学模型；基于连续性的一般固有模态信号的概念和实际信号的一般固有模态信号的组成原理，提出并建立了一般固有模态信号严格的数学模型；从理论角度研究并提出HHT中的包络线构造方法，克服了原EMD的包络线构造和边界处理的盲目性和随意性；研发一台基于一般固有模态信号分解的虚拟式时频分析仪，使之可以更深入、准确地揭示非线性非平稳信号的时频局部特征。

Based on the modem FEM with the dynamic substructure method, itd dynamic equation is established with almost no limits to DOFs of the system, in which the left side is the first approach of the nonlinear system and the right side is the excitation and coupling nonlinear pseudo forces. The modal analysis method is used to get the eigen solution to the reduced linear homogeneous dynamic differential equation. When the system is excited by the harmonic excitation at the right side of the equation, the nonlinear dynamic response can be calculated by the numerical method to give quantitative analysis.

基于近代有限元和子结构模态综合法的动力学建模方法，获得非线性系统动力学微分方程，其自由度几乎没有限制，对左端首次近似齐次方程进行模态分析，选取对响应有贡献的部分本征对，同样对右端激励和非线性伪力作模态变换，得到减缩后非线性系统耦合动力学微分方程。

A kind of model of rotor-bearing-seal system dynamics is set up integrally in this thesis. Within this model, a new modal order-reduction method is presented, which takes the influence of nonlinear forces into account in the process of modal transformation, which makes the determination of the transformation matrix more reasonable and accurate.

提出了一种模态降阶新方法，在模态变换过程中充分考虑系统中非线性力的影响，使得模态变换矩阵的选取更为合理准确。

In this paper, modal reduction criterion is derived based on the system response taking as the model of Euler-Bernoulli beam, edi ting modal according to the value of modal costs. The conclusion can be used in a lar ge flexible complex structure system.

该文以欧拉－伯努利梁为模型，推导出基于系统响应梁的模态截断准则，根据模态价值大小取舍模态，其结论可推广到大型复杂结构系统。

Firstly, the 3D solid model of the analyzed object is built directly in the FEM software ANSYS 8.0 without using other CAD software. The influence of the side sizes of solid elements on computing results and the influence of coupling ways between different parts on the modal parameters are researched by simply modeling. And a new connecting method about joints in ANSYS is proposed and applied to finite element modeling of the test-bed for spindle system. Furthermore, several different computing techniques for modal parameters extraction are compared in solving the finite element model of spindle system test-bed. Many modal solutions are also done to achieve the relationships between the whole or part stiffness value and computed modal parameters. The laws about joint rigid parameters" influences on modal parameters are discussed by means of altering their values for conjoint parts. And by changing local rigid parameter values, the different location selections" influence on computed modal parameters is also studied.

本文通过使用ANSYS 8.0软件直接建立研究对象的实体结构模型，而没有借助其他的CAD软件；通过构建简单的模型研究实体单元边长大小对计算结果的影响，部件之间不同的联结方式对模态参数的影响，探讨在ANSYS中实现结合部的方法，提出一种新的联结方法，并建立主轴系统试验台的有限元模型；对建立的主轴系统试验台有限元模型求解，比较几种不同模态提取方法；通过改变结合部联结单元的刚度参数进行的计算，寻找联结刚度对模态参数变化的影响规律；改变局部联结单元的刚度参数，研究刚度值位置差异对计算模态参数的影响。

Disjunction normal form theorem in the modal logic system S5 is inductively proved, which can be used for representing complex modal formulas by means of conjunction and disjunction of simplest modal formulas with depth at most 1 in the system S5. As application, it is proved that a knowledge base could answer KB-queries if and only if it could answer queries of non-modal propositions and their negations, which is a basic problem on knowledge base.

研究了模态逻辑系统S5中的析取范式定理的归纳证明，给出了在S5中用深度至多等于1的最简模态公式通过析取与合取运算表示含有多重模态词的公式的方法，作为范式定理的应用，讨论了知识库中的一个基本问题，证明了知识库能够回答KB命题式问题的充要条件是该知识库能够回答相关的非模态命题及其否定命题的问题。

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 method is a well-revised approach, as greatly reduce the computation works.

采用模态特性矩阵来判别网壳风振主要贡献模态及分析模态相关性影响，计算量大大减小，是个改进的方法。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。