非线性振动

Let the obtained modality parameters be substituted into the coupling vibration partial differential equation and transform the complex partial differential equation into the variable coefficient nonlinear or...

把所得模态参数代入耦合振动偏微分方程中，将复杂的偏微分方程转化为变系数非线性常微分方程组，用Runge-Kutta方法获得方程的数值解。

Then the stability solution of the variable cross-section compression bar, that is discribed by a partial differential equation with variable coefficient is transformed into solving a set of algebraic equations established in the subspace.

首先以均匀梁的低阶纵向振动模態函数构成求解子空间，然后在此子空间中把变截面压桿稳定由变系数偏微分方程描述的求解问题转化为非线性代数方程组的求解，从而简化了计算过程。

It is pointed out that the solution of the differential equation is a periodic function.

建立了水平方向静电悬浮非线性系统微分方程形式的数学模型，指明了该微分方程的解是振动周期函数。

A nonlinear model is studied in this paper on the simulation of Pogo vibrations in liquid rockets.

本文针对液体火箭推进系统中的Pogo振动现象提出了一种非线性的仿真方法。

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。

Modeling of a rigid-flexible coupled dynamic system.we derivedthe equations of a rigid-flexible coupled dynamical system by usingLagrange Method,including the rigid's space three-dimensionmotion,the beam's vibration and the non-linear joint.

针对某一刚柔耦合多体系统，应用拉格朗日方程建立了含有刚体空间三维运动、柔性体弹性振动及非线性弹性铰的较为完善的动力学方程，由此可以根据不同的实际情况进行简化而得到相应的方程，免去了重新进行烦琐推导的过程。2。

These issues mainly include simulation offlexible soil container, selection of dynamic constitution model of soil, simulation of the changing-status non-linearity on soil-structure interface, meshing, treatment of reinforcements in structure,using of symmetry principle and so on.

按照本文的建模原则和计算方法，对土-桩基-结构相互作用体系振动台试验进行三维有限元计算分析，计算中土体采用等效线性模型，利用面-面接触单元考虑土体与结构交界面的状态非线性。

The results show that electromagnetic vibration of hydropower generator rotors exhibits nonlinear characteristics, including the jumping phenomenon of amplitude-frequency curve and the obvious soft characteristics.

结果表明，动态偏心条件下水轮发电机转子的电磁振动呈现非线性特征，幅频曲线在一定条件下将出现跳跃现象，系统呈现明显的软特性。

The results of computation show that this method is very effective for reducing and controlling the transverse oscillation of wave motion and for the calculation of wave particle velocity of wave motion on free surface, w...

计算表明：这种0—1混合型边界元的剖分方式，在控制和减缓波浪"横向振动"幅度及水面单元水质点波动速度的计算方面，显示出了其独到的优越和灵活之处，为时域内的波浪非线性变形计算提供了时步上的数值保证

The different methods of controlling wake flow in engineering are introduced according to concept of absolutely and convectively unstable wake.

本文利用数值方法研究了静止圆柱和振动圆柱在不同流动条件下绕流流场的非定常性、不稳定性和非线性特征。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。