查询词典 oscillation equation

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。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

Firstly, the mechanism of heat transfer enhancement by oscillation heat surface is discussed in natural convection scene. For different oscillation amplitude and Rayleigh number, the frequency that the heat transfer rate of oscillation heat surface is higher than non-oscillation condition is found and called critical oscillation frequency. The limitation enhancement of similar physical model is still researched by this study in mixed and forced convection scenes for different amplitude and Grashof number. Generally, that a heat surface subject to a oscillation motion is advantageous to convective heat transfer is a well-known tuition.

首先探讨在垂直管道内振动高温面於自然对流领域内提升高温面热传效率的机制，并且针对不同的振幅与雷利数求得加入振动条件后，高温面散热效果可以优於稳态非振动高温面散热效果的临界振动频率；进而探讨当垂直管道流进入混合对流与强制对流范围时，在不同的振幅与葛瑞秀夫数下，亦可发现加入振动条件后，振动高温面之散热效果可以优於稳态非振动高温面散热效果的临界振动频率。

The experiment shows that:(1) In certain light intensity and electric field ranges (145～305V/cm) the material Si∶ with a resistivity of 1E4Ω·cm exhibits a current oscillation phenomenon at liquid nitrogen temperature;(2) At a certain electric field,the waveform of the current oscillation is stable and does not change with time;(3) The dependence relation between the oscillation frequency and light-intensity can be expressed by f=f0(L/L0)α where L0 is the minimum light-intensity needed to stimulate oscillation,f0 is the frequency under L0,L is the intensity of the light,and α is a coefficient that increase with electric field;(4) The modulating coefficient K K=(Imax-Imin/Imax decreases as the light increases;(5) The maximum value of the oscillation Imax decreases with the increase of the light-intensity while the minimum value of oscillation Imin increases slowly.

结果表明：在一定光照和电场范围内（276～305V/cm ，电阻率为10.4Ω·cm的材料在液氮温度下显示出电流振荡特性；在一定的电场下，电流振荡波形是固定的，不随时间变化；振荡频率随光照强度的增大而线性增大；调制系数随着光强的增强而减弱；振荡的最大值随着光照强度增大而减小，最小值随着光强增大而缓慢增大。

This paper compared continuous casting mold oscillation types between nonsinusoidal oscillation and triangle oscillation, analyzes their oscillation waves and oscillation parameter s.

本文对非正弦振动和三角形振动这两种不同的连铸结晶器振动方式进行比较，分析二者振动波形及振动参数，确定适合高速连铸的振动参数的选择范围，选出最佳的振动形式。

The oscillation performance of jet, as oscillation frequency, is the essential data for designing the fluidic device, which is also the key factor that influence the coupling effect of fluidic device and receiving tube. This paper does experiment on the oscillation availability and frequency of feedback jet-oscillation gas wave refrigeration. As a conclusion, the jet oscillates only in a certain range of geometrical sizes and operating conditions. Under the condition of high pressure ratio, the frequency of the jet"s oscillation is only affected by the feedback tube"s length and chamber remarkably. Under the condition of low pressure ratio, the frequency descends with rise of the pressure ratio.

本文将跨音速正反馈射流振荡器与接受管耦合，对耦合后的射流振荡气波制冷机的可振性、振荡频率以及它们的影响因素作了实验研究，得出如下结论：射流只在一定的操作条件和几何结构尺寸范围内才能稳定振荡；射流的振荡频率在较高压比下只受反馈管长和反馈管容腔大小的显著影响，在小压比下随压比的增大而增加；其它结构尺寸和操作条件只影响可振性。

Firstly, the mechanism of heat transfer enhancement by oscillation heat surface is discussed in natural convection scene. For different oscillation amplitude and Rayleigh number, the frequency that the heat transfer rate of oscillation heat surface is higher than non-oscillation condition is found and called critical oscillation frequency. The limitation enhancement of similar physical model is still researched by this study in mixed and forced convection scenes for different amplitude and Grashof number.

首先探讨在垂直管道内振动高温面於自然对流领域内提升高温面热传效率的机制，并且针对不同的振幅与雷利数求得加入振动条件后，高温面散热效果可以优於稳态非振动高温面散热效果的临界振动频率；进而探讨当垂直管道流进入混合对流与强制对流范围时，在不同的振幅与葛瑞秀夫数下，亦可发现加入振动条件后，振动高温面之散热效果可以优於稳态非振动高温面散热效果的临界振动频率。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

Therefore, the multi-stage interaction structures with losses and severed structure were more stability for absolute instability and gyrotron backward oscillations. This study presents a nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation and reflective oscillation. The multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of the absolute instability, gyro-BWO, and reflection oscillation.

所以在本研究分析中，藉由了解磁旋行波放大器中的自发振荡物理原因及特性，将有助於高功率放大器的设计，并且引用非线性程式进行磁旋行波放大器稳定分析，并且采用兼具隔离管及散布式损耗结构的磁旋行波放大器，同时提升绝对不稳定、磁旋返波振荡及反射振荡的稳定性能有效提升磁旋行波放大器输出功率和频宽。

He proved that the left ward turning of Yangtze river diluted water is mainly resulted from the interaction between the bottom declining and the lag of the transversal pressure gradient, made the numerical simulation and preliminary study on the thermohaline staircase structure formation mechanism, improved American Academician Wunsch's inverse method of ocean circulation, jointed the discover of " Mindanao Under Current", which is the first ocean current found and named by Chinese scientists and widely accepted over the world, simulated the horizontal and vertical carbon fluxes in East China Sea by a simple ecosystem model, estimated the photosynthesis efficiency less than 8% in Jiaozhou Bay, applied statistical downscaling technology to Chinese coast and Japanese islands realizing the simulation and forecast of sea level low frequency variations, pointed out that the quasi-periodicity of El Nino events should be resulted from the interaction between the 3~4 year oscillation in tropical Pacific and decadal oscillation in the northern Pacific of middle latitudes of the air-sea coupled climate system and at decadal time scale the precipitation influence on sea level variation along Chinese coast and Japanese islands becomes more important, which is closely related to the decadal oscillation of air-sea coupled climate system, therefore precipitation most likely play a major role for the decadal oscillation formation;; proposed Extended Associate Pattern Analysis to analyse combined observed datasets of sea surface temperature and sea level pressure or geopotential hight at 1000 hPa (GH1000) over the Pacific and related seas.

论证了长江冲淡水向左转向主要由于底形下倾与横向压力梯度滞后相互作用的结果。对温盐阶梯结构的形成过程及物理机制进行了数值模拟与初步探讨。改进了美国科学院院士Wunsch的大洋环流反演法。与胡敦欣院士共同发现了"棉兰老潜流"，这是第一支由中国科学家发现、命名并得到普遍承认的洋流。借助较为简单的生态模式数值模拟了东海的水平与垂直碳通量；胶州湾浮游植物的屏蔽效应可以使底层海水温度在升温季节降低2度，由此推算出其光合作用的效率应小于8%；浮游植物春季水华的生物过程实际上强化了海水层化的物理过程。将统计学降尺度技术应用于日本列岛和我国沿海，实现了海平面长周期变化的模拟与预报。

He became prime minister in 1997 and won international acclaim for his role in the Northern Ireland peace process.

他在1997年成为总理，并且因为在北爱尔兰的和平进程中发挥的作用受到国际社会的赞许。

Mixed Page Sorting Method Using the cuttable user model, this thesis proposes a mixed page sorting method by using cutted user model in server-side and complete user model in client-side.

隐私分级利用的混合式页面排序方法针对个性化搜索中搜索结果排序的问题，本文利用隐私可控开放的用户偏好模型，提出一个在客户端和服务器端分步进行的隐私分级利用的混合式页面排序方法。