wave equation

wave equation的基本解释

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[计] 波动方程

与wave equation相关的网络例句 [注：此内容来源于网络，仅供参考]

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

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。

Angular spectral is spectral value map formed by estimating semblable coefficients of fast and slow shear wave or the variation of amplitude ratio of fast and slow shear wave with times and angles at a specified space point based on semblable theory of fast and slow shear wave, the angle value of this space point at a given time can be got by picking the maximum of angular spectral; the study reveals that fast and slow shear wave with different polarization direction should be separated using different rotation formula, eight formulas of separating fast and slow shear wave using clockwise rotation and counterclockwise rotation have been derived, and gained energy assignment rule and phase coincidence rule, in real data estimation, the rotation formula used for separating fast and slow shear wave can be uniquely determined on the two discriminating rules. On the basis of semblable theory of fast and slow shear wave, the delay time corresponding to the maximum of semblable coefficients at a specified point in a given time window is the delay time of fast and slow shear wave, delay time section of fast and slow shear wave can be got by moving space point and smoothing time window. The vertical variation values of delay time of fast and slow shear wave reflect the effect degree of vertical fractured reservoir on fast and slow shear wave which is defined as anisotropic coefficient, and section map of anisotropic coefficient can be obtained.

角度谱就是利用快慢横波的相似性原理，在某一空间点求出快慢横波的相似系数或快慢横波的振幅比值随着时间和角度的变化而形成的谱值图，拾取其极大值就得到该空间点某一时间的角度值；在研究中发现分离不同偏振方向的快慢横波应该采用不同的旋转公式，推导出了利用顺时针旋转和逆时针旋转分离快慢横波的八个公式，并给出了能量分配准则和相位一致性准则两个判别准则，在实际计算中利用这两个判别准则能唯一地确定分离快慢横波的旋转公式；根据快慢横波的相似性原理，在某一给定点和给定时窗内最大相似系数对应的延迟时间就是快慢横波的延迟时间，随着空间点的移动和时窗的滑动就可以得到快慢横波延迟时间的剖面图；快慢横波延迟时间与慢横波传播时间的比值定义为裂缝密度，并求出了裂缝密度剖面图；快慢横波延迟时间纵向上的变化值的大小反映了纵向上裂隙层对快慢横波影响的大小，定义为各向异性系数，并求出了各向异性系数的剖面图。

与wave equation相关的网络解释 [注：此内容来源于网络，仅供参考]

wave equation：波动方程

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