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nonlinear equation相关的网络例句

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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。

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。

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。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分:在一维情形,我们考虑了一类带导数项的Ginzburg—Landau方程,通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计,证明了当粘性系数趋于零时,Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解,并给出了最优收敛速度估计;在二维情形,我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性,以及在某种特殊情形下,GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解;在一般情形下,我们讨论了一类Ginzburg—Landau方程的非齐次边值问题,通过几个积分恒等式,同时估计解的H〓模及法向导数在边界上的模,证明了整体弱解的存在性。

In the algorithm, the conditional linear state equation is first inserted into the measurement equation, which fuses the linear state process noise and the original measurement noise, whereafter the GHF is used to estimate the nonlinear states. Then the estimated means of the nonlinear states are inserted into the linear state equation and the original measurement equation to estimate the linear states by the KF. Moreover, in order to improve the accuracy of the estimates, the estimated variances of the nonlinear states are fed back to modify the estimations of the linear states using the KF.

算法将模型中的条件线性状态方程代入观测方程,并融合线性状态的过程噪声和观测噪声,由GHF获得非线性状态的估计;再将非线性状态的估计均值代入线性状态方程与观测方程,由KF获得线性状态的估计;获得的非线性状态估计方差还用于修正由KF估计的线性状态,以提高精度。

In the Gaussian sum filter-Kalman filter algorithm, the conditional linear state equation is first inserted into the measurement equation, which fuses the linear State process noise and the original measurement noise. And the GSF is applied to the new measurement and nonlinear state equations to estimate the nonlinear states. Then the estimations of the nonlinear states are inserted into the linear state equation and the original measurement equation to estimate the linear states by the KF.

算法将模型中的条件线性状态方程代入观测方程,并融合线性状态的过程噪声和观测噪声,再与非线性状态方程联立,由高斯和滤波器(Gaussian sum filter, GSF)获得非线性状态的估计;然后将估计值代入线性状态方程与观测方程,由卡尔受滤波器(Kalman Filter, KF)获得线性状态的估计。

The paper firstly analyze for nonlinear stiffness characteristic of the air spring and provide four type of hypothesis to nonlinear stiffness of the air spring, that is: rubber material nonlinear、composite of rubber and lining cloth nonlinear、 contact nonlinear and geometry nonlinear. Using test method relation curve between stiffness of air spring and on/off time of electro-magnetic valve had been established and the formula has been drawn up.

本人在2001年承担了吉林省科技厅资助的&汽车电控空气悬架系统研究开发&项目,论文的内容是该项目的核心部分,重点在于控制算法的研究和控制系统的设计,为最终在整车上实现空气悬架的自动控制进行前期的基础研究和必要的设计准备工作。

Establish the steady-state and transient model using the three hydrodynamics equations (Continuity equation, Momentum equation and Energy equation). By comparing different state equation, it selects the BWRS state equation which is considered the most accurate state equation in current natural gas measurement. It calculates compression factor, density and other Thermal parameters based on BWRS state equation. In Numerical solution of the steady-state and transient model, compression factor, friction coefficient and all the other Thermal parameters are recalculated in each small time step to reduce the numerical calculation error.

在稳态模型的建立上,利用流体力学三大方程(连续性方程、运动方程和能量方程),通过比较不同的状态方程选用了目前被认为最精确的用于天然气计量的BWRS状态方程,并以此方程为基础进行压缩因子、密度等热物性参数的计算;在稳态模型的求解上,选用容易计算,精度较高的标准型龙格—库塔(Runge-Kutta)法进行数值求解,并且在迭代过程的每一小步都重新计算燃气的压缩因子,摩阻系数等所有的计算参数,以减少数值计算的误差。

It is a generalization of the nonlinear diffusion equation proposed by Perona-Malik and the method presented by Cuesta, and interpolates between the nonlinear parabolic equation and the nonlinear hyperbolic equation, thus can effectively control the diffusion process so that noises can be removed and details of the image such as edges can be preserved as much as possible simultaneously.

提出了一种包含对时间的分数阶导数的非线性扩散方程,它是对Perona-Malik的非线性扩散方程和Cuesta提出的方程的推广,介于非线性抛物方程和非线性双曲方程之间,从而能有效地控制扩散过程,使得在去除图像噪声的同时能够尽可能地保留图像的边缘等细节信息。

Firstly, the author establish the functions of stability on the basis of the spline function method ,according to the theory of geometrical nonlinear and the theory of stability, educe the stability equation of structure based on variational principle, then carry through the flexuosity analysis of CFST arch.The big distortion geometrical nonlinear was considered by the stability equation,the author simplified the problem of geometrical nonlinear through ignored quadratic term and reserve the simple term, at last boiled down to solve the linear stability equation of eigenvalue .

利用样条函数方法、根据几何非线性变形理论和结构稳定性理论,先建立起结构稳定的泛函,再由变分原理导出结构的稳定方程,进行钢管混凝土拱屈曲分析;本文所建立的稳定方程考虑了几何非线性的大变形效应,通过忽略几何非线性的二次项,保留一次项,将几何非线性问题简化,最后归结为求解线性稳定问题的特征值稳定方程,建立了结构非线性静力稳定性问题的新算法及失稳类型判别准则。

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