模方程

Due to the symmetry of the plate, there are symmetric and antisymmetric mode vibrations with respect to the median plane of the plate.

首先建立了在偏压电场作用下压电介质的运动微分方程，进而根据对称模态和反对称模态的特点，分别在自由表面电学开路和电学短路情况下得到了Lamb波传播的相速度方程。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

These modes are calculated in the paper by wave equation, finite element equation and model established, and computer procedure.

本文通过推导的压力波动方程、建立的有限元方程与计算模型、编制的计算机软件，计算出燃烧压力波动的多阶模态及各模态下的压力分布。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g，当n阶矩阵A的特征多项式为不可约的，我们给出了矩阵方程g=A有解的判定定理；当A的特征多项式为可约的，把域F上的n维线性空间M作为由A导出的F -模，我们利用模论知识来决定矩阵方程g=A有解性，从而使这一问题变了简单，研究思路更加清晰。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

Based on the concept of the non-proportional damping which may be divided into the proportional part for dissipation of energy and the nonproportional part for transformation of energy, a new modal superposition pseudo-force method is presented if the approximate decoupling method is not suitable. In this method the coupled modal equations are solved by iteration in which the coupling terms are treated as pseudo-force and set to the right side of the equations.

在不能进行近似解耦分析时，基于非比例阻尼可分为耗散能量的比例部分和转换能量的非比例部分这种概念，建立了一种拟力实模态叠加法，即把正则化的耦合模态方程中代表非比例阻尼部分的耦合项作为虚力，放到方程的右端，再运用迭代法求解。

Its improved form of three terms series including Rubin second-order approximate terms and their exact residual term is then obtained.

采用叠加法和删除保留模态法导出了自由界面精确剩余模态三项和公式，它在Rubin二级近似项上增加了精确余项，导出非线性精确综合方程，构造了具有超收敛性质的迭代求解方程。

In the analysis, a nonlinear wave vibration equation of the thin cylindrical shell including damping and items due to geometric nonlinearities was established and then transformed by Galerkin's method. With different combinations of modes different nonlinear differential equations in modal coordinates were obtained. The Runge Kutta method was used to solve the equations numerically and some features of nonlinear wave vibration were discussed.

在研究过程中，首先，考虑阻尼并引入几何非线性项，建立薄壁圆柱壳的非线性波动方程，然后，采用Galerkin方法对波动方程进行转换，选取不同的模态组合，得到相应模态坐标下的非线性微分方程，最后用Runge-Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析。

Results of analysis show that Generalized Paris Law can consider the complex crack propagation in the material of the pavement structure. The fatigue life of the pavement increases with increasing thickness of surface layer in a power function. Use of a thicker surface layer may extend the service life of the asphalt pavement. The fatigue life increases with decreasing modulus of surface layer in a power function with a negative exponent. However, since reduced modulus would scarify the structural strength and might cause rutting-related distress, caution should be taken when using low modulus materials for improving fatigue performance of asphalt pavements. The fatigue life increases with increasing modulus of base material in a power function. However, the fatigue life can not infinitely increases with increasing modulus of the base.

计算与分析表明：广义Paris公式可以考虑沥青路面结构内材料复杂的裂缝扩展：沥青面层的疲劳寿命随着面层厚度的增加以幂函数的形式增加，适当增加沥青面层厚度可以提高路面的使用寿命；沥青面层的疲劳寿命随着面层材料模量的降低以负指数的幂函数形式增加；由于材料模量的降低将牺牲路面的整体强度并可能引起路面车辙类损坏，以此提高疲劳寿命的方法应慎重对待；沥青面层的疲劳寿命随着基层材料模量的增加呈幂函数的形式增加，但由疲劳方程可以看出，寿命并不是随基层材料模量的增加而无限的增加，疲劳曲线在经过一个上升段后，逐渐趋于一个常数值，这说明，这时基层模量对寿命已不作关键性贡献；随着底基层厚度的增加，面层的疲劳寿命近似地呈线性函数增加，但效果并不很明显。

In this dissertation the"Penalty"finite element method was employed to compute the velocity of the three-dimensional flow of power-law fluid in a profile die. In order to decrease the needed computer memory and raise the stability of numerical simulation, a set of decoupled methods such as PFEM, pseudo-body force method and transformation of momentum equation to the elliptic equation was developed to establish the general finite element equations to compute the distributions of velocity and viscoelastic stress of the three-dimensional viscoelastic flow of the Phan ThienTanner fluid in a profile die. During numerical simulation of the extrudate swell of the PTT fluid, the flow in the die and out of the die was analyzed separately, which demands less computer memory.

本文建立了求解挤出口模内幂律流体流动速度场的通用三维罚有限元模型；对于非线性粘弹性的Phan Thien-Tanner流体，为了降低模拟计算对计算机硬件的要求，并使模拟计算更加稳定，采用了一种去耦算法，包括罚有限元方法、拟体力方法和动量方程的椭圆类方程转化方法，并建立了求解速度场和粘弹性应力场的总体有限元方程；对于PTT流体的挤出胀大问题，提出了挤出胀大熔体口模内外分离模拟法，这样可以显著降低数值模拟对计算机硬件的要求。

He and Nina moved to California and lived at 2005 Ivar Street, Apt.

他和Nina搬到加州，并在2005年伊瓦尔街，公寓生活。

Droperidol （ potently inhibits transfected HERGchannels and this is the probable mechanism for QT prolongation.

氟哌利多有效地抑制了转染的 HERG 钾通道，可能是 QT 间期延长的机制。