查询词典 second boundary condition

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

In the symplectic system of plane elasticity in rectangular coordinates, by separating variables and abandoning the homogeneous boundary condition, the symplectic solution of a rectangular beam subjected to distributed load in a power function form is obtained.

在弹性力学平面直角坐标辛体系中，采用分离变量法，放弃齐次边界条件，得到了矩形梁侧边受幂函数形式分布荷载问题的辛解答，给出了这类问题在辛体系中的一般解法，分别对矩形梁受法向和切向分布荷载的问题进行了求解，显示了此方法的有效性。

Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.

第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。

Some new method is presented in this paper: A. An Integrated parameters computation method to analysis asynchronous operation of the turbine generator is given, including the equivalence of short circuit and open circuit of field windings, deducing boundary condition of 〓 method and computing frequency parameters. B. A new memory structure for sparse complex matrix and a PCCG method based on it are introduced to save memory and computation time. C. An equivalent method of vacuum is presented, and effectively eliminate the effect of corner point and accelerate convergence of PCCG method. D. Coupling the computation of electromagnetic and temperature field is discussed and model for computing temperature field of the turbine generator rotor at asynchronous operation is built.

文中提出了以下新方法：(1)在失磁异步运行转子三维涡流场计算中提出了完整的参数计算方法，其中包括励磁绕组开、短路的等效，〓法边界条件的推导及频率参数的计算方法；(2)提出了铁心内空气域的等效方法，有效地解决了开槽引起的角点奇异问题，并提高了方程组的迭代收敛速度；(3)在〓法有限元模型中，创立了一种能节约内存、提高计算速度的压缩存储矩阵格式，并建立了基于该格式的方程组解法；(4)提出了涡流电磁场和温度场两种不同场计算的合理结合方法，建立了转子三维稳态和时变温度场的有限元计算模型。

This OCVC problem was converted to a typical two-point boundary-value problem according to Pontryagin maximum value principle, and this TPBVP was a first order optimality condition which could be solved by Radau collocation method.

根据Pontryagin极大值原理建立该协调电压控制问题的1阶最优性条件，该条件是一个典型的两点边值问题。在此基础上采用拉道排列法求解这个两点边值问题。

The scattering wave velocity potential to the flexible circle pile was the solution of the Laplace equation, which satisfied the cylindrical surface non-homogeneous boundary condition.

采用动力Winkler弹性地基梁模型模拟桩土动力的相互作用，通过求解满足柱面非齐次边界条件的Laplace方程，直接构造波浪对柔性桩的散射速度势，考虑了流体和桩体的相互作用，由解析法给出了埋置圆桩在波浪荷载下的动力响应。

The primitive variable and pressure Poisson equation formulation is employed for the numerical solution of the N-S equations, in tensor forms, on an H-0 type of non-staggered grids that makes it convenient to apply a strict inflow and outflow boundary condition.

计算网格采用H-O型非交错网格系统，易于采用严格的入流和出流边界条件。

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。

At the same time we provided the double trigonometric progressional solution at the common boundary condition. And combining with the taken test of such plate abroad this analysis method was proved to be accurate and credible.In the third chapter, reasonable finite element models for such structure were established and a static non-linear analysis was made, and we summarized the rule of this structure about the aspects of force, deformation and destruction.

第三章对薄壁箱体现浇混凝土空腹板楼盖结构建立了合理的有限元分析模型，进行了静力全过程分析，侧重分析其在竖向荷载作用下的受力性能，总结出此结构体系的内力、变形分布及破坏过程的规律，并结合国外试验和国内现行混凝土结构设计规范，对这种结构的冲切计算进行了简单的探讨，提出了冲切计算的修正公式。

The projection gradient method will be a possible way to solve the problem that we just get. It has been shown that the projections of the every directions, of which is the boundary point in linear restraint problems, are the possible decent directions, and the projection of negative grads direction is a decent direction. In 1960, Rosen proposed the basic idea of projection gradient methods, and then lots of researchers have been tried to find the convergence of this method. But most of them get the convergence with the condition to amend the convergence itself.

在约束最优化问题的算法中怎样寻找有效的下降方向是构造算法的重要内容，在寻找下降方向方面可行方向法中的投影梯度法有效的解决了下降方向的寻找问题，利用线性约束问题边界点的任意方向在边界上的投影都是可行方向，而负梯度方向的投影就是一个下降方向。60年代初Rosen提出投影梯度法的基本思想，自从Rosen提出该方法以后，对它的收敛性问题不少人进行了研究，但一般都是对算法作出某些修正后才能证明其收敛的，直到最近对Rosen算法本身的收敛性的证明才予以解决。

Researches reveal that students who suffer from corporal punishment tend to resort to violence in their future life.

研究表明遭受过肉体惩罚的孩子倾向于在他们今后的人生中使用暴力。

Total sugar of sarcocarp and chlorophyll of pericarp increased firstly, and then decreased afterward along with altitude; Titratable acidity, ascorbicacid and anthocyanin of pericarp were increased along with altitude; The content of protein increased firstly and decreased afterward along with altitude; Carotenoid of pericarp were decreased along with altitude.

果肉总糖和果皮叶绿素含量随海拔高度升高先升高后降低；可滴定酸、维生素C和果皮花青苷含量均随海拔升高而升高；蛋白质在1720m处最大，1420m处最小；果皮类胡萝卜素随海拔升高而降低。