查询词典 galerkin equations

The governing equation of in-plane vibration of cable-restraint system is derived by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations by Garlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is made to prove that this vibration control has obvious damping effects and then the influence of cable tension, support mass, natural frequency and spring stiffness on the damping are discussed. Eventually, the approximate analytic solution of the optimum damping parameter is obtained to provide a simple and effective reference and design method for the engineers.

通过D'Alembert原理建立拉索－弹性约束系统振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格－库塔积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼参数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。

Based on the Von Karman theory of thin plate with large deflection, the nonlinear dynamic differential equations of elastic elliptical plate are first established.

然后应用Galerkin技术和KBM法求解了此微分方程，并讨论了有关参数对粘弹性椭圆板动力学行为的影响

The Galerkin's method was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary differential equations with time dependent coefficients,which can be solved with numerical methods.

对于电梯工业来说，目前世界上绝大部分电梯仍然是依靠钢丝绳提升的曳引式电梯。

By Galerkin meshless method, the equations of motion of static rectangular membrane is established. The first ten natural frequencies of the different aspect ratios and the different pull ratios of rectangular membrane with four clamped edges, three clamped edges and one free edge, two opposite free edges and other two clamped edges were calculated. It is feasible and valid to solve the transverse vibration problem of membrane by Galerkin meshless method.

采用伽辽金无网格法，建立了矩形薄膜横向自由振动的运动方程，并对四边固支、三边固支一边自由、一对边固支另一对边自由三种边界条件下，薄膜的不同长宽比及不同单位长度拉力比作用下的矩形薄膜的前十阶固有频率进行了数值计算，结果说明伽辽金无网格法用于求解薄膜横向振动问题是切实可行的。

The present method is applied to two-dimensional potential problems and the corresponding discrete equations are derived. Because the shape functions so-obtained possess the Kronecker delta property, the essential boundary conditions can be enforced as the FEM; furthermore, the Heaviside step function is used as the test function, there is no domain integral, and only a regular boundary integral is involved.

因为滑动Kriging插值方法构造的形函数满足Kronecker函数性质，所以本文建立的改进的无网格局部Petrov-Galerkin法可以像有限元法一样直接施加边界条件；由于采用Heaviside分段函数作为局部弱形式的权函数，因此在计算刚度矩阵时只涉及边界积分，而没有区域积分。

To obtain the RCS of dipole-array antennas, the system of electric field integral equations is turned into a linear algebra system whose coefficient matrix is a symmetric block Toeplitz complex matrix by using Calerkin method with pulse basis functions.

为计算线天线阵列的雷达散射截面，用脉冲函数为基函数的Galerkin法将线天线阵列的电场积分方程组转化为一个线性方程组，其系数矩阵是一个对称的二重复Toeplitz矩阵。

Based on the Galerkin Method the variational problem for the point source 2.5-dimensional electricfield is derived and the corresponding finite element equations are obtained.

基于Galerkin法推导了点源2.5维电场的变分问题，得到了对应的有限元方程组。

In chapter 1, Galerkin alternating-direction procedures and an approximation to the Jacobian of the isoparametric map are applied to discuss a three-level and a four-level Galerkin alternating-direction procedures for two kinds of nonlinear hyperbolic equations which are given on a nonrectangular, curved region.

第一章结合[10]中对矩形域上双曲型问题提出的交替方向有限元方法和[19]中利用等参元，等参变换的Jacobi行列式的逼近来研究的思想，给出了两类非线性双曲型方程在非矩形域上的交替方向有限元方法。

A detailed model of non-linear parametric excitation vibration coupling the stay cable and the girder, in which the static sag as well as the geometric non-linearity are considered, is proposed in this paper. Based on several numeric examples investigated by the Galerkin method composed with the integration strategy, several kinds of factors effecting stay cable parameter vibration are studied. Another parameter vibration model by the axial excitation is presented and the corresponding nonlinear equations are derived. The smallest excitation amplitude,the transient state and steady state resonance amplitudes, and the changing characteristics of the axial force are obtained by using harmonic balance method. According to numerical examples calculated by numerical integration method, the effects of the inner damping of the stay cables are investigated.

本文创新地提出了斜拉桥拉索-桥面耦合参数振动模型，推导了索-桥耦合非线性参数振动方程组，联合Galerkin法及数值积分方法，对各种特性的拉索进行了数值求解，得出了影响拉索参数振动的各种因素；提出了斜拉索受轴向端激励参数振动模型，导出了模型的非线性振动方程，使用谐波平衡法得出了产生参数振动需要的最小激励幅值、共振时瞬态及稳态的振动幅值及索拉力的变化特性，并用数值积分方法对实际斜拉桥拉索进行了计算，分析了拉索阻尼对参数振动的影响。

Nonlinear partial differential dynamic equations of bending vibration of a tilting stepped drive shaft with two supports were built under non-inertia movement coordinate system by theorem of the motion of mass center and Heaviside function. According to the condition of equal displacement in an adjoining plane of the shaft, an equivalent shaft and its equation were obtained. A motion equation of the equivalent shaft was obtained by method of Galerkin. An approximate steady-state solution of the main resonance was obtained by method of multiple scales. The influence factors, motion stability, amplitude jump of main resonance of a stepped drive shaft and so on were analyzed.

用质心运动定理、Heaviside函数建立了非惯性系下倾料两端支承阶梯传动轴的非线性弯曲振动偏微分动力学方程，并根据相邻轴段的衔接面处位移相等的条件，得到阶梯轴的当量轴及其动力学方程；用Galerkin法得到当量轴的弯曲运动方程，用多尺度法求得稳态下当量轴的主共振的一次近似定常解，分析了影响阶梯传动轴主共振的因素、运动稳定性、振幅突变性等。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。