查询词典 simultaneous equations

In this dissertation, considering the influence of transverse shearing deflection and noncoincidence of torsion center and gravity center, the equilibrium formulas of variable-curvature box-girder with rectangular cross section were established. Based on deformation expression of arbitrary point on the girder and relationship between inner forces and displacement equations, considering noncoincidence of torsional center and gravity center, the governing differential equations for variable-curvature box-girders were generalized.

针对具有竖直对称轴的矩形断面变曲率箱梁，考虑了挠曲剪切应变和曲梁剪心和形心分离的影响，推导了变曲率箱梁的平衡方程；通过箱梁内任一点的位移方程和内力-位移关系，推导了考虑曲梁剪心和形心分离的变曲率箱梁的挠曲扭转控制微分方程。

Based on the averaged equations of the nonlinear nonplanar flexible cantilever, thenormal form of the averaged equations is obtaineiby the Maple program given in the appendix.

在平均方程的基础上，利用前面得到的规范形计算程序对平均方程进行简化，得到了平均系统的规范形。

The equations of motion for the nonlinear nonplanar flexible cantilever are derived by using the generalized Hamiltons principle. Then, the Galerkin procedure and the method of multiple scales are used to give the perturbation analysis of the system and the average equations. The three resonant cases are considered in this dissertation.

对于非线性非平面运动悬臂梁，利用广义Hamilton原理详细推导了运动微分方程，综合运用Galerkin离散方法和多尺度法对非线性非平面运动悬臂梁的动力学方程进行摄动分析，得到了三种共振情况下的平均方程。

The plastic hinge model of perforated liner casing is built up to calculate the collapse pressure according to the strength and deformation behavior of perforated liner casing subjected to external pressure. The calculation equations of collapse pressure of perforated liner casing with initial ovalization are deduced by energy method. The influences of phrase angle, diameter of perforation, shot density, initial ovalization, diameter-thickness ratio and yield stress on the collapse pressure of perforated liner casing are studied. The model and equations are used to calculate the collapse pressure of an actual perforated liner casing as example.

摘摇要：根据煤层气完井筛管受力特点建立了筛管受力的塑性铰模型，利用能量法推导出带有初始椭圆度筛管抗挤强度的计算公式，分析了相位角、射孔直径、射孔密度、初始椭圆度、径厚比和屈服强度等影响因素对筛管抗挤强度的影响规律，并对某煤矿使用的筛管抗挤强度进行了计算，与已有的实验数据和有限元计算结果进行了对比。

The plastic hinge model of perforated liner casing is built up to calculate the collapse pressure according to the strength and deformation behavior of perforated liner casing subjected to external pressure. The calculation equations of collapse pressure of perforated liner casing with initial ovalization are deduced by energy method. The influences of phrase angle, diameter of perforation, shot density, initial ovalization, diameter-thickness ratio and yield stress on the collapse pressure of perforated liner casing are studied. The model and equations are used to calculate the collapse pressure of an actual perforated liner casing as example.

根据煤层气完井筛管受力特点建立了筛管受力的塑性铰模型，利用能量法推导出带有初始椭圆度筛管抗挤强度的计算公式，分析了相位角、射孔直径、射孔密度、初始椭圆度、径厚比和屈服强度等影响因素对筛管抗挤强度的影响规律，并对某煤矿使用的筛管抗挤强度进行了计算，与已有的实验数据和有限元计算结果进行了对比。

With the frequency and mode shape being regarded as functions of damage parameters, the overdetermined algebraic equations with damage parameters as unknowns can then be constructed by differentiating frequency and mode function on the basis of structure mode finite element formula, the damage parameters of which are obtained via Taylor expansion. The whole damage parameters can be found via solving the algebraic equations.

本方法从结构模态有限元算式出发，把频率和振型看作损伤参数的函数，经过泰勒展开获得频率、振型对损伤参数的一阶偏导数，然后构造以损伤参数为未知量的超定线代方程组，求解得到全部损伤参数值。

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

为了研究两自由度机械手系统的动力学稳定性，基于拉格朗日方程给出了它的运动微分方程，并用扰动理论确定系统周期运动具有周期系数的扰动微分方程；根据F loquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析，并用数值方法研究了平衡点失稳后的倍周期分岔过程。

In some limit conditions, by using the perturbative method, the equations may take on concise forms, i.e Mathieu equations.

如果我们所讨论的问题仅局限于原点附近，可以对场进行泰勒级数展开，得到一个场

The two combining equations of the oxygen balance and the enthalpy balance for prereduction and smelting reduction reactors are formulated respectively- Two equations can be related reasonably by means of calculating thermodynamic results and the Rist dia...

由热力学计算，将上、下两部有机联系起来，得到全过程Rist操作线图。从而，建立了竖炉-铁浴二步法熔融还原过程数学模型，可用来计算全过程氧耗和燃料比等操作参数。

The Jacobi pseudospectral methods are applied to numericalsolutions of singular differential equations,differential equations in infinite intervals andin disc.

事实上，通过适当的变量代换，我们可把无界区域问题转化成某些特定的退化系数的有界区域上的奇异问题。

It's bell can reach over a meter in diameter.

它的身体最大可以达到直径1米多。

Now they are overdue and I shall have to pay a fine.

现在他们过期了，我不得不付罚款。