查询词典 consistent equations

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。

The basic data obtained from the experimental research were calculated and disposed with computer and concluded an important principle of Li〓O by silicon thermoreduction. The factors affected the reduction such as temperature, pressure and time were dicribed by methematical equations. The relation ships of reduction rate with temperature, pressure and time were directly expressed by three-dimension figures. The relating mathematical equations described the process derived from research were proved to be coincided with the practice. Therefore, the obtained results were accurate and reliable and of important value.

运用计算机对试验研究得到的基本数据进行计算和处理，得到了氧化锂硅热还原的重要规律；用数学方程描述了温度、压力和时间还原的影响；用三维立体图直观地表现了温度、压力和时间〓与还原率的关系；研究得到的描述过程的有关数学方程，经验证与实际相符，因此得到的结果准确可靠。

The kinematic model of vibration system is established and the kinematics differential equations are obtained. On the basis of analyzing unbalancing response, the plane separation equations are achieved.

建立了该振动系统两自由度摆动的动力学模型，得到其运动微分方程，进行了不平衡响应分析，获得求解校正质量的平面分离方程。

Based on division of regions of a typhoon and characteristic scales of physical quantities done by Anthes,sets of equations governing different parts of the typhoon are derived with scale analysis and wave energy equations for each part are obtained with the WKB method. Discussions indicated that physical factors contributing to typhoon development are unconstant in all parts of the typhoon,respectively shown as vertical changes in vorticity and tangential wind for the core and outer mid-tropospheric area,...

利用Anthes关于台风的区域划分以及物理量特征尺度的结果，采用尺度分析方法导出了台风不同区域的控制方程组，又用WKB方法得到各区的波能量方程并进行了讨论，指出影响台风发展的物理因子在各区的异同点：各区都有非定常因子；同时，台风内核及外围中层对流层的因子有涡度和切向风的垂直变化，外围边界层有热成风及其偏差，外围流出层有水平位温梯度，这些因子与重力波适当的移向相配合，可使台风能量发展，强度增大。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。