导出方程

A formula of the frequency change has been deduced from the wave equation to the first order approximation.

从波动方程出发，导出频率改变的一级近似公式。

The equations of buckled equilibrium were derived based on the displacement field of the first order shear-deformation theory.

用一阶剪切变形理论的位移场推导出5个屈曲平衡方程。

By using virtue work principle and first order shear plate theory,the finite element formulations of piezoelectric sensors and actuators arederived.

给出了采用虚功原理及一阶剪切变形理论导出的压电传感和作动有限元方程。

The measurement equation of four point method and three point method flat form error separation is given.

列出了四点法－三点法平面误差分离的测量方程，导出了这类方法所对应系统的传递函数G的通式，指出G（0，0）＝0是平面形状误差赖以先行分离的先决条件。

On the theroy and method of analysing the longitudinal inertia force of railway goods some fresh views are presented.

本文从分析作用于货物的纵向惯性力入手，对铁路货物运输的稳定性问题进行了理论探讨，导出了车载货物的纵向动力学方程及其有关推论，对铁路货运领域在货物纵向惯性力问题上的理论和方法提出了一些新的见解，建议统一查定我国铁路货车在各种运行和调车工况下的加速度值，做为日常确定货物稳定性的科学依据。

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

With the knowledge of linear algebra, general formula for arbitrary order Taylor finite difference has been derived. In this paper, the analysis of spectral property and computational error of arbitrary order TFD is presented in detail. Then it is applied into the numerical solution of Maxwell's equations. Stability condition and numerical dispersion relation are derived.

本文借助于采样定理，详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差，并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中，严格导出了稳定性条件和数值色散关系的表达式，引入了新的误差定义来衡量算法的好坏。

Under some suppositions a general lubrication equation of natural human joints is obtained in the paper.

在作了一系列假定后，导出了具有一般意义的关节润滑方程。

Based on the analytic model of an eccentric slider crank mechanism with elastic effects at both joints of the coupler and four coupler Mathieu-typed equations of motion in terms of the generalized coordinates of the system,the extract solution is developed from the improved Hill method with accelerated convergence.

在所建立的连杆接头处具有弹性效应的曲柄滑块机构的动态解析模型以及在广义坐标下推导出的4个马修型运动方程的基础上，由具有加速收敛性的改进希尔法进行了精确求解。

From elastic piezoelectric theory and Hamilton Principle, theory of non-conform piezoelectric finite element method is derived.

根据弹性压电理论与Hamilton原理导出了机电耦合有限单元动力学方程的一般形式，然后引入了非协调元的概念，并应用于压电结构，对压电层合梁进行了较为详尽的分析，还介绍了程序中使用的动力学计算方法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。