the differential 
Deduction of the Differential Equation of the BoxLike Thin Wall Contortion (Distortion) of the CrossSection and the Approximate Calculation of the Normal Stress 
箱形薄壁截面歪扭(畸变)微分方程的推导及法向应力的近似计算 

As for the variable depth box girders, difference method is applied to solve the differential equations and the boundary conditions of the variable depth box girders, which are derived according to the differential equations of the constant depth box girder. 
对于变截面箱梁，利用等截面箱梁所得到的微分方程和边界条件演化为变截面箱梁的微分方程，采用差分法来求解变截面箱梁的微分方程和相应的边界条件。 

Based on the Terzaghi consolidation theory and the Carrillo theorem, the differential equations for vertical, radial and total consolidation of gravel pile composite foundation under embankment are derived, as well as their analytic solutions. 
在Terzaghi 固结理论的基础上,应用Carrillo 定理建立了路堤荷载下碎石桩复合地基的径向、竖向及整体固结微分方程,并得出其解析解。 

First expatiate the differential equation of heat exchange, then confirm the boundary condition. 
第三章首先对热传导的微分方程作了阐述。 之后确定温度场的边界条件。 

In order to find the dynamic response of the free span, combining Matteo Luca Facchinetti's wake oscillator model with the differential equation of the free span to get the coupling equations between pipe and fluid, the finite element method combined with the simple iteration is used to solve the system of equations. 
为考察海底管道悬跨段的动力响应,将尾流振子模型与海底管道悬空段振动微分方程相结合,得到管道与流体的耦合振动方程,用有限元法及迭代法进行求解,得到管道涡激振动响应。 

As for the variable depth box girders, difference method is applied to solve the differential equations and the boundary conditions of the variable depth box girders, which are derived the constant depth box. 
对于变截面箱梁,利用等截面箱梁演化为变截面箱梁的微分方程,并采用差分法来求解该微分方程和边界条件; 

And dynamic responses of plate girder are analysed with movable vibration mode and then creat bridgevehicle interaction differential eguation of plate girder. The Newmark method is used to solve the differential eguation. Also analyse the dynamic responses and impacting factor of plate girder with different speed of vehicle and different span of bridge. 
其次又用车桥振动模型对板梁桥进行分析,建立了车桥振动微分方程,并用Newmark法进行求解,同样分析了不同跨径不同速度下板梁的动力响应,在此基础上又分析了板梁桥的冲击系数,并考虑了速度与跨径对冲击系数的影响。 

To begin with, we derive them by taking the contortion (distortion) deflection as the unknown, Then we base on the closed thin wall stanchion theory and the energy method, we converse them into the differential equation of r(z). 
本文以歪扭(畸变)挠度W为未知量,用闭口薄壁杆件理论与能量法进行推导,然后换算成γ(z)的微分方程。 

Considering the particle's velocity and acceleration of a cylindrical metal sample during the process of forging,the author has established the differential equations of the hammer's velocity and acceleration in rela tion to the compression rate,and has obtained the numerical solutions by a FORTRAN program. 
本文计入了圆柱体在镦粗过程时质点的速度和加速度的影响,建立了模具的速度、加速度与试件压缩比各之间的微分方程,编成计算程序,在微机上实行计算,监将计算结果同实测作了对比,讨论了各个参数对锻造成形的影响。 

The differential equation governing the flexural deflection of a pile of uniform symmetric cross section under simultaneous axial and transverse loading within the scope of the winkler hypothesis is derived in this paper. 
本文导得了按Winkler假设范围内轴向与横向力同时作用下等截面均质桩基挠曲的微分方程。 

In the light of the several assumptions,the differential equation and the spline expressione of aerodynamic force on flutter are derived. 
根据片条假定以及所取用的力学模型，导出颤振微分方程和关于颤振导数的空气动力矩阵（气动阻尼阵和气动弹性阵）。 

The differential equation governing the flexural deflection of a flexible wall of the underground structures under the Winkler's assumption which includes the effect of the axial force is derived in this paper. 
本文导得了在轴向力作用下地下结构柔性墙轴挠曲线的微分方程,并给出墙轴水平位移、转角、弯矩及剪力间的微分关系及其无量纲解。 

The differential equationis derivd form the theory of minimum potential energy and its solution is then obtained. 
用最小势能原理推出了控制微分方程及其解,计算简便。 

The differential equations of general potential energy with continue displacement method are derived. These equations are made to be very simplified by introducing the unit curvature and deducing the model of warping displacement first. 
引入单位曲率,从而先算出轴向翘曲位移模式,使推出的连续化位移法控制微分方程大为简化。 

Making use of Lagrange's equations,the differential equations of motion of the cable stayed pipe bridge system are established. 
利用Lagrange方程,建立了斜拉管线桥体系在竖向地震作用下的运动微分方程。 

The homogeneous solution of the differential e quation for the shear lag was taken as the displacement pattern of finite segment. 
取控制微分方程的齐次解作为梁段的有限元位移模式. 

In this paper the differential model developed by Wen is used for describing the hysteretic restoring force model of isolation devices. Combined with wilsonθ and Fourth RungeKutta Method, the computation formulas for nonlinear seismic response analysis of isolation systems for continuous girder bridges are established The isolation effects of isolation devices for continuous girder bridges are discussed. 
对于桥梁结构的隔震、耗能装置采用Wen所提出的微分型恢复力模式，结合Wilson－θ法和四阶Runge－Kutta法推导出桥梁隔震体系非线性地震反应计算公式，分析了这些隔震、耗能装置对于连续梁桥的隔震作用。 

The differential equations of the motin of masses of flour in the positive pneumatic conveying system were firstly established in this paper. The author used Runge Kutta method to solve the differential equations of motion and obtained the numerical simulation results of the motion of flour in different elbows under different conveying conditions, analyzed in detail the numerical simulation results, and drew some valuable conclusions. 
建立起面粉在气力压运系统弯管内的颗粒群运动微分方程，采用RungeKuta方法求解运动微分方程，得出面粉在弯管内的运动数值模拟解（在5种不同空间布置形式的弯管，不同的输送条件下），并对数值模拟结果进行了详细地分析，得出了一些在理论上和工程应用上都有价值的结论。 

On the basis of Hamilton priciple, the differential equation of solid liquid coupling vibration of Timoshenko pipe conveying fluid is derived. 
根据Ham ilton 原理推导了Tim oshenko 管道的固液耦合振动微分方程。 

The alongwind gust velocity and its nonlinear item have been introduced into the expressions of selfexcited forces in this paper,and the differential equations of 1order and 2order moment of bridge section moving in two directions have been formulated by using the theory of Stochastic Differential Equation and Moment equation. 
将脉动风速及其非线性项引入到桥梁的自激力公式中 ,运用随机微积分理论与矩方程理论 ,得到双方向运动的桥梁断面的一阶矩与二阶矩的微分方程组。 
