导出方程

Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell are presented, and thermal stresses mixed state equation for axisymmetric problem of closed cantilever cylindrical shell is established.

导出层合柱壳轴对称问题的平衡方程和边界条件的弱形式，提供了方程和边界条件放在一起的算子形式，建立了悬臂柱壳轴对称问题的热应力混合方程，给出了正交异性层合悬臂柱壳在热荷载和机械荷载作用下的弱形式解·本文提出的方法弱化了求解方程和边界条件，化解了问题，具有一般性并便于推

Thus it is shown there may be dissipative compressional wave and shead wave in viscous compressible fluid.

本文在小扰动条件下，从粘性可压缩流体的运动方程、状态方程以及连续性方程导出了它的波动方程，从而表明粘性可压缩流体中能够存在有耗损的纵波与横波。

Based on the magnetic-elasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magnetic-elasticity kinetic buckling equation of a current-carrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magnetic-elasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

Based on the magneticelasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magneticelasticity kinetic buckling equation of a currentcarrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magneticelasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

By introducing reasonable fundamental assumptions and the Green strain in orthogonal curvilinear coordinates,geometric equations expressed by the Green strain tensor for solving thin shells with large deformation are derived in this paper.

将正交曲线坐标下的格林应变张量引入到薄壳大变形分析，通过建立恰当的基本假设，直接导出了用格林应变张量表示的壳体变形几何方程，将该方程代入到本构方程，由能量原理得到了小应变非线性变形平衡方程、内力方程和边界条件，在此基础上提出了大应变变形的简化分析方法。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Its improved form of three terms series including Rubin second-order approximate terms and their exact residual term is then obtained.

采用叠加法和删除保留模态法导出了自由界面精确剩余模态三项和公式，它在Rubin二级近似项上增加了精确余项，导出非线性精确综合方程，构造了具有超收敛性质的迭代求解方程。

The nonparallel linear stability of the two-dimensional and three-dimensional disturbance waves are studied by the parabolized stability equation which is developed in recent years and the local method based on the Landau expansion.

本文从Navier-Stokes方程出发，导出不同形式的流动稳定性方程，包括采用小扰动理论得到的Orr-Sommerfeld方程、基于流向慢变特性而得到的抛物化稳定性方程以及在一小范围内计算的局部法方程。

In this thesis, different types of stability equations, including Orr-Sommerfeld Equation and Parabolized Stability Equation based on the"slow change"hypothesis and the local method equation which is computed in local range, are derived from Navier-Stokes equation with"small disturbance"hypothesis.

摘要本文从Navier-Stokes方程出发，导出不同形式的流动稳定性方程，包括采用小扰动理论得到的Orr-Sommerfeld方程、基于流向慢变特性而得到的抛物化稳定性方程以及在一小范围内计算的局部法方程。

In this thesis, different types of stability equations, including Orr-Sommerfeld Equation and Parabolized Stability Equation based on the"slow change"hypothesis and the local method equation which is computed in local range, are derived from Navier-Stokes equation with"small disturbance"hypothesis.

本文从Navier-Stokes方程出发，导出不同形式的流动稳定性方程，包括采用小扰动理论得到的Orr-Sommerfeld方程、基于流向慢变特性而得到的抛物化稳定性方程以及在一小范围内计算的局部法方程。

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。