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set of equations
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  方程组
     The finite voluem method is used to discretize the Navier-Stokes equation together with a standard k-ε double equation turbulence model for closing the set of equations.
     采用有限体积方法离散Navier Stokes方程,标准k ε两方程紊流模型封闭方程组
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     The charachteristics of the proposed approach are that the formulation of the set of equations for special configuration analysis is simple and that all the special configuratinos can be found for a planar linkage.
     以eiθj(θj为机构中运动变量)为变量建立并采用连续法求解平面机构特殊位形分析方程组,使得平面机构特殊位形分析方程组的推导过程大为简化、并可方便求得机构的所有特殊位形。
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     Traditional model of ATC consists of a set of equations with constraints.
     传统的ATC模型是含参数的等式-不等式约束方程组
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     This paper starts from the equations of motion in generalized curvilinear coordinates and the model of Head's two-dimensional entrainment theory, and derives a set of equations along surface curve on normal profile of a yawed wing for a compressible three-dimensional turbulent boundary layer.
     本文从广义曲线坐标运动方程出发,以及根据Head的二维牵引理论(entrainment theory)模型导出沿侧滑翼法向翼剖面表面曲线的三维可压缩湍流边界层运动方程组
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     A complete set of equations for determining the energy levels and the wavefunc-tions with different symmetry of electronic states of the ideal divacancy in cubic semiconductors is obtained using the Koster-Slater Green's function method.
     利用Koster-Slater的格林函数方法,给出了决定立方半导体中理想双空位在禁带中引入的不同对称态的能级和波函数的完整的方程组
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  “set of equations”译为未确定词的双语例句
     The set of equations can lead to FT, CZT,STFT and PRONY methods.
     FT、CZT、STFT和PRONY等方法都可以由此方法导出。
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     This set of equations is general in the sense that it can be used to the optimizations of either the number of ADM's or the number of wavelengths or both of them simultaneously;
     这组方程对环中的流量疏导问题具有普遍的意义,它既可以优化网络中的ADM数,也可以优化波长数,还可以对它们进行混合优化;
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     The Climatology and peristance (CLIPER) models for predicting typhoon motion were proposed from regression analysis of the future zonal and meridional displacements based on climatology, persistance and some combined predictors for the South China Sea (113-123°E, 10-25°N) , and a set of equations to predict the zonal and meridional displacements of typhoon track were derived based on entire samples at24 h to 120 h intervals.
     基于南海(113°—123°E,10°—25°N)台风的气候学、持续性和一些组合因子,根据与未来的经向、纬向位移的回归分析,发展了一种预报台风路径的气候与持续的(CLIPER)模式。
短句来源
     The Climatology and persistance (CLIPER) models for predicting typhoon motion were proposed from regression analysis of the future zonal and meridional displacements based on climatology, persistance and some combined predictors for the South China Sea (113-123°E, 10-25°N), and a set of equations to predict the zonal and meridional displacements of typhoon track were deriyed based on entire samples at24 h to 120 h intervals.
     基于南海(113°─123°E,10°─25°N)台风的气候学、持续性和一些组合因子,根据与未来的经向、纬向位移的回归分析,发展了一种预报台风路径的气候与持续的(CLIPER)模式。
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     From the exact solution of stress along the direction θ=0° and θ=90° at crack-tip of mode Ⅰ、Ⅱ and Ⅲ, a set of equations is produced for determination of stress intensity factor by photoelasticity and holo-photoelasticity.
     本文根据裂纹尖端应力场沿θ=0°和θ=90°的精确解,导得了用光弹性和全息光弹性方法确定Ⅰ型、Ⅱ型和Ⅲ型裂纹尖湍应力强度因子的计算公式。 按这些公式进行计算,不但可提高结果的可靠性,而且可放宽量测区域的范围。
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  相似匹配句对
     (L) and set
     (L),证明了范畴Set_0(L)与(?)
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     The set
     集合(英文)
短句来源
     ON THE DEFINITION OF THE SET
     关于集合的定义
短句来源
     The Structure of Measurable Set
     可测集合的结构
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     B.equations.
     方程则不能得到正确的结果 .
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  set of equations
The issues of approximate solution of an infinite set of equations for the moments are discussed.
      
A closed set of equations where higher-order correlation moments of statistical fields serve as transferable entities is derived.
      
The basic principles of the model, set of equations, and the initial and boundary conditions are described.
      
This formula enables one to directly calculate the solubility of steam in compressed gas without using the previously suggested solution of the set of equations.
      
It is shown that the associated-mass effect has a pronounced impact on the acoustic characteristics of the set of equations.
      
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Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear...

Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear terms in the dynamical equations can be neglected. Furthermore the size of vortices which form the turblent flow is regarded small, so within the range of each vortex the mean turbulent velocity and its gradient can be considered to be independent of the changes of the space coordinates. We now seek the following approximate solution of the linearized equations of turbulent velocity fluctuation; one part of the turbulent velocity fluctuation represents the final stage motion of homogeneous isotropic turbulence, while the other is proportional to the gradient of mean velocity, the latter part being smaller than the former. From this approximate solution the shearing component of the Reynolds stress is found to be directly proportional to the gradient of mean velocity. As a special example of the general solution we consider the case of the two-dimensional wake. Within the wake we put, furthermore, a plane grid normal to the plane of symmetry of the wake. This grid then creates in its downward stream a homogeneous isotropic turbulence field superimposed upon that of the wake. Our solution is applicable to places far downstream both from the body which creates the wake and from the grid. Since the flow here is nearer to the grid, so the turbulence level of the homogeneous isotropic turbulence would be higher than that of the wake. Consequently the conditions of the general solution can be satisfied. The present paper presents the solutions of the mean velocity and the mean squares of turbulent velocity fluctuation of the wake. These theoretical results can all be tested by experiment. On account of that we only discuss the final stage motion of free turbulence, the question how to lay down the upstream boundary condition of the flow field when solving the differential equations of the mean flow needs further consideration by other methods.

具有剪应力的自由湍流到下游相当远的地点由于能量的逐渐耗损将衰变成为类似均匀各向同性湍流的后期运动。如同处理后一种流动问题一样,我们现在根据湍流是由涡旋所组成的概念来求自由湍流的后期运动解。求涡旋运动解的动力学的基础是湍流速度涨落方程。在后期湍流场中湍流Reynolds数比较小,故方程中的非线性项可以略去。再考虑到组成湍流的涡旋尺寸比较小,在每个涡旋范围内平均湍流速度和它的坐标梯度可以近似地认为和坐标的改变无关。我们求线性化了之后的湍流速度涨落方程如下的近似解:涨落速度的一部分代表均匀各向同性湍流的后期运动:另一部分是和平均流速的坐标梯度成正比,后一部分要比前一部分为小。从这样的近似解得出的Reynolds剪应力是和平均流速的坐标梯度成正此。当作这一般解的特例我们求一个二元尾流的后期运动。在产生尾流的物体的后面还置放一个平面与尾流对称平面成垂直的栅格。这个栅格在它的下游可产生一个迭加在物体所产生的尾流场上的均匀各向同性的湍流(?)。我们的解是适用在离物体和栅格相当远处的后期运动,但此处的流场距栅格较近,所以栅格所产生的均匀各向同性湍流要比尾流的湍流度为高,因此一般解的近似条件是可以满足的。本论文给出尾流平均流速...

具有剪应力的自由湍流到下游相当远的地点由于能量的逐渐耗损将衰变成为类似均匀各向同性湍流的后期运动。如同处理后一种流动问题一样,我们现在根据湍流是由涡旋所组成的概念来求自由湍流的后期运动解。求涡旋运动解的动力学的基础是湍流速度涨落方程。在后期湍流场中湍流Reynolds数比较小,故方程中的非线性项可以略去。再考虑到组成湍流的涡旋尺寸比较小,在每个涡旋范围内平均湍流速度和它的坐标梯度可以近似地认为和坐标的改变无关。我们求线性化了之后的湍流速度涨落方程如下的近似解:涨落速度的一部分代表均匀各向同性湍流的后期运动:另一部分是和平均流速的坐标梯度成正比,后一部分要比前一部分为小。从这样的近似解得出的Reynolds剪应力是和平均流速的坐标梯度成正此。当作这一般解的特例我们求一个二元尾流的后期运动。在产生尾流的物体的后面还置放一个平面与尾流对称平面成垂直的栅格。这个栅格在它的下游可产生一个迭加在物体所产生的尾流场上的均匀各向同性的湍流(?)。我们的解是适用在离物体和栅格相当远处的后期运动,但此处的流场距栅格较近,所以栅格所产生的均匀各向同性湍流要比尾流的湍流度为高,因此一般解的近似条件是可以满足的。本论文给出尾流平均流速和速度涨落平方平均值的解。?

In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering two and...

In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering two and three coupled modes succesively. For the two coupled-modes case, our results agree with those by Louisell and Unger. Solution for the three coupled-modes problem has not been appeared in literatures heretofore. A numerical evaluation of the spurious modes in an S-shaped bend is given. Further applications are discussed.

在本文中作者提出了耦合本地正规波型的广义理论;它建立在作者在另一篇论文中提出的数学方法——“缓变系数法”的基础上。为了说明这种方法的应用,依次解出了考虑两个及三个耦合波型的缓变曲率波导弯曲问题。在两个耦合波型的情形下,所得结果与Louisell及Unger已得结果相符合。三个耦合波型的问题在以前的文献中尚未讨论过。本文讨论了所提出的理论及数学方法在其它方面的应用。

The first part of this paper deals with a brief survey and discussion of the limit analysis in solid mechanics. Since the complete establishment of the well-known theorems of the upper and lower bounds, considerable advances have been made in the limit analysis as a branch of applied plasticity. Now, exact calculation of the plastic limit load is feasible with no apperciable difficulty for rigid framed structures, consisting of systems of members subjected mainly to bending action. In the field of two and three...

The first part of this paper deals with a brief survey and discussion of the limit analysis in solid mechanics. Since the complete establishment of the well-known theorems of the upper and lower bounds, considerable advances have been made in the limit analysis as a branch of applied plasticity. Now, exact calculation of the plastic limit load is feasible with no apperciable difficulty for rigid framed structures, consisting of systems of members subjected mainly to bending action. In the field of two and three dimensional structures, especially in the plate and shell problems, although many results have also been found for a wide variety of practical problems, but further progress seems to be very difficult in encountering with more complicate problems. Progress is restricted by the fact that, the limit theorems cannot in these cases give results sufficiently approached to the upper and lower bounds. Moreover, the application of lower bound theorem is especially difficult.The second part of this paper suggests a generalized variational principle, in which both stress distribution σij and velocity field vi are introduced and vary independently. This variational principle is equivalent mathematically to the whole set of equations, which must be satisfied by the limit analysis: equalibrium, mechanism, yield condition and flow law. It is proved that with independently assumed kinematically admissible velocity field and statically admissible stress distribution, the generalized variational principle gives the approximate plastic limit load, lying between the upper and lower bounds obtained from bound theorems. Moreover, numerical examples for circular plates are carried out to show that, the generalized variational principle gives rather stable answers for different combinations of assumed stress distribution and velocity field. It is remarked, furthermore, that the generalized variational principle can be applied to the limit analysis dealing with non-homogeneous as well as anisotropic perfectly plastic materials.

本文簡单回顾和討論了作为应用塑性力学分支的极限分析的发展和現状。自从著名的上限定理和下限定理奠定以后,极限分析逐漸受到重視并有了相当迅速的发展。現在对于主要是受弯构件組成的刚架結构,通常可以找到既是上限又是下限的完全解。至于对于二維和三雒連續体,特別对于板壳,虽然已經完成了一些工作,但是現在的进展显得迟緩了。这是因为具体应用这两个基本定理时一般很难找到足够接近的上限和下限。特别是下限定理的应用困难很大。 本文还提出了应力場与速度場彼此独立变分的一个一般变分原理,它与极限分析所应滿足的全部方程(平衡、机动、屈伏和流动定律)等价。与上限和下限定理比較,如果采用同样的应力場和速度場,通过这个变分原理得出的极限載荷将在上下限定理給出的上限和下限之間。以圓板問題为例表明,采用各种不同的应力場和速度場,能給出比較稳定的极限載荷值。此外这个变分原理还适用于材料是非均貭或各向异性时的极限分析。

 
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