查询词典 dependent equations

They include the fundamental concepts of jet bundle geometry needed in describing time-dependent mechanical systems, decomposition of jet bundles into a direct sum according to the constraints, horizontal distributions on constraint mainifolds, the global formulation of D'Alembert-Lagrange's equations and Chaplygin's equations, and nonholonomic mechanics on a Riemann-Cartan manifold. Meanwhile, the geometric significance of Chetaev's conditions and $\rd$-$\delta$ commutation relation are discussed in depth.

本文主要综述非完整约束系统几何动力学的外附型和内禀型Lagrange理论，包括非定常力学系统所需要的射丛几何学的基本概念、射丛按约束的直和分解、约束流形上的水平分布、 D'Alembert-Lagrange方程与Chaplygin方程的整体描述、以及Riemann-Cartan流形上的非完整力学，文中对Chetaev条件和d-δ交换关系的几何意义作了深入讨论。

Based on pedagogical experience, a scheme of diagrammatic representation of fundamental dependent equations relating thermodynamic functions is suggested.

通过多年教学实践，归纳出热力学函数间基本关系式的图示法。

Many natural phenomena and physical laws can be described by time dependent nonlinear differential equations, such as heat conduction equation, sound wave and elastic wave equation, reaction diffusion and convection diffusion equation, fluid and aerodynamics equations, etc.

大多数的自然现象与物理规律都可归结为与时间相关的非线性偏微分方程，诸如热传导方程、声波与弹性波方程、反应扩散与对流扩散方程、流体与气体力学方程组等发展方程。

And then the influence of two of the damage models, the Kachanov and the gradient dependent constitutive equations, on the well posed properties of the fundamental equations in continuum damage mechanics is studied according to th.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即 Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

The Galerkin's method was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary differential equations with time dependent coefficients,which can be solved with numerical methods.

对于电梯工业来说，目前世界上绝大部分电梯仍然是依靠钢丝绳提升的曳引式电梯。

By using the theory of linear evolution systems and Sadovskii's fixed point theorem, chapter3 deals with the existence of mid-solutions,strong solutions for the Cauchy problems of neutralabstract functional differential equations dependent on time with unbounded delay, here theright function in the equations satisfies the Caratheodory conditions.

第三章利用线性发展系统理论和Sadovskii不动点定理研究了具有无穷时滞中立型时变泛函微分方程Cauchy问题mild-解、强解的存在性。其中方程的右端函数满足Caratheodory条件。

Initial boundary value problem of two dimensional unsteady diffusion equations is solved in this paper. By using time-dependent fundamental solution of two dimensional diffusion equations and the extension of double layer potential, we establish virtual boundary integral expression of diffusion equations. Then virtual boundary element method is used to implement the numerical computation.

本文在求解二维非定常扩散方程的初边值问题时，利用二维扩散方程与时间有关的基本解，基于双层位势的延拓，建立二维扩散方程的虚边界积分表达式，然后利用虚边界元法进行数值计算。

This paper mainly consists of three parts:(1) Based on the Reddy's higher-order shear deformation plate theory and general von Kármán-type equations, put forward the governing equations of pre- and post-buckled vibration of several hybrid FGM plate forms which have not been studied adequately, triumphantly applying the perturbation technique combined with Galerkin method into equations solving, and get the comparatively simple result forms with complicated deduction at last;(2) As a new type of materials, piezoelectric fiber reinforced composite actuators were applied to optimal vibration control, interrelated informatons be depicted in this paper;(3) During the investigative cource, some factors not been considered adequently in other researches were discussed fully in the postbuckled vibration analysis, such as the temperature-dependent material coefficients, heat conduction and nonlinear vibration characteristic etc.

本文的研究工作主要包括：(1)基于Reddy高阶剪切变形板理论和广义Kármán型方程，给出了几类现有研究成果较少或没有彻底解决的FGM混合板结构的屈曲前和屈曲后振动特性研究的控制方程，成功将摄动-Galerkin混合法应用于求解过程，并给出了各控制方程相对直观且易于计算的解析解形式；(2)单向压电纤维增强复合材料(Piezoelectric Fiber Reinforced Composite，简称PFRC)是一种新型压电材料，本文将其应用到了结构振动控制研究当中，发现通过压电纤维体积含量的选择可以实现混合板结构的优化振动控制；(3)围绕几种有代表性的FGM混合板结构，讨论其屈曲后的振动特性，在分析中同时考虑热传导，材料物性参数的温度相关性，以及机/热/电荷载耦合效应对非线性振动特性的影响，最后给出了大量数值计算结果。

Based on orthogonal function unfolding theory, the transverse fields can be represented as a superposition of waveguide modes. And according to coupled-wave theory, the time-dependent multi-mode coupling-wave equations (or the generalized telegrapher's equations) and the coupling coefficients among the different modes were deduced. The generalized telegrapher's equations are a set of coupled one-dimensional partial differential equations for the amplitudes of the modes.

应用正交函数的展开理论，将变截面波导中的电磁场表示为横电波和横磁波本征模式的级数；然后根据耦合波理论，推导了考虑波导金属壁有限电导率的变截面波导时域多模耦合波方程组及各模式间耦合系数的表达式。

And then the influence of two of the damage models, the Kachanov and the gradient-dependent constitutive equations, on the well-posed properties of the fundamental equations in continuum damage mechanics is studied according to the characteristic method of the quasi-linear partial differential equations under the case of one dimension elastic damage.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷