查询词典 structure equations

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。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

The influence of initial imperfections on the stability ofcomposite laminated plates was studied by solving the nonlinear governing equations for laminated plates with elastical restraints subject to in-plane loading using the energy variational principle and nonlinear geometric equations incorporating the initial imperfection. The governing equations were solved using generalized Fourier series to obtain the effect of the non-uniform order term.

为深入研究初始缺陷对复合材料层板稳定性的影响，利用能量变分原理和考虑初始缺陷的非线性几何方程，建立了具有弹性约束的层合板在面内载荷作用下的非线性稳定性控制方程组，运用广义傅立叶级数法对其进行求解，并进一步获得了影响非线性稳定性控制方程组的性质的非齐次项。

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

The Hankel transformation method has been used to turn the basicdisplacement equations and displacement-stress constitutive equations intoa system of first order non-homogenous ordinary differential equations inwavenumber domain,and by us of the matrix method,the transfer matrix ofthe medium layered is established.

利用Hankel变换，将轴对称静力问题的位移基本方程和位移应力本构方程转化为波数域内非齐次一阶常微分方程组，利用矩阵法，建立了介质层的传递矩阵，导出了层状弹性半空间轴对称静力问题奇异解的一般解析表达式。

The model is usually an inhomogeneous system of linear equations. It is pointed out that the general solution of the homogeneous system of linear equations can satisfy the request of making the wires tight, and the special solution of the inhomogeneous system of linear equations are not smaller than zero, so their sum is greater than a given mumble.

由于多自由度绳牵引并联机构的静力学模型一般是一个非齐次线性方程组，本文指出可让对应齐次方程组的通解的最小值满足绳保持张紧的条件；让非齐次线性方程组的特解非负，而避免利用对应齐次线性方程组的通解保证非齐次线性方程组的解不小于给定的最小值。

Based on the hydrokinetics study of jigging process, the free vibration equations of ideal fluid and actual flow vibration equations have been established. These equations are the theoretical foundation to set the operation parameters and air pressure of the jig. The similar criteria and their related equation of model jig have been deducted by actual flow vibration equation. These similar criteria can be used for parameter transformation between model jig and industrial jig. One set of single cell model jig with measuring system has been constructed in laboratory.

本文通过对跳汰过程的流体动力学研究，建立了跳汰机中理想流体的自由振动方程和实际水流的振动方程，为跳汰机工作制度及风源风压的确定提供了理论依据；利用跳汰机中实际水流的振动方程推导出了跳汰机模型试验的相似准数，建立了模化准则关系式，为工业跳汰机与实验室跳汰机之间的参数转换提供了理论依据；并设计建造了一套实验室单槽模型跳汰机及其实验检测系统，为深入开展跳汰理论的研究创造了条件。

In the two-dimensional simulation, the fully implicit difference scheme is used for the continuity equations to ensure numerical stability; Jacobian iteration is used to solve the difference equations, and only nonzero elements in the coefficient matrixes of these equations are dealt with, which reduce the requirement for memory and shorten the calculation time.

在两维模拟计算中，对连续性方程采用全隐式差分方案以保证数值稳定性；运用雅可比迭代法求解差分方程组，并且在求解过程中，只对差分方程组系数矩阵中的非零元素进行处理，因此减少了对内存的需求量，而且缩短了计算时间。

Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcame. Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性；最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

Green quasifunction method is applied to Poisson's equations. Fredholm integral equations of the second kind are obtained. Irregularity of the kernel of integral equations is overcome by choosing a suitable form of the normalized boundary equation.

应用准格林函数方法，可将Poison方程化为第二类Fredholm积分方程，通过边界方程的适当选择，积分方程核的奇异性被克服了。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。