Free nonaxisymmetric vibrations of radially polarized hollow piezoceramic cylinders of finite length

The three-dimensional problem of free nonaxisymmetric vibrations of hollow piezoceramic cylinders with axial polarization is considered. An efficient numerical analytic method to solve boundary-value problems is proposed. The original three-dimensional problem of electroelasticity is reduced to a two-dimensional problem by representing the displacement components as standing circumferential waves. Spline collocation with respect to the axial coordinate is used to reduce this two-dimensional problem to an eigenvalue boundary-value problem with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental-search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed in a wide range of their geometric characteristics     

On penalty function methods in the finite-element analysis of flow problems

In this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier-Stokes equations. Conditions for the equivalence of two penalty-finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.     

边界粒子法结合正则化技术求解Robin反问题

运用一种边界型无网格算法——边界粒子法求解Robin反问题,结合Tikhonov正则化技术消除反问题的不适定性。该方法仅需边界测量数据,计算精度高,特别适用于反问题的求解。数值算例显示该方法在求解Robin反问题上具有很好的稳定性和收敛性。     

On One Approach to the Solution of Stress Problems for Noncircular Hollow Cylinders

An approach is proposed to solve three-dimensional stress problems for noncircular hollow cylinders. The end conditions are such that the problem can be reduced to a two-dimensional problem. This problem is reduced to a one-dimensional problem by introducing additional functions into the resolvable system of equations. These functions are determined using discrete Fourier series. The one-dimensional problem is solved by a stable numerical method. As an example, the stress state of cylinders with an elliptic cross section is analyzed depending on their thickness and degree of ellipticity.     

龙子湖水文工程地质条件分析与渗漏控制

在详细分析了龙子湖地区水文地质条件和工程地质条件的基础上,根据龙子湖的设计方案,指出龙子湖建成后可能存在渗漏量过大的问题,从而影响该区的生态环境等环境地质问题。本文建立了三维渗流数值模型,通过数值模拟证实了龙子湖建成后确实存在渗漏量过大的问题,并为解决这些环境地质问题提供参考方案,还预测分析了环境水文地质条件改变后可能进一步出现的问题并提出了相应的解决方案。     

Calculation of neutral monotonic instability curves in the problem of concentration convection in a mixture with an infinite number of components

The Oberbeck-Boussinesq approximation for concentration convection in a mixture with an infinite number of components is constructed. The features of the formulation of the problem are described in detail. The large-parameter asymptotics are constructed for the linear problem of hydrodynamic stability. The problem is substantially simplified and equations not previously encountered in hydrodynamic stability theory are obtained. In the case of the non self-adjoint problem the asymptotics of the eigenvalues and eigenfunctions are obtained. Numerical results which, in particular, show that the spectrum of the boundary value problem is not connected are presented. The critical values obtained make it possible to solve the important practical problem of improving the process of mixture separation by the isoelectric focusing method.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 11–20, September–October, 1995.     

Nonclassical models of the theory of plates and shells

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each sought function (stresses and displacements) by segments of Legendre polynomials are also reviewed.     

Direct and inverse problems of oscillations of an elastoliquid layered medium

A plane problem of forced oscillations of an ideal compressible liquid bounded from above by an elastic layer with a rough lower surface and an inverse geometric problem of determining the shape of the rough lower surface of an elastic layer from the wave characteristics on the upper surface are considered. Three methods are used to solve the direct problem: the small parameter method, the boundary element method, and the Born approximation. Solving the inverse problem is reduced to solving the integral Fredholm equation of the first kind. Results of a numerical experiment are presented.     

Optimal synthesis in the time minimization problem under phase constraints

The time minimization problem in a linear system with a scalar control under phase constraints is considered. This problem is reduced to the problem of maximum deviations. Necessary conditions of control optimality are obtained. The results are applied to the problem of uniaxial stabilization of a satellite with consideration of a gravitational torque. The stabilization is performed by a flywheel engine with a limited angular momentum.     

Une transformation du problème d'élasticité linéaire en vue d'application au problème de l'inclusion et aux fonctions de Green

A simple transformation of the problem of the linear elastic structure is presented. The transformed problem corresponds to a new problem of linear elastic structure with different behaviour, geometry and prescribed forces and displacements. The transformed problem can be easier to study, or can correspond to cases with well-known solutions. By means of this transformation, the problem of ellipsoidal inclusion is transformed into a problem of spherical inclusion, the analytical results known for the Eshelby tensor for an isotropic or transversely isotropic matrix are extended to more general cases of matrix behaviour, and finally, close form expressions of the Green function for an infinite medium are derived for some cases of elastic behaviour without transversal isotropy or orthotropy.     

New Statement of the elasticity problem for a layer

The problem on the equilibrium of an inhomogeneous anisotropic elastic layer is considered. The classical statement of the problem in displacements consists of three partial differential equations with variable coefficients for the three displacements and of three boundary conditions posed at each point of the boundary surface. Sometimes, instead of the statement in displacements, it is convenient to use the classical statement of the problem in stresses [1] or the new statement of the problem in stresses proposed by B. E. Pobedrya [2]. In the case of the problem in stresses, it is necessary to find six components of the stress tensor, which are functions of three coordinates. The choice of the statement of the problem depends on the researcher and, of course, on the specific problem. The fact that there are several statements of the problem makes for a wider choice of the method for solving the problem. In the present paper, for a layer with plane boundary surfaces, we propose a new statement of the problem, which, in contrast to the other two statements indicated above, can be called a mixed statement. The problem for a layer in the new statement consists of a system of three partial differential equations for the three components of the displacement vector of the midplane points. The system is coupled with three integro-differential equations for the three longitudinal components of the stress tensor. Thus, in the new statement, just as in the other statements in stresses, one should find six functions. In the new statement, three of these functions (the displacements of the midplane points) are functions of two coordinates, and the other three functions (the longitudinal components of the stress tensor) are functions of three coordinates. It is shown that all equations in the new statement are the Euler equations for the Reissner functional with additional constraints. After the problem is solved in the new statement, three components of the displacement vector and three transverse components of the stress tensor are determined at each point of the layer. The new statement of the problem can be used to construct various engineering theories of plates made of composite materials.     

The general and basic boundary value problems of plane steady jet flows and the corresponding nonlinear equations

The general boundary value problem, including known plane steady jet flows of an ideal incompressible fluid, is formulated. The simplest problem retaining all the specific features of the general problem, known as the basic problem, is separated from the general problem. The solution of the basic problem is reduced to solving a non-linear integro-differential equation and also to solving nonlinear integral equations. Examples of flows whose determination is reduced to' solving the basic problem are cited.     

Free vibrations of axially polarized piezoceramic hollow cylinders of finite length

The problem of the free axisymmetric vibrations of longitudinally polarized piezoceramic hollow cylinders is solved by a numerical analytic method. The spline-collocation method with respect to the longitudinal coordinate is used to reduce the original problem of electroelasticity to an eigenvalue boundary-value problem for ordinary differential equations with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed for a wide range of their geometric characteristics     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID (Ⅰ)

1　IntroductionandSignsForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1- 3].Andthereislessdiscussiononitsillposedness[4 ,5 ].Inthedifferentialfunctionclasses,BaouondiandGoulaouicprovedthattheCauchyproblemonthecompactmanifoldofEulerequationshasuniquesolutionwellexpectaconstant[4 ].InthebooktitledSolutionsAnalytiquesdeQuelquesEquationsauxDerivesPartiellesenMecaniquedesFluides,thest…     

On the Riemann problem for liquid or gas-liquid media

Self-similar solutions to the Riemann problem for water with the modified Tait equation of state are presented. The methods of Smoller for gas dynamics are employed to reduce the problem to the solution of a single non-linear equation. The same methods are used for solving the Riemann problem at a gas-water interface. In both cases the method of interval bisections affords a solution technique free of problems with convergence.     

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular dielectric waveguide filled with nonlinear isotropic homogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found.     

关于薄壁曲梁与直梁解析解的进一步讨论

薄壁曲梁的受力问题通常利用弹性力学平面问题的极坐标解法求解,其解法与直角坐标系下直梁受力问题的求解有着异曲同工之处。结果表明,当曲梁的曲率半径趋近于无限大时,可以得到直梁问题的解,从而展示了曲梁与直梁受力问题的内在联系。

     

Two dimensional half-space problems for the Broadwell discrete velocity model

Stationary boundary value problems for the Broadwell model in a half-space and in a half-infinite channel are considered. By means of the analogy between the stationary boundary value problems for the Broadwell equations and the initial-boundary value problem of Carleman's system, solutions are found for various situations. Uniqueness and non-uniqueness of solutions is discussed as well. The non-uniqueness problem in the channel leads to the investigation of the initial value problem for Carleman's equation with partly negative initial densities. Some new results for this problem are given. Received January 20, 1996     

Optimal Microstructures Drag Reducing Mechanism of Riblets

We consider an optimal shape design problem of periodically distributed three-dimensional microstructures on surfaces of swimming bodies in order to reduce their drag. Our model is restricted to the flow in the viscous sublayer of the boundary layer of a turbulent flow. The costs for the optimization problem are very high because the three-dimensional flow equations have to be solved several times. We avoid this problem by approximations: the microscopic optimization problem is reduced applying homogenization. Considering a special geometry (riblets) the resulting so-called macroscopic optimization problem can be additionally reduced to a two-dimensional problem. We analyze the drag reducing mechanism of riblets which are believed to be optimal structures. Therefore we perform direct simulations on the total rough channel for different shapes of microstructures: riblets and fully three-dimensional structures.     

多层层合板圣维南问题的解析解

将哈密尔顿体系理论引入到多层层合板问题之中，建立了一套求解该问题的横向哈密尔顿算子矩阵的本征函数向量展开解法，并成功地求解出圣维南问题的解析解．进一步显示了弹性力学新求解体系的有效性及其应用潜力