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1.
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 相似文献
2.
J. N. Reddy 《国际流体数值方法杂志》1982,2(2):151-171
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. 相似文献
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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. 相似文献
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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. 相似文献
7.
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. 相似文献
8.
P. S. Uglich 《Journal of Applied Mechanics and Technical Physics》2009,50(5):850-857
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. 相似文献
9.
V. V. Aleksandrov A. D. Belen’kii A. V. Lebedev E. Matlalcuatzi Rugerio 《Moscow University Mechanics Bulletin》2012,67(1):23-27
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. 相似文献
10.
《Comptes Rendus de l'Académie des Sciences》2000,328(6):437-443
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. 相似文献
11.
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. 相似文献
12.
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. 相似文献
13.
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 相似文献
14.
沈臻 《应用数学和力学(英文版)》2003,24(5):545-554
1 IntroductionandSignsForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1- 3].Andthereislessdiscussiononitsillposedness[4 ,5 ].Inthedifferentialfunctionclasses,BaouondiandGoulaouicprovedthattheCauchyproblemonthecompactmanifoldofEulerequationshasuniquesolutionwellexpectaconstant[4 ].InthebooktitledSolutionsAnalytiquesdeQuelquesEquationsauxDerivesPartiellesenMecaniquedesFluides,thest… 相似文献
15.
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. 相似文献
16.
《Wave Motion》2018
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. 相似文献
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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 相似文献
19.
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. 相似文献
20.
多层层合板圣维南问题的解析解 总被引:9,自引:2,他引:9
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 相似文献