Plate Of Finite Dimensions Research Articles

ПЕРЕМАГНИЧИВАНИЕ И НЕОДНОРОДНЫЙ МАГНИТОЭЛЕКТРИЧЕСКИЙ ЭФФЕКТ В НАНОРАЗМЕРНОЙ ДВУХСЛОЙНОЙ ФЕРРОМАГНИТНОЙ ПЛЕНКЕ С КОМБИНИРОВАННОЙ ОДНООСНОЙ И КУБИЧЕСКОЙ АНИЗОТРОПИЕЙ В СЛОЯХ

A numerical study of the magnetization reversal of a two-layer exchange-coupled ferromagnetic plate of finite dimensions, which has a combined uniaxial anisotropy (of the "easy axis" type for the upper layer and «easy plane» for the lower one) and cubic anisotropy with orientation [111]. It is shown that, in the presence of cubic anisotropy, the ground state of magnetization turns out to be uniform in the plane of the film. However, there is discontinuity at the interface between the film layers. This inhomogeneity can lead to the appearance of electric polarization due to the magnetoelectric effect. The electric polarization vector in this case lies in the plane of the film. Its modulus increases with increasing cubic anisotropy. In addition, with an increase in cubic anisotropy, a hysteresis of electrical polarization is observed.

Methods of Pseudo-Inverse Algebra in State Identification Problems for Thick Elastic Plates

The authors solve identification problems for the three-dimensional function of transverse displacements of points of a thick elastic plate of finite dimensions, whose dynamics can be described by a linear differential model with discrete and continuous observations of the initial---boundary-value external dynamic perturbations of the plate. The working criterion is the RMS criterion of fitting the obtained solution and observations of the plate and methods of linear pseudo-inverse algebra. The conditions of accuracy and uniqueness of the identification results are formulated.

Mathematical Modeling of Three-Dimensional Fields of Transverse Dynamic Displacements of Thick Elastic Plates

We investigate the dynamics of an elastic plate of finite dimensions. The three-dimensional field of dynamic transverse displacements of the plate is constructed as a solution of two-dimensional differential equations parametrically dependent on the transverse coordinate. We consider the cases of discrete and continuous sets of the initial and boundary conditions that are satisfied by the mean square criterion. We describe the features of the solution of the problems in unbounded space---time domains.

Thickness or phase velocity measurements using the Green's function comparison method

The acoustic guided wave propagation for plate thickness measurement is generally treated in free space to simplify the formal approach. In this paper, propagation in a closed environment is treated by dealing with plates of finite dimensions and arbitrary geometries and linear boundary conditions. The present approach considers the plate Green's function to be composed of two terms. The first term corresponds to the Green's function of an infinite plate. The second term corresponds to a correction term which, in addition to the first term, satisfies all equations. Assuming the boundary conditions to be linear, it is found that the acoustic wave generated by a point source is proportional to that of a circular array of sources centered on it. By measuring the ratio between the two signals, either the plate velocity or plate thickness can be determined. This new method has been successfully applied to isotropic and anisotropic homogeneous plates of different geometries, on inhomogeneous plates, and also in a passive mode, without an active transmitter.

Computer analysis of the configuration of the magnetic fields of surface discontinuity flaws of finite dimensions in a ferromagnetic plate of finite dimensions by the spatial integral equation method

The spatial integral equation method is used to perform a numerical analysis of the magnetic-field configuration for ferromagnetic objects of finite dimensions having surface discontinuity flaws of arbitrary shape and finite dimensions. The range of application of the software developed for the design of technical devices for inspecting objects of irregular geometry was determined.

A new approach on MHD natural convection boundary layer flow past a flat plate of finite dimensions

A new approach on MHD natural convection boundary layer flow from a finite flat plate of arbitrary inclination in a rotating environment, is presented. This problem plays a significant role on boundary layer flow control. It is shown that taking into account the pressure rise region at the leading edge of the plate leads to avoid separation and the back flow is reduced by the strong magnetic field. It is also shown that the frictional drag at the leading edge of the plate is reduced when the inclination angle α=π/4. In the case of isothermal flat plate, the bulk temperature becomes identical for any value of Gr (Grashof number) when the value of M 2 (Hartmann number) and K 2 (rotation parameter) are kept fixed.

Displacement fields in waves generated by flexural oscillations of plates

A technique has been suggested for calculating acoustic displacement fields in waves generated by flexural oscillations in plates of finite dimensions in gaseous media at different frequencies, plate dimensions, and elastic parameters in both pulsed and cw modes. Acoustic fields in flexural resonant transducers with emitters shaped as round plates have been studied both theoretically and experimentally.

Natural convection heat transfer from plates of finite dimensions

A new approach to the model of natural convection from an isothermal inclined plate and a simplified analytical solution of this model are presented In this model two separate regions with different fluid motions are distinguished In the first region, the direction of fluid flow inside the boundary layer and parallel to the plate buoyancy force component converge, while in the second one these directions are opposite The theory presented is verified experimentally

A theoretical method of determining the limiting state of a plate with a hole

The author is describing the new method of calculating the limiting state of plates of finite dimensions weakened by a hole. The method is based on the combined application of the strength criteria of crack mechanics and mechanics of solids. The proposed method makes it possible to determine the acting stress at the edges of the plate at which the standard element fails, as well as the critical size of the zone of the limiting stage of the material at the hole. An example of calculating the plate with a hole using the method is described. The largest difference between the experimental and theoretical data does not exceed 9%.

Analysis of open waveguides with arbitrary topology of the transverse cross section and piecewise-uniform gyrotropic filling by the method of singular integral equations

An electrodynamically exact solution of Maxwell's equations is proposed for the analysis of dispersion relations and electromagnetic fields of the characteristic modes of waveguides with an arbitrary topology of the transverse cross section and with a piecewise uniform gyrotropic filling under conditions of longitudinal bias magnetization. The characteristics of the first four modes of an open rectangular ferrite rod on a metallic plate of finite dimensions are studied numerically as a function of the width of the rod, the frequency of the signal, and the magnetization of the ferrite.

Structure of the flow of a viscous gas near the trailing edge of a flat plate

Solution of the complete system of Navier-Stokes equations forms the basis for a study of the nature of flow of a viscous heat-conducting gas in the neighborhood of a trailing edge of a flat plate. The problem was solved in accordance with a difference scheme of the third order of accuracy [1]. The calculation was carried out under the same conditions as the experiment of [2], in which a plate of finite dimensions (L = 12 cm) had supersonic M = 2, Re∞, = 1000 gas flow round it. In order to obtain a thickness of the boundary layer which was acceptable for the purpose of making the measurements (of the order of 2 cm), the unperturbed gas was slightly rarefied. In the study of such problems [3–7] it is necessary to use the complete system of Navier-Stokes equations, since in the immediate neighborhood of the trailing edge one of the important assumptions in the theory of the boundary layer, ∂2u/∂y2 ≫ ∂2u/∂x2, does not hold. As a result the flow upstream near the trailing edge of the plate will depend on the flow immediately behind the edge, since the perturbations propagate both upstream and downstream in this case. The rarefaction of the gas creates additional difficulties in the formulation of the boundary conditions on the plate with flow round it when this problem is studied numerically.

An Analysis of the Squeeze Film between Porous Rectangular Plates Including the Surface Roughness Effects

The paper describes a theoretical analysis of the effects of unidirectional surface roughness on the response of a squeeze film between two porous rectangular plates of finite dimensions. The problem is solved analytically using Fourier expansions. It is shown that the nominal geometry as characterized by the aspect ratio of the plates has a profound effect on the system.

Two problems of convective diffusion to the surfaces of poorly streamlined bodies

Problems of diffusion to particles of nonspherical shape at large Peclet numbers have been analyzed in many papers (see [1–7], for example). The solution of the problem of mass exchange of an ellipsoidal bubble at low Reynolds numbers was obtained in [1] while the solution at high Reynolds numbers was obtained in [2, 3]. In [4] an expression is given for the diffusional flux to the surface of a solid ellipsoidal particle over which a uniform Stokes stream flows. Generalization to the case of particles of arbitrary shape was done in [5, 6], while generalization to any number of critical lines on the surface of the body was done in [7, 8]. The two-dimensional problem of steady convective diffusion to the surface of a body of arbitrary shape is analyzed in the approximation of a diffusional boundary layer (ADBL). The simple analytical expressions obtained are more suitable for practical calculations than those in [5-8], since they allow one to determine at once, in the same coordinate system in which the field of flow over the particle was analyzed, the value of the diffusional flux to its surface (from the corresponding hydrodynamic characteristics). The plane problem of the diffusion to an elliptical cylinder in a uniform Stokes stream is solved. The problems of the diffusion to a plate of finite dimensions (in the plane case) and a disk (in the axisymmetric case) whose planes are normal to the direction of the incident stream are considered. It is shown that, in contrast to the results known earlier (see [4, 6-15], for example), where the total diffusional flux was proportional to the cube root of the Peclet number, here it is proportional to the one-fourth power.

Temperature distribution in a parallelopiped under the influence of heat source with boundary conditions of second kind

In the present paper, the general expressions for temperature distribution in an orthotropic plate of finite dimensions have been derived under the influence of an arbitrary volume heat source and arbitrary initial temperature distribution. The boundary conditions prescribed on the faces are of second kind. The solution is obtained by constructing an eigen value problem.