Magnetohydrodynamic lubrication theory for a cylindrical bearing

Liquid metal, which is a conductor of electric current, may be used as a lubricant at high temperatures. In recent years considerable attention has been devoted to various problems on the motion of an electrically conducting liquid lubricant in magnetic and electric fields (magnetohydrodynamic theory of lubrication), Thus, for example, references [1–3] study the flow of a conducting lubricating fluid between two plane walls located in a magnetic field. An electrically conducting lubricating layer in a magnetohydrodynamic bearing with cylindrical surfaces is considered in [4–8] and elsewhere.The present work is concerned with the solution of the plane magnetohydrodynamic problem on the pressure distribution of a viscous eletrically conducting liquid in the lubricating layer of a cylindrical bearing along whose axis there is directed a constant magnetic field, while a potential difference from an external source is applied between the journal and the bearing. The radial gap in the bearing is not assumed small, and the problem reduces to two-dimensional system of magnetohydrodynamic equations.An expression is obtained for the additional pressure in the lubricating layer resulting from the electromagnetic forces. In the particular case of a very thin layer the result reported in [4–8] is obtained. SI units are used.     

On the theory of stability of a cylindrical hydrodynamic suspension

The stability of a cylindrical hydrodynamic suspension is investigated with complete account for the dependence of the fluid velocity distribution profile on the radial coordinate in the supporting layer without an a priori representation of the inertial terms in the fluid layer in terms of the velocity averaged over the clearance cross-section. It is shown that the central position of a light inner body in the cylindrical hydrodynamic suspension is asymptotically stable. The suspension remains asymptotically stable for a fairly long time as the light inner body is displaced from the central position along the dynamic equilibrium curve. The central position of a heavy inner body is unstable; however, as it is displaced from the central position under the action of a constant external decentering force a stability domain develops.     

Buckling analysis of cylindrical thin-shells using strain gradient elasticity theory

The stability problem of cylindrical shells is addressed using higher-order continuum theories in a generalized framework. The length-scale effect which becomes prominent at microscale can be included in the continuum theory using gradient-based nonlocal theories such as the strain gradient elasticity theories. In this work, expressions for critical buckling stress under uniaxial compression are derived using an energy approach. The results are compared with the classical continuum theory, which can be obtained by setting the length-scale parameters to zero. A special case is obtained by setting two length scale parameters to zero. Thus, it is shown that both the couple stress theory and classical continuum theory forms a special case of the strain gradient theory. The effect of various parameters such as the shell-radius, shell-length, and length-scale parameters on the buckling stress are investigated. The dimensions and constants corresponding to that of a carbon nanotube, where the length-scale effect becomes prominent, is considered for this investigation.     

Radial instability of one- and two-layer cylindrical shells during impulsive compression

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 77–81, January–February, 1991.     

To the problem of stability of a cylindrical shell under axial compression

The classical problem of stability of a thin elastic cylindrical shell loaded by axial compressions forces is considered. The axially symmetric and non-axisymmetric buckling modes of isotropic and orthotropic shells are studied. In contrast to the traditional approach, the well-known expressions for the critical load are obtained by analyzing the equations for the shell behavior and are independent of the boundary conditions.     

Effect of bearing pressure on the strength of a rock mass containing cylindrical cuts

The three-dimensional problem of stress distribution in a rock mass in the vicinity of two cylindrical holes located in the zone of elevated mountain pressure is solved using the boundary-element method. The technogenic disturbance of the mass with regular strength anisotropy was estimated quantitatively using specially introduced parameters.     

Asymptotic analysis of the unsteady problem of waves in a two-layer flow

The problem investigated is the unsteady problem of the internal waves generated in a two-layer flow by a certain periodic perturbation which leads to small deviations from the basic flow. A method of constructing an approximate solution uniformly valid throughout the region of variation of the variables and the parameters of the problem is indicated. It is confirmed that for large times and near-resonance parameters the motion of the fluid is described by the mixed problem for a cubic Schrödinger equation. Certain qualitative properties of the solution of this nonlinear problem are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 82–90, November–December, 1987.The author is grateful to V. I. Bukreev and to I. V. Sturova for their interest in his work.     

Hydrodynamic theory of the spherical gas bearing

The problem of the spherical gas bearing has been considered in [1,2]. In the present study, following [3], to improve the convergence of the series for the pressures use is made of the method of separation of the singularity, which allows the solution to be used also for large eccentricities.     

Non-linear analysis of functionally graded plates in cylindrical bending under thermomechanical loadings based on a layerwise theory

A layerwise theory is used to analyze analytically displacements and stresses in functionally graded composite plates in cylindrical bending subjected to thermomechanical loadings. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The non-linear strain–displacement relations in the von Kármán sense are used to study the effect of geometric non-linearity. The equilibrium equations are solved exactly and also by using a perturbation technique. Numerical results are presented to show the effect of the material distribution on the deflections and stresses.     

Dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells using higher-order theory

Here, the dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells subjected to thermal/mechanical load is carried out based on higher-order theory. The formulation accounts for the variation of the in-plane and transverse displacements through the thickness, abrupt discontinuity in slope of the in-plane displacements at the interfaces, and includes in-plane, rotary inertia terms, and also the inertia contributions due to the coupling between the different order displacement terms. The strain–displacement relations are accurately accounted for in the formulation. The shell responses are obtained employing finite element approach in conjunction with direct time integration technique. A detailed parametric study is carried out to bring out the effects of length and thickness ratios, eccentricity parameters and number of layers on the thermal/mechanical response characteristics of non-circular shells.     

Parametric expansions in the linear theory of cylindrical shells

Summary Concepts of parametric expansions, leading to univocal definitions of classes of solutions (according to the behaviour of derivatives by vanishing thickness parameter) and, for each class, to a unique classification of terms in equations, are applied to cylindrical shells.In the introduction by Cicala, the fields of application of the various classes of solutions are related to loading and boundary conditions.In the subsequent section, Sassi Perino presents the second approximation formulation for rapid variation solutions for circular cylindrical shells. The first approximation form coincides with Donnell's theory. The second approximation terms take into account effects neglected by the ordinary theory, such as elongation of normal fibers and transverse shear deflections.The next section by Siniscalco contains the second approximation form of the long cylinder theory. The first approximation coincides with the Wagner-Vlasof semimembrane theory. The second approximation includes the deformation of midsurface fibers. For the circular cylinder, the resultant equations are obtained in simple form.

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Sommario Gli sviluppi parametrici, sono applicati al guscio cilindrico.Nell'introduzione Cicala mette in relazione i campi di applicabilità delle varie soluzioni con le situazioni di carico e le condizioni al contorno. Nella parte seguente, Sassi Perino ricava la formulazione di seconda approssimazione per le soluzioni di classe1/2. In prima approssimazione si ha la coincidenza con la teoria di Donnell. I termini di seconda approssimazione tengono conto di effetti che l'ordinaria teoria trascura, come l'allungamento delle fibre normali e le deformazioni dovute al taglio trasversale. Nella sezione seguente Siniscalco ricava la forma di seconda approssimazione della teoria del cilindro lungo. La prima approssimazione coincide con la teoria semimembranale di Wagner-Vlasof. Nella seconda approssimazione intervengono le deformazioni delle fibre della superficie media. Per il cilindro circolare viene ottenuta l'equazione risultante in forma semplice.

     

High-frequency response of isotropic-laminated cylindrical shells modeled by a layer-wise theory

In this paper, the high-frequency response of isotropic-laminated cylindrical shells is investigated using a layer-wise theory. The cylindrical shell is discretized in an arbitrary number of layers in the radial direction, and a three-dimensional stress state is assumed in each layer. Approximate numerical results obtained by the layer-wise theory are compared with the exact wave-dispersion analytical results. The very good agreement between approximate and exact results indicates that the layer-wise theory can accurately describe of the dynamic response of cylindrical shells in the high-frequency (short-wavelength) range.