Dynamics of a homogeneous ball on a horizontal plane with sliding,spinning, and rolling friction taken into account

We analyze the dynamics of a homogeneous ball on a horizontal plane with friction of all kinds, namely, sliding, spinning, and rolling friction, taken into account. The qualitative-analytic study of the ball dynamics is supplemented with numerical experiments.     

Determination of optimal shape of a moving punch with friction taken into account

The optimization problem for the contact interaction between a rigid punch and an elasticmediumis considered. It is assumed that that the punch is under the action of some prescribed forces and momenta and moves along a surface bounding a half-space filled with an elastic medium. It is also assumed that themotion is quasistatic and the friction forces arising in the region of contact are taken into account. The punch shape is considered as the desired design variable, and the integral functional characterizing the discrepancy between the pressure distribution in the region of contact that corresponds to the optimized shape of the punch and a given goal distribution of pressure is taken as the minimizing criterion. The optimal shape can be determined efficiently by solving the following two problems: first, to obtain the optimal pressure distribution and then to solve a boundary value problemfor the elastic half-space under the action of the obtained normal pressure and friction forces. By way of example, the optimal shape is analytically determined for a punch of rectangular shape in horizontal projection.     

First-order approximation in a steady fluid flow problem with surface forces taken into account

The plane problem of finding the shape of the free surface of an ideal incompressible fluid is considered for a fully developed discharge from an infinite layer through a point sink. The gravitational and surface stress forces are taken into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 166–169, November–December, 1974.The author thanks G. V. Shcherbina for formulation of the problem and valuable advice.     

Mixing of plane laminar relaxing gas jets with radiation taken into account

The influence of a chain pumping reaction mechanism in a diffusion-type continuous-action chemical amplifier on an RF molecule is investigated. The actual flow picture is simulated by boundary-layer equations taking account of coherent radiation. It is shown that the efficiency of a chemical amplifier in a mode with partial fluorine dissociation is sufficiently high under the condition of the presence of a line with 0 v5.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 137–142, May–June, 1978.The authors are grateful to B. S. Aleksandrov, Yu. V. Lapin, and M. Kh. Strelets for numerous useful discussion.     

Sliding of a spherical indenter on a viscoelastic foundation with the forces of molecular attraction taken into account

The problem of sliding of a spherical indenter on a viscoelastic foundation is solved in a quasistatic formulation taking account the forces of adhesive attraction which are considered different at the entrance to and exit from the contact region due to changes in the surface properties during the interaction. It is found that the contact characteristics and the frictional force due to the imperfect elasticity of the foundation depend on the surface and bulk properties of the materials of the interacting bodies and the interaction conditions (load, velocity, etc.).     

Problem concerning a plane explosion in a heterogeneous atmosphere with account taken of the post-breakthrough stage

The problem is considered concerning a plane explosion in an exponential and standard atmosphere. The heterogeneity of the medium exerts an extremely marked influence on the gas flow. As shown in [1], under the conditions of an exponential atmosphere the upper part of the shock-wave front recedes to an infinite distance, after a finite time. This phenomenon has received the name breakthrough of the atmosphere. A numerical investigation of a powerful plane explosion in an exponential atmosphere at the stage before breakthrough is contained in [2]. In [3], asymptotic boundary conditions are proposed which permit the gas flow after breakthrough to be calculated. In the present paper, a numerical solution of this problem is obtained at an interval of time which exceeds by a factor of 10–15 the time of break-through. The effect of counterpressure and gravity is studied. Some results are given for a plane explosion in a standard atmosphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–131, May–June, 1976.The authors thank L. A. Chudov for attention to the project and for useful advice.     

Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is defined by two random functions of coordinates. Formulas for calculating the stress variance are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 140–146, March–April, 2007.     

Thermocapillary instability of a plane layer with a vertical temperature gradient

The oscillating disturbances in a plane layer with a temperature gradient are analyzed. It is shown that for heating from below taking the deformability of the free surface into account leads to the appearance of short-wave oscillatory instability, which becomes the most dangerous mode. Moreover, the interaction of the capillary and thermocapillary instability mechanisms results in the appearance of oscillating disturbances of a new type, which lead to equilibrium crisis at high Marangoni numbers. It is established that when the free boundary is heated, the onset of convection is possible only with respect to oscillatory disturbances.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 19–23, May–June, 1992.     

On equations of the linear theory of shells with surface stresses taken into account

We construct equations of equilibrium and constitutive relations of linear theory of plates and shells with transverse shear strain taken into account, which are based on reducing the spatial elasticity relations with surface stresses taken into account to two-dimensional equations given on the shell median surface. We analyze the influence of surface elasticity moduli on the effective stiffness of plates and shells.     

Determining the maximum calculated stresses under the contact site with heat release taken into account

We consider a spatial contact problem for two elastic bodies with heat release taken into account and obtain formulas for determining in-depth stresses (under the contact site).We use these formulas to study the distribution of the maximum calculated stresses according to the third theory of strength. We consider an example where the contact site is an ellipse.     

Experimental study of the behavior of a cylindrical shell under impulsive loading with ambient humidity taken into account

A procedure and results of experimental determination of the vibroacceleration of a cylindrical shell that is in contact with an ambient medium are presented. It is revealed that the vibroacceleration of the shell is maximum at resonance. Its dependence on the height from which a weight is dropped on the shell to generate a shock load is established