Free-molecular gas flow in plane channels and grids

The problem of the flow of a rarefied gas in plane channels and grids in the free-molecular regime is considered. The parameters of the grid (channel) cells and the over-all geometrical dimensions of the grid are considered smaller than the mean free path of the molecules. The grid profiles are considered thin, the profile material is a perfect heat conductor. For the case of diffuse reflection of the molecules from the surface of the grid (channel), a calculation is made of the probability of passage of a molecule and the aerodynamic characteristics of the grid are determined.     

Polymer indentation: Numerical analysis and comparison with a spherical cavity model

Three dimensional analyses of indentation of a polymer by a rigid indenter are carried out. The polymer is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out with a dynamic finite element program used to simulate quasi-static behavior. Two types of indenter are considered; a conical indenter and a pyramidal indenter. For each indenter type, different values of the sharpness of the indenter are considered and two rates of indentation are analyzed. Significant sink-in is found to occur in all cases considered. The amount of sink-in is found to be smaller for sharper indenters. The calculated values of both the nominal and true hardness do not differ significantly for the two indenter shapes. An expanding spherical cavity model is also considered and the predictions of this model are compared with the finite element results for various indenter shapes and indentation rates. The spherical cavity model is found to give fairly good agreement with the predictions of the finite element analyses for the nominal polymer hardness for both indenter shapes.     

Evaporation and Condensation Fronts in Porous Media

Flow of a fluid through a porous medium is considered with allowance for heat conduction. Both fronts at which the liquid is transformed into steam or a liquid-steam mixture and fronts with inverse transformations are studied. The evolutionarity conditions of these fronts are considered and a model of their structure is proposed.     

Thin viscous fluid film flows over rotating curvilinear surfaces

Thin viscous fluid film flows over rotating curvilinear surfaces are considered. The steady-state flow is studied for large and finite Ekman numbers. The possibility of obtaining a film of given thickness is considered. The wave formation on the surface of an inhomogeneous film and the development of nonlinear waves are also investigated. The film flow parameters in the cases of flow over a plane disk and a curvilinear surface are compared.     

Singularity analysis of Duffing-van der Pol system with two bifurcation parameters under multi-frequency excitations

Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed： （1） λ 1 is considered as bifurcation parameter, （2） λ 2 is considered as bifurcation parameter, and （3） λ 1 and λ 2 are both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space is divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions are obtained, which provides a theoretical basis for optimal design of the system.     

Stability of high-frequency periodic motions of a heavy rigid body with a horizontally vibrating suspension point

The motion of a heavy rigid body one of whose points (the suspension point) executes horizontal harmonic high-frequency vibrations with small amplitude is considered. The problem of existence of high-frequency periodic motions with period equal to the period of the suspension point vibrations is considered. The stability conditions for the revealed motions are obtained in the linear approximation. The following three special cases of mass distribution in the body are considered; a body whose center of mass lies on the principal axis of inertia, a body whose center of mass lies in the principal plane of inertia, and a dynamically symmetric body.     

Wing of simple planform in a sharp-edged gust

The entry of a wing into the zone of a sharp-edged gust is considered in the linear formulation. The case is studied when the wing velocity is supersonic and its edges satisfy the supersonic flow condition. The gust intensity is considered to be variable, and its edge may move into the undisturbed medium. Equations in finite form are obtained for the forces and moments for a rectangular wing of infinite span, and also for triangular wings with positive and negative sweep, for the case when the gust intensity varies linearly. Sudden envelopment of the wing and penetration of the wing into a gust whose edge is fixed relative to the undisturbed medium are considered.     

On deformations of cracked anisotropic slabs

The effect of a crack on the bending and shearing of an anisotropic elastic slab is considered. The problems considered are reduced to simultaneous Fredholm equations which may be solved numerically.     

Taking into account van der Waals interaction in some problems of elasticity

We obtain the correction due to van der Waals forces to the flexural rigidity of a layer. The cases of a monolayer and a film consisting of several monolayers are considered. The correction due to van der Waals interaction to the force acting on an indentor is obtained. Two versions of determining the elastic forces at the microlevel are considered. Numerical estimates of the parameter values for which the correction is essential are given.     

Stability of liquid flow between heated rotating cylinders

The effect of a radial temperature gradient on stability of steady-state flow of a viscous liquid between two solid concentric cylinders both rotating in the same direction is considered. The linear stability problem is considered in the Boussinesq approximation. Sufficient stability and instability conditions for the flow relative to rotationally symmetric perturbation are obtained. Neutral curves are computed for a wide range of problem parameters.     

Tangential oscillations of a differentially rotating spherical fluid layer

The natural harmonic oscillations of a differentially rotating fluid layer under the action of a potential force are considered. The rise in the layer level is assumed to be negligible. The oscillations satisfy an ordinary second-order differential equation with singular coefficients that depend on the spatial coordinate. This equation is solved by the method of local separation of singularities based on the use of the properties of the Fuchs series for a bounded solution. Various laws for the latitude dependence of the angular rate of ocean rotation and the effect of these laws on the problem spectrum are considered. An equation is obtained for the streamlines of the oscillations investigated. Two cases in which the latitude dependence of the base flow velocity coincides with the real dependence for a celestial body are considered and the corresponding modes are found.     

半无限大体广义电磁热弹耦合的二维问题

基于Lord和Shulman广义热弹性理论,研究了热、电可导的半无限大体电磁热弹耦合的二维问题。半无限大体受热和外加恒定磁场的作用,文中建立了电磁热弹性耦合的控制方程,利用正则模态法求解得到了所考虑物理量的解析解,并用图形反映了各物理量的分布规律,从分布图上可以看出,介质中出现了电磁热弹耦合效应,各物理量的非零值仅在一个有限的区域内。     

Dynamic extension and twist of a non-linear elastic tube

The propagation of waves in a non-linear cylindrical elastic membrane is considered when one end is fixed and the other is subjected to a dynamic extension and twist. The governing equations are derived for a hyperelastic material with a general strain energy function. In order to obtain specific results the equations are specialised to deal with neo-Hookian materials and in this case we show that there are three real wave speeds in each direction along the cylinder. Numerical results are given and a limiting case considered which provides a check on these results.     

The lateral migration of solid particles in a laminar flow near a plane

The lateral inertial migration of a solid spherical particle suspended in a laminar flow over a vertical wall is considered theoretically. Formulae for the migration velocity are obtained for both neutrally buoyant and non-neutrally buoyant particles and also for the case of zero flow over the wall. Situations in which the particle is either free to rotate or prevented from rotating are considered. Such results are found to agree qualitatively with known experimental data.     

Elasto-viscoplastic-viscous theories of granular and porous media

The mechanics of granular and porous media is considered in the light of the modern theories of structured continuum. The basic laws of motion are presented and several constitutive relations are derived. The special case of elastic porous media is considered in detail and the basic field equations are derived and the possible application of the results to soil dynamics is pointed out. The theory of the flow of granular media is also considered and basic equations of motion are derived where the results of Goodman and Cowin are recovered. The viscoplastic flow of porous media is studied and the possible application to soil mechanics is also discussed.     

Indentation of a semi-infinite fluid-saturated poroelastic medium by an undeformable porous punch

Summary The following mixed boundary value problem in deformation theory of porous and elastic medium is considered. The bounding surface of the semiinfinite medium has a prescribed normal displacement within a circular area and prescribed stresses outside the circle. The techniques of integral transform are used. The expressions for the stresses and displacements are written down. As a special case, the indentation by a flat ended cylinder is considered and the distribution of pore-fluid pressure in the neighbourhood of the loaded area is shown graphically.     

Shape control of thin rigid inclusions and cracks in elastic bodies

The paper is concerned with a control of thin rigid inclusion and crack shapes in elastic bodies. It is assumed that rigid inclusions are delaminated; thus, cracks are located on the boundary of inclusions as well as outside of inclusions. We provide the problem formulations and analyze the shape sensitivity with respect to geometrical perturbations in the frame of free boundary models. Inequality type boundary conditions are considered at the crack faces to guarantee a mutual non-penetration between crack faces. Inclusion and crack shapes are considered as control functions. The cost functional, which is based on the Griffith rupture criterion, characterizes the energy release rate and provides the shape sensitivity with respect to a change of the geometry of the structure. We prove an existence of optimal shapes in the problems considered.     

Viscosity of a suspension of ellipsoidal ferromagnetic particles in a magnetic field

The motion of a suspension of solid magnetized ellipsoids of rotation in a uniform magnetic field is considered. The ellipsoids are assumed to be magnetized along the axes of symmetry. Relaxation processes in the solid phase are not considered. The stress tensor of the suspension is calculated taking into account the rotational Brownian motion of the particles. It is shown that the viscosity tensor contains six independent kinetic coefficients, which are even with respect to the magnetic field. The relation between these coefficients and the field and the ratio of the semiaxes of the ellipsoid is obtained. As an example, the effect of the magnetic field on the symmetrical flow of the suspension in a contractile cylinder is considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 75–82, September–October, 1973.     

Acoustic scattering of a plane wave by a circular penetrable cone

The paper is devoted to the diffraction of a plane wave by an acoustically transparent semi-infinite cone. The problem of diffraction is reduced to a singular integral equation in the framework of the incomplete separation of variables. The Fredholm property and regularization of the integral equation are discussed. Some important integral representations of the wave field are considered. The detailed study of the far-field asymptotics is given. Expressions for the diffraction coefficient of the spherical wave scattered from the vertex of the cone are considered. The reflected from the conical surface waves and those transmitted across the surface are also discussed.     

Steady motion of a rigid disk of finite thickness on a horizontal plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady-state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line or in a circle. Oscillations about steady state are discussed and conditions for stable motion established. The bifurcations of steady motions on a smooth surface are also considered.