Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2017 number 1

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which is used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤4.

A one-dimensional model is proposed for transportation of a two-phase fluid (sand-containing fluid and pure fluid) in the Hele-Shaw cell with permeable walls through which the pure fluid can escape as the sand concentration increases. The model describes the process of pure fluid displacement with the emergence of the Saffman — Taylor instability and extends the Koval' model to the case of sand concentration variation owing to pure fluid outflow through the cell walls. The Riemann problem is analyzed. New flow configurations, which are not predicted by the Koval' model, are discovered.

The behavior of hydrogen molecules in carbon nanopores of different shapes (slit, cylindrical, and spherical) is investigated using the molecular dynamics method. It is shown that an adsorbed molecular layer with increased density is formed near the nanopore walls, and dynamic equilibrium is established between this layer and the gas in the central region of the nanopore. The distribution of the density of gas molecules over the cross section is found to depend on the size and curvature walls of the nanopores: with a reduction in the size of the nanopores, the density of the adsorbate increases more rapidly in spherical nanopores, whose walls are characterized by greater mean curvature.

The principle of the exchange of stabilities for magnetohydrodynamic multicomponent convection is established. If this sufficient condition holds and there are perturbations, oscillatory motions of neutral or growing amplitude can exist in the fluid. The upper bounds for the complex growth rate of such motions when at least one of the boundaries is rigid are obtained.

This paper considers the dynamic coupled problem of harmonic oscillations of a layered inhomogeneous electromagnetoelastic medium subjected to an oscillating mechanical or electrical load under various electric and magnetic field conditions specified on the surface and internal boundaries of this medium. Green's function for the medium is constructed. Dispersion curves and phase velocities for different boundary conditions and materials are obtained.

Simultaneous effects of heat and mass transfer in peristaltic transport of a viscous fluid are considered. Mathematical modeling is provided in the presence of the Joule heating and the Soret and Dufour effects. The analysis is performed using the long wavelength and low Reynolds number considerations. Perturbation solutions are obtained for a small Brinkman number.

A steady two-dimensional magnetohydrodynamic stagnation-point flow of an electrically conducting fluid and heat transfer with thermal radiation of a nanofluid past a shrinking and stretching sheet is investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis. A similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher-order nonlinear ordinary differential equations. The result shows that the velocity, temperature, and concentration profiles are significantly influenced by the Brownian motion, heat radiation, and thermophoresis particle deposition

This paper presents the solution of the linear hydroelastic problem of stabilized forced vibrations of a semi-infinite ice cover under the effect of localized external load. The ice cover is simulated by a viscoelastic thin plate, the thickness of the liquid layer is assumed to be small, and the shallow water theory is used. The liquid is limited by a solid vertical wall, and the straight edge of the elastic plate adjacent to the wall can be both free and clamped. The solution is obtained with the help of the Fourier integral transform. The behavior of the ice cover is studied in terms of the frequency of the external load and boundary conditions on the edge of the plate. It is shown that, in the case of a free edge of the plate, there are considerable bends on the edge, which could be comparable with bends at the center of the pressure impact region. It is established that, due to the existence of wave movements of the type of edge waves, the external load energy is transferred to larger distances along the free edge, and there are significant bending moments on the edge of the clamped plate, which can lead to fracture of the ice cover at sufficiently great intensity of the external load.

The formation of a cavity during vertical impact and subsequent deceleration of a circular cylinder semi-submerged in a liquid is investigated. The problem with unilateral constraints is formulated to determine the initial regions of separation and contact of liquid particles and the perturbation of the internal and external free boundaries of the liquid at small times. The problem is solved using a direct asymptotic method which is effective at small times. Examples of numerical calculations of the formation of one or two cavities near the boundary of the body are given. It is shown that the acceleration of the cylinder has a significant impact on the liquid flow pattern near the body at small times.

An analytical solution of the problem of the passage of a plane sound wave through a discretely inhomogeneous thermoelastic layer adjacent to inviscid heat-conducting liquids. Results of calculations of the dependences of the transmission coefficient on the wave incidence angle and frequency for discretely inhomogeneous and continuously inhomogeneous thermoelastic layers are given. It is shown that a thermoelastic layer with continuously inhomogeneous thickness can be simulated using a system of homogeneous thermoelastic layers.

In this numerical study, the effects of variable thermal conductivity models on the combined convection heat transfer in a two-dimensional lid-driven square enclosure are investigated. The fluid in the square enclosure is a water-based nanofluid containing alumina nanoparticles. The top and bottom horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. Five different thermal conductivity models are used to evaluate the effects of various parameters, such as the nanofluid bulk temperature, nanoparticle size, nanoparticle volume fraction, Brownian motion, interfacial layer thickness, etc. The governing stream-vorticity equations are solved by using a second-order central finite difference scheme coupled with the conservation of mass and energy. It is found that higher heat transfer is predicted when the effects of the nanoparticle size and bulk temperature of the nanofluid are taken into account.

An analysis is performed to study the effects of the chemical reaction and heat generation or absorption on a steady mixed convection boundary layer flow over a vertical stretching sheet with nonuniform slot mass transfer. The governing boundary layer equations with boundary conditions are transformed into the dimensionless form by a group of nonsimilar transformations. Nonsimilar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasi-linearization technique combined with an implicit finite difference scheme. The numerical computations are carried out for different values of dimensionless parameters to display the distributions of the velocity, temperature, concentration, local skin friction coefficient, local Nusselt number, and local Sherwood number. The results obtained indicate that the local Nusselt and Sherwood numbers increase with nonuniform slot suction, but nonuniform slot injection produces the opposite effect. The local Nusselt number decreases with heat generation and increases with heat absorption.

This paper re-examines the creep life methodology based on the continuum damage mechanics (CDM) of the Kachanov and Rabotnov theory. Uniaxial creep and multiaxial creep rupture formulations are presented taking into account the primary creep effect. The scalar damage parameter is computed up to time-to-rupture as a function of time and stress. The methodology implemented is based on the uniaxial time-to-rupture obtained experimentally. The times-to-rupture for bars with different notches are calculated. It is demonstrated that the use of the damage parameter is vital to indicate the critical damage location where failure occurs. Results are compared to those obtained experimentally. It is shown that the primary creep inclusion has a significant effect on the damage distribution zone.

This paper describes an experimental setup consisting of a drop hammer and a shock tube filled with a liquid, where a shock wave is formed, and results of experiments performed with fully clamped rectangular plates subjected to an impact load of the water shock wave. The results are presented in terms of the central deflection of the plates as a function of the kinetic energy of the drop hammer. The singular value decomposition method is used in conjunction with dimensionless numbers to obtain analytical dependences of the central deflection of the plates on the impact load parameters.

This paper touches upon changes in the temperature field near the ends of a slit of variable width under the action of an inhomogeneous stress field. The solution of the boundary-value problem on the equilibrium of the slit with partially contacting edges (there is adhesion of the edges on a certain part of the contact zone and slippage on another one) under the action of the outer inhomogeneous stress field, temperature field, and efforts on the contacting surfaces of the slit of variable width comparable with displacements in an elastic state is reduced to the problem of linear conjugation of analytic functions.

The development of main cracks in a coal bed due to rapid unloading is analyzed using the methods of theoretical physics. A fracture criterion and a criterion for the time to fracture of a site on the edge of the bed are obtained.

A kinetic model of creep-rupture strength is constructed using the physicomathematical theory of irreversible strains of metals. An algorithm for the mathematical modeling of the processes occurring during tension of specimens. Results of experimental verification of a uniaxial model of creep-rupture strength are given. It is shown that the proposed model differs from available models fact in that it contains physical structural parameters (scalar densities of dislocations and microcracks) and kinetic equations for them.

The hypotheses of the Reissner theory are used to formulate the problem of equally stressed reinforcement (ESR) of transversely bent elastic plates by fibers with a constant cross section. The corresponding system of governing equations and boundary conditions is performed. The model problem of ESR of rectangular elongated plates subjected to cylindrical bending with various types of loading of one of the longitudinal edges and rigid clamping of the other one. It is shown that there could exist two solutions of the problem of ESR, one of which is regular and the other one singular. The edge effects occurring in the presence of the torque applied to the edge, which significantly affects both the stress-strain state of the binder material and the reinforcement structure.

A model for predicting the strength of a cement ring adjacent to a production well bore without consideration of internal and temperature stresses is proposed based on solutions of the Lame problems for one- and two-layer tubes and the Huber-Mises yield criterion using the model of a perfectly plastic isotropic body.