Vol 58, No 1 (2017)

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 are 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.

The behavior of hydrogen molecules in carbon nanopores of different shapes (slit-shaped, 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 wall curvature of nanopores: with a reduction in the nanopore size, the density of the adsorbate increases more rapidly in spherical nanopores, whose walls are characterized by greater mean curvature.

This paper considers the dynamic coupled problem of harmonic vibrations of a layeredinhomogeneous 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 of 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.

This paper presents the solution of the linear hydroelastic problem for steady 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 fluid layer is assumed to be small, and the shallow water theory is used. The fluid is limited by a solid vertical wall, and the rectilinear 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 depending on 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 deflections on the edge, which could be comparable with deflections 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 with sufficiently great intensity of the external load.

An analytical solution of the problem of the propagation of a plane sound wave through a discretely inhomogeneous thermoelastic layer adjacent to inviscid heat-conducting liquids is obtained. 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.

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 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.

The development of main cracks in coal seams due to rapid unloading is analyzed using the methods of theoretical physics. A fracture criterion and a criterion for the time to fracture of an area at the edge of a coal seam are obtained.

The hypotheses of the Reissner theory are used to formulate the problem of uniformly stressed reinforcement (USR) of transversely bent elastic plates by fibers with a constant cross section. The analysis of the corresponding system of governing equations and boundary conditions is performed. The model problem of USR 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 USR problem, 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, are revealed.