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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.

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.