Vol 57, No 4 (2016)

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.

A time-varying flow through a porous medium of a dusty viscous incompressible Bingham fluid in a circular pipe is studied. A constant pressure gradient is applied in the axial direction, whereas the particle phase is assumed to behave as a viscous fluid. The effect of the medium porosity, the non-Newtonian fluid characteristics, and the particle phase viscosity on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is investigated. A numerical solution is obtained for the governing nonlinear momentum equations by using the method of finite differences.

A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.

This paper presents a method for the analytical calculation of the flow velocity of the gas mixture and the concentration of the growth component during vapor-phase epitaxy in a reaction chamber with a rotating substrate holder disk. The concentration of the growth component is analyzed in relation to some epitaxy process parameters.

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models.

This article addresses the boundary layer flow of a thixotropic fluid past an exponentially stretching sheet with heat transfer. The governing partial differential equations are reduced to an ordinary differential equation whose solution is found by the homotopy analysis method. The numerical values of the skin friction coefficient and Nusselt number are compared with available data.

Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fractions of the constituent materials vary continuously across the plate. The effective properties of the FGM plate are estimated by using the Mori–Tanaka homogenization method. A graded finite element method based on the Rayleigh–Ritz energy formulation is used to solve the problem. Effects of different volume fractions of the materials and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data.

This paper presents the results of determining the free vibration frequency of a structurally anisotropic, cylindrical fiberglass shell reinforced by annular ribs and containing flowing fluid. Boundary Navier conditions are imposed on the ends of the shell. Natural vibration frequencies are calculated as dependences of the frequency on the fiberglass winding angle and fluid flow velocity for different values of the wave formation parameters and the parameters characterizing the geometric dimensions of the shell.

A theoretical and experimental method for determining the elastic and damping characteristics of materials is proposed based on analysis of vibrograms of damping flexural vibrations of test specimens with different structures. It is shown that during tension–compression and shear of a carbon fiber-reinforced plastic made of Porcher 3692 carbon fabric and EDT-69NM polymer binder, its dynamic elastic modulus decreases considerably with increasing frequency of deformation in the range of 0–120 Hz. The amplitude dependences of the logarithmic vibration decrements of the carbon fiber-reinforced plastic are determined by minimizing the discrepancy between the experimental and calculated internal-damping parameters of the test specimens in tension–compression and shear.

This paper describes the derivation of extreme conditions of each elasticity coefficient (Young’s modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the principal axes of anisotropy, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. The example of a material with cubic symmetry is given.