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A method is proposed for calculating the Darcy friction coefficient in a flat channel formed by two infinite parallel plates, depending on the values of the Reynolds number and the rarefaction parameter of the gas in the channel. Maxwell's diffuse reflection model is used as a model for the reflection of gas molecules from the channel walls. The isothermal gas flow is due to the presence of a small absolute pressure gradient directed along the channel walls. The proposed method is based on solving the linearized ellipsoidal-statistical Boltzmann kinetic equation with homogeneous boundary conditions using the Chebyshev polynomial approximation. An unknown function that interpolates the solution of this equation is represented as a partial sum of a series in Chebyshev polynomials of the first kind. Using the properties of finite sums for an orthonormal system of Chebyshev polynomials, the problem is reduced to a system of linear algebraic equations with respect to the values of the desired function at the interpolation nodes. The analysis of the obtained results was carried out

Using the results of experimental studies, a comparison is made of the space-time distributions of the amplitude of controlled pulsations in the linear and weakly nonlinear phases of the development of a wave train in homogeneous and inhomogeneous boundary layers on a flat plate at a Mach number M=2. (The inhomogeneity of the flow is caused by a longitudinal stationary perturbation generated by a pair of weak shock waves. Controlled perturbations were generated locally from the surface at a fixed power of the high-frequency glow discharge inside the model.) It is established that the inhomogeneity of the flow changes the mechanism of interaction of subharmonic perturbations. It is shown that in the center of the wave train there is a violation of the spatial synchronism of pulsations of subharmonic frequency

The transport of a two-phase multicomponent gas condensate mixture in the vicinity of a vertical production well is considered taking into account the possible nonequilibrium of the process, namely, the kinetics of the gas-condensate phase transition. Results of numerical solution of the transport problem are presented for different well production rates and different rates of relaxation to the thermodynamic equilibrium of the reservoir mixture. It is shown that the effect of nonequilibrium increases with increasing well production rate

Resolving equations describing stationary flows of an incompressible viscoelastic polymer fluid through a circular pipe are derived on the basis of the rheological mesoscopic Pokrovskii-Vinogradov model. Exact solutions of the equations are obtained, and restrictions on the values of the rheological parameters that ensure their existence are formulated. These results enable one to constructively describe the destruction of Poiseuille-type laminar flow. The size and orientation of the macromolecules of the polymer fluid play a key role in the mechanics of this process. liquids. The mathematical description of the process uses the singular points of the solutions

The paper presents an analytical solution of the problem of stress relaxation in a bended viscoelastic plate. The effect the difference in the viscous properties of the material in tension and compression on the relaxation of the bending moment is investigated. The deformation is assumed to be finite, and the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic components is used. Two different material models with tension-compression asymmetry are compared

Since in modern high-performance sports, the technical component is decisive, an important element of skiing race is the sliding surface of skis. This paper presents a review of papers on sliding mechanics and discusses modern ways to improve it and prospects for the development of this area in modern energy and environmental conditions. A detailed analysis of various factors affecting the sliding mechanics, in particular, snow cover albedo, and microroughness of the sliding surface of skis is given

The efficiency of two ways to reduce vibration and sound emission of a plate made of paper-laminated plastic (high-pressure laminate) has been investigated. It has been found that the inclusion of a polymer polyvinyl acetate film in the plastic structure or using constrained damping layer treatments based on polyvinyl acetate film and aluminum foil or plastic leads to a significant improvement in its vibroacoustic characteristics. The greatest reduction in vibration and sound emission was obtained when applying a coating with aluminum foil whose thickness was six times less than that of the damped plastic plate

The solution of the system of nonlinear elasticity equations was found the described the stress-strain state of a two-layer incompressible material. The solution can be used to describe the compression of a two-layer material by rigid plates that approach each other with constant acceleration

This paper describes the use of a nonlinear viscoelastic model with material properties depending on the strains in the lengthwise fracture analysis of an inhomogeneous cantilever beam structure. The viscoelastic model is obtained by placing a~nonlinear spring and a nonlinear dashpot in parallel to a series of a linear spring and a linear dashpot. The modulus of elasticity of the nonlinear spring and the coefficient of viscosity of the nonlinear dashpot depend on strains. The strain energy release rate is determined. The balance of the energy is analyzed to prove the correctness of the strain energy release rate solution.

A method for determining the limiting expansion coefficient of cylindrical pipes using conical equipment is considered which allows a fairly accurate calculation of the moment of fracture of a workpiece taking into account the nonlinear plasticity of the material and the change in thickness. The method is based on the use of forming limit diagrams to predict the fracture of the workpiece and the method of variable elasticity parameters to determine the stress-strain state