Variational principle of coupled heat and mass transfer,taking the finite perturbation velocity into account

A variational principle for coupled heat and mass transfer is obtained for the case of finite perturbation velocity.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 134–138, January, 1981.     

Thermal conductivity of laminated composite finite bodies of complex cross section taking thermal contact resistances into account

A new analytical method of solving the three-dimensional stationary problem of the thermal conduction of laminar composite finite bodies of complex cross section when there is imperfect thermal contact between the layers is proposed, which is based on the simultaneous use of integral transformations for each layer, a structural method, and the Bubnov-Galerkin method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 115–119, January, 1981.     

Thermoelasticity models taking account of a finite heat propagation rate

An analysis is made of the stationary wave process in a one-dimensional thermoelastic medium on the basis of two heat-conduction models. The nature of the change in the phase velocities, the damping coefficients, the coefficient of connectedness, and the phase-shift angle are established.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 2, pp. 344–351, August, 1978.     

Studying heat conduction taking into account the finite rate of heat propagation

By introducing relaxation corrections to the heat flux and to the temperature gradient, hyperbolic equations of heat conduction are obtained involving the third and fourth derivatives over the spatial coordinate and time (mixed derivatives). The obtained formula for the heat flux that is used in obtaining the aforementioned hyperbolic equations coincides with the formula by Lykov, which is derived from the Onsager generalized system equations using the hypothesis about the finite diffusion rate of heat and mass. Investigations of the obtained analytic solutions to the hyperbolic equations allow us to conclude about the temperature discontinuities in the vicinity of the boundary of the space coordinate where the boundary condition of the first kind is given. This testifies that instantaneous heating (cooling) of the body up to the temperature of the environment is impossible in no circumstances of external heat exchange.     

Tensile fracture of concrete at high loading rates taking account of inertia and crack velocity effects

Experiments on concrete have shown a considerable increase of apparent tensile strength with increasing loading rate. This phenomenon can be attributed to various mechanisms such as kinetics of energy barriers and inertia effects in the vicinity of a running crack. After a general introduction into the behaviour of concrete under a uniaxial tensile stress, a model is presented which accounts for flaws in concrete and the inertia effects around a crack at high loading rates. It turns out that the quite crude model predicts rather accurately the relation between apparent strength and loading rate, the influence of concrete quality on this relation, and the relation between crack propagation velocity and loading rate.     

Stability of elastic and viscoelastic plate in gas flow taking into account shear strains under stochastic excitation

Summary. For the solution of stability problems for nonconservative systems the Bubnov–Galerkin method is often applied. In such a case functions of displacements are expanded in forms _i (x) of proper oscillations of the elastic system. For obtaining more correct results in the expansion of displacements a significant number of terms should be kept. However, it should be kept in mind that with the increase of an ordinal number of modes in the indicated expansion of displacements the effect of shear strains and of the rotatory inertia increases, too. In the present work this problem is investigated for elastic and viscoelastic plates in a supersonic gas flow under a stochastic excitation.     

Propagation of elastic vibrations in snow

At rather low temperatures snow is characterized by three velocities of sound, two of which are related to propagation of longitudinal and transverse waves through a solid skeleton formed by ice crystals and the third of which is related to propagation of longitudinal waves through air in snow pores. The main laws governing propagation and absorption of these waves are determined. Analytical formulas that express the dependence of the coefficient of attenuation of waves on frequency are obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 77, No. 6, pp. 124–130, November–December, 2004.     

Model of diffusion taking into account sorption

The problem of the diffusion of a material in an adsorbing porous medium is considered. In the equation for the concentrations in the porous medium and the sorption layer a delay time is introduced.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 3, pp. 453–455, March, 1976.     

On flexural vibrations of micropolar elastic cylinders

An exact derivation of the frequency equation for the flexural modes of free vibrations of an infinite solid circular cylinder made of an isotropic homogeneous centrosymmetric micropolar material is presented and some particular cases are noted.     

Application of mixed variational formulations based on the finite element method to the solution of problems on natural vibrations of elastic bodies

We consider mixed variational formulations and the application of the mixed approximations of the finite element method to the solution of problems on natural vibrations of elastic bodies. To solve the generalized spectral problem, three forms of the mixed variational formulations are proposed. The correctness and stability of mixed variational formulations for displacements, strains and stresses are investigated. Matrix equations of the mixed method are given whose solution is performed using the modified algorithm of the steepest descent method. The results of calculations for natural frequencies of free vibrations of a straight and a circular beam are presented that are obtained in the solution of the problem in a two-dimensional formulation based on the classical and mixed finite-element method approaches. __________ Translated from Problemy Prochnosti, No. 2, pp. 121–140, March–April, 2008.     

The micropolar elastic vibrations of a circular cylinder

The fundamental vibrations of a long circular cylinder of a micropolar elastic solid are analysed and their dispersion equations are discussed. Solutions of these equations, valid in the cases of small cylinder radius or of weak coupling, are obtained explicitly.     

Convective motion of a conducting liquid in an electromagnetic field,taking into account finite wall thickness and thermal conductivity

The effect of the temperature-dependent electrical conductivity of the liquid and the finite wall thickness and the thermal conductivity on stability is investigated in a linear formulation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 1, pp. 123–128, January, 1980.