Mechanics

Coupled Dynamic Problems of Hyperbolic Thermoelasticity

Authors: Kovalev V. A., Radaev Y. N., Semenov D. A.

In the present paper in the framework of the linear non-dissipative coupled thermoelasticity (GNII, hyperbolic thermoelasticity), treating the heat transport as propagation with finite speed of undamped waves of second sound, harmonic coupled thermoelastic waves propagating in an infinite free from tractions thermoisolated cylinder are studied. Dispersionrelation is derived for this type of thermoelastic waves for an arbitrary azimuthal order. Numerical results for wave numbers depending on frequency are obtained.

Mathematical Models and Contemporary Theories of Physical Fields

Authors: Kovalev V. A., Radaev Y. N.

Elements of the classical field theory based on a variational formulation of the Hamilton type are discussed and corresponding 4- dimensional Lagrange formalism is presented both as the variational and the group theoretical script. Variational symmetries (geometric and generalized) of field equations and the Noether theorem providing a regular way of obtaining a conservation law for every given variational symmetry are revisited in the study in order to give a complete version of the contemporary field theory. All developments are presented in the non-linear frame (i.e.

About Oblique Impact by Perfectly Rigid Body with Plane Boundary on the Nonlinear Elastic Half-Space

Authors: Dudko O. V., Potyanikhin D. A.

In this paper the impact interaction of perfectly rigid body and nonlinear elastic solid, which have plane boundaries, are investigated. Suppose that the moving rigid body has constant velocity, resulting in self-similar formulation of the problem. Possible variants of wave combinations, arising from such interaction, are discussed. The existence condition for evolutionary shock waves and the thermodynamic discontinuities compatibility condition serve as criterions for choosing the wave pattern.

On Some Problems of Reconstruction of Inhomogeneous Pre-Stressed State in Elastic Solids

Authors: Vatulyan A. O., Dudarev V. V.

Presents a general approach to the problem of reconstruction of the inhomogeneous pre-stressed state in an elastic body on its amplitude-frequency response, measured in part of its border. Based on the previously defined generalized reciprocity is the ratio of the sequence of linear ill-posed problems, allowing for refinement of the procedure for pre-stress tensor component. As an example, presented a series of computational experiments on the restoration of monotone functions of the distribution of pre-stressed state the problem of bending vibrations of a rod. 

The Evolutionary Equation for Wave Processes of the Shift Deformation

Authors: Burenin A. A., Ragozina V. E., Ivanova Y. E.

One-dimensional process of formation and the subsequent motion of a flat cross shock wave is studied on the basis of solutions of the corresponding nonlinear evolutionary equation. This equation defines behaviour of the solution in front area of wave process and follows from interior lines of a method of matched asymptotic expansions. Comparative transient analysis of strains of a deformation and volume will be carried out and their basic differences are specified.

Multimodulus Behevior of the Grained Composites on the Base of Unsaturated Polyetheres

Authors: Bessonov D. E., Zezin Y. P., Lomakin E. V.

The results of the investigation of elastic properties of grained composite based on the unsaturated polyetheres were presented. This material was designed to substitute natural rocks in civil and mechanical engineering. The experimental values of elastic modulus and the Poisson‘s ratio under the tension and compression were obtained. It was shown that the investigated composite exhibits the dependence of elastic properties on the type of the stress state.

The Contact Problems for the Elastic Foundation with the Functionally Graded Coatings of the Complicated Structure

Authors: Aizikovich S. M., Krenev L. I., Trubchik I. S.

The contact problemfor the impression of axisymmetrical indenter into a functional graded elastic half-space is considered. Analytical methods for solving this problem have been developed. It is assumed that the indenter has a parabolic shape and contact between the indenter and the coating is smooth. The used method make it possible to find the analytical asymptotically exact problem solution.

Electornic Publications and Scientific-Educational Resources of the Internet

Authors: Polyanin A. D., Zhurov A. I.

The paper presents current developments and trends in electronic publications in Russia and abroad. It is explained why authors may find it useful to publish their papers and books online. Web addresses with brief descriptions of major mathematics and physics Internet resources are given. Suggestions are offered for the development of scientific online resources in Russia.

The One-Dimensional Micropolar Theory of Elastic Rods Basic Parities Construction

Authors: Ilyukhin A. A., Timoshenko D. V.

The reduction from a three-dimensional problem of the asymmetrical theory of elasticity to one-dimensional by means of splitting a three-dimensional problem on set of two-dimentional and one-dimensional problems is carried out. Kinematic parameters with which it is necessary to involve are specified that together with system Kirchoff differential equations to receive the closed system of the equations of the one-dimensional micropolar theory of cores. Other geometrical sizes are found from parities defining them.

The Stabilization of Program Motions of Firm Body on a Moving Platform

Authors: Bezglasnyi S. P., Mysina O. A.

We consider firm body with fixed point on a moving platform. We solve the problem of construction asimptotically stability programm motion. The programm motion can be any function. Control is received in the form the analytical solution. We solve the problem of stabilization by the direct Lyapunov’s method and the method of limiting functions and systems. In this case we can use the Lyapunov’s functions having constant signs derivatives.

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