Vol 53, No 2 (2018)

The problem of describing the behavior of a highly filled polymeric material under compression, which was preceded by preliminary compression and unloading, is considered. The peculiarity of the compression diagrams obtained in the experiment is the downward convexity of the curves of the stress modulus versus time. To solve this problem, a variant of the non-linear endochronic theory of aging viscoelastic materials with several aging and viscosity functions and a numerical-graphical method for identifying the properties of viscoelasticmaterials proposed by the authors earlier, suggesting comparison of the deformation diagrams of intact samples and those that received preliminary damage, are used.

A general scheme for identifying the constitutive equations of superplasticity, according to which the values of material constants are calculated by the results of technological experiments using interpretation techniques based on the adoption of additional hypotheses of the stress-strain state nature in the deformation region, is proposed. The verification of the result is carried out by comparing the experimental data with the corresponding solutions of the boundary problems for superplasticity mechanics obtained using software complexes such as ANSYS and ABAQUS. The obtained result is used as input data for a program, and the solution of the boundary value problem is found without additional hypotheses of the stress-strain state nature. The practical application of the proposed approach for the standard power model of superplasticity shows that the accuracy of the forming duration simulation is no less than 4%.

On the basis of classical methods for mathematical physics and mechanics, the stability problem of a thermoelastic web moving at a constant speed without friction along a cylindrical surface is investigated. The web is modeled by a stretched and heated string. At a sufficiently high speed and heating of a string, a loss ofmotion stability and the stringmovement in a direction normal to the cylindrical surface occur. To study the instability, a static method based on the consideration of stationary nontrivial modes of stability loss, that is, on the study of the problem for bifurcation of solutions (eigenvalue problem) for the corresponding differential equations is used. The case of the web motion along the circular cylinder is separately considered and an expression for the critical velocity leading to the instability is found.

The article deals with a linear theory describing the elastic properties and thermodynamics of deformation for a mixture, which is an elastic material and a liquid dissolved in it, in the approximation of small deformations. Theory’s equations are obtained by the linearization of the corresponding equations for the nonlinear theory. In the framework of the linear theory, the formulation of the basic problems for the mechanics of mixture is considered. Their connection with the classical problems of the theory of elasticity and thermoelasticity is shown. The general theory is exemplified by the description of the elastic properties and thermodynamics for the deformation of polymer gels in a solvent medium.

The paper presents a unified mathematical approach for describing the dynamic stressstrain state of mechanical structures from heterogeneous materials possessing a double coupled system of pore channels filled with fluid. New dynamic equations describing the oscillations of poroelastic systems based on the developed model of a continuous medium with additional degrees of freedom in the form of various pressures of the components constituting the liquid phase of the material are obtained. The equations and the method of obtaining them have a greater degree of generalization than those encountered in the literature. Theoretical results can be used to study the propagation of vibrations in fractured geological rocks saturated with liquid, to develop technical systems of new structural materials with a porous structure, for the analysis of micro streams of fluid in the hierarchical system of microporous bone tissue.

Standing waves of a Timoshenko beamof finite length and their connectionwith running waves for an infinite beam are considered. It is shown that the principle of a “closed cycle” of a running wave is completely identical to the usual procedure of direct satisfaction from the side of the general solution for an infinite Timoshenko beam, to the boundary conditions of a beam of finite length. The question of the existence of a second frequency spectrum under arbitrary boundary conditions of a beam is discussed. A “relaxed approach” to the concept of the second frequency spectrum is proposed. The results of the theoretical analysis are confirmed by numerical calculations for the Timoshenko beam with elastic supports and elastic sealing of its end sections.

The formulation of a new task of realizing a given relative motion of two rigid bodies by means of a robot having two manipulators is given. A method for constructing the movements of two-armed robots is proposed, which consists of solving the direct and inverse problems of manipulator kinematics, taking into account additional conditions for eliminating the dangerous rapprochement of links.

Equations of relationships of parameters of relative motion of the working links of the manipulators are obtained with the relative movements of their adjacent links assumed for control functions. Expressions for control functions of manipulators are obtained for the realization of a given relative motion of the general form of two rigid bodies, and also for plane motion.

Pointing to the possibility of crossing the working links under the action ofmanipulators in one work area, and obtained the relationships that allow these intersections to be avoided.

Currently the practice of constructing various algorithms of inertial navigation, including strapdown navigation system (SINS), indicates that two mathematical methods for describing rotation are mainly used: using quaternions or direction cosines. Moreover, in SINS algorithms it is often convenient to use two of these parameter systems in parallel: quaternions for the angular motion algorithms (the orientation problem), and the direction cosines for the problem of calculating speed and position. In this case, parallel calculation of these two groups of parameters is carried out under the assumption of an exact isomorphic accordance between them. However, if the formalism of quaternions is single-valued, then the apparatus of matrix operations using direction cosines does not possess such a feature and admits several interpretations, which should be borne in mind. From this point of view, the question posed in this article makes sense not only as the question of the existence of an isomorphic accordance (there is no doubt about it), but in what form it exists for the matrix formalism of direction cosines.