Vol 19, No 9.2 (2013)

We consider singularly perturbed differential systems which describe the dynamics of manipulator with flexible joints in conditions of small dissipation. The existence of decoupling transformation which converts original multirate system to "block triangular" form with independent slow subsystem. Decoupling transformation is constructed as asymptotic series.

In this paper, modified 3D epidemiologic SIRS model with the so-called saturation incidence is considered. In the course of research the considered model was enlarged by means of adding spatial constituent and diffusion process. The aim of the work is to prove the existence of spatial heterogeneous periodic solutions in the system that takes place when bifurcation of periodic solutions happens not only along temporal but spatial variable and to simulate them numerically.

Based on experimental data it is supposed that the boundary of the area in which the process of accumulation of damages takes place, is semiellipse and beams that are parallel to the edges of the crack. Setting by this hypothesis the form of area of the process, asymptotic decompositions of component of tensor of strain and damage are defined.

On the basis of the theory of plastic flow the peculiarities of application of plasticity condition connected with level lines of strain state surface for work-hardening incompressible rigid-plastic body at different stressed states realized in the context of plane and axisymmetric strain, plane stressed state are considered. Comparison of the proposed condition with plasticity conditions of Mises and Tresca is carried out on the basis of construction of yield curves in deviatoric plane and in planes corresponding to certain stressed states. It is shown that the proposed plasticity condition describes plastic flow on the edge of Tresca prism in conditions of axisymmetric deformation.

On the basis of photoelasticity method the experimental study of near crack tip stressed strain state in specimens under mixed loading conditions is performed. Carried out experimental investigation allows to obtain coefficients of full asymptotic expansions of stress and displacement fields in the vicinity of the crack tip and alos to find coefficients of highest approach in Williams full asymptotic expansion.

The article deals with the development of digital speckle interferometer with superimposed bundles and speckle modulated reference wave for the study of vibration characteristics and deformation displacements of elements of energy installations excited by statistic loadings. It is experimentally established that at vibration studies thanks to the possibility of using in optical scheme of digital camera in speckle interferograms obtained with the use of interferometer showed that dispersion of speckle noise is from 2.5 up to 3.2 times lower than in speckle interferograms obtained with the traditionally used interferometers with separated bundles and smooth reference wave.

In the paper asymptotic solution to the problem of growth of fatigue crack in conditions of repeated loading in a damaged medium in the coupled elasticity-damage statement of the problem is given. Asymptotic expansions of stress fields and continuity fields in which two summands are retained in asymptotic representation are derived. The problems of determination of amplitude coeffl-cients of obtained asymptotic expansions are discussed.

The review of methods that can be used to define the asymptotic stabilized state of an inelastic structure under cyclic loading is given in the paper. Due to the growth of interest for the knowledge of the asymptotic behaviour of the structure under cyclic loading, incremental (with the use of finite element method) and direct methods (methods of optimal control theory and decomposition of residual stresses in Fourier series) began to develop.

In the work definition of area of possible limiting conditions of thin-walled covers from an ideal elastoplastic material with not through blind fractured defect (scratch) is considered. Areas of possible limiting conditions for scratches of variable depth are considered. Comparison of experimental and theoretical data is given. The problem of determination of limiting extent of defects which at the set level of operational loadings can lead to catastrophic destruction of all construction is solved.

Mono-harmonic junction in the interaction of porous space rock stress in oil/gas saturated reservoirs and averaged hydro-dynamic flows of viscous oil towards wells obtained as a result of innovative decisions in oil industry in general is presented. Within the frames of block homogeneous models of a well through the application of 3D linear theory of wave diffusion along the surface of geophysical emission layer, mathematical statement of asymmetrical filtration challenge with finite velocity of effect is presented. Dispersive ratios for constrained and resonant dissipative structures in a shear layer of viscous-elastic filtration at the edge of a slug of water-oil displacement are given. The redistribution results for the averaged inflow profile of viscous Newtonian filtration into asymmetrical energy-stable stress-deformation status inside the saturated porous media at various constraints: in conditions of enclosed or capillary-clamped boundary and in non-constrained conditions - at the frontier of displacement or with stimulation of water-flood displacement in zones of stagnation is presented.

The approach to the synthesis of optimal control of multidimensional composite linear system based on solutions of optimal control problems for inclusion in its structure of partial linear systems with scalar controls is considered. Control tasks are reduced to the problem of moments in the L\ space for minimum functionals of the norm type, on minimum maximal Ноlder norms level (with indicators 2 and то) for the vector control composite system.

The main aim of this research is the creation of program tool for quantitative and qualitative comparison of different schemes of well location applied at waterflooding: the estimates were supposed to be carried on the basis of solution of the problem of advancement of border of OWC in time. The achieved results may be used for designing of waterflooding of real oilfields. At the heart of program complex lies the model of infinite homogeneous layer of fixed thickness, the surface of which is covered by doubly periodic grating with upstream and blowing wells in their cells. For describing of the process of combined filtration of water and oil modified Weierstrass dzeta-function was used.

The paper is concerned with the investigation of the model of dynamics of population of caterpillar budworm (Choristoneura fumiferana). The system solutions behavior depending on the parameters values has been investigated, conditions of origination of canard curves have been found.

Atom-field entanglement in two-atom system in different initial states in Jay-nes-Cummings model with degenerate two photon transition with dependant from intensity of the field of parameter of atom-field interaction is considered. It is shown that consideration of discontency of parameter of atom-field interaction for some initial states of atoms leads to damping or collapse of instant death of entanglement effect and changes of disentanglement time.