## Scientific journal “Processes in GeoMedia” № 3 (7) 2016

Аннотации статей

**TRANSVERSE WAVES IN A TWO-LAYER MEMBRANE WITH GEOMETRICAL NONLINEARITY**

**N.I. Arkhipova, N.P. Semerikova**

**Институт проблем машиностроения РАН**

**Нижегородский государственный университет им. ****Н.И. Лобачевского**

The article shows that sophisticated (non-classical) core models can be used to describe the dynamic processes in layered structural elements. Arguments are the example of a two-layer membrane taking into account the geometrical nonlinearity making cross fluctuations. Within this mathematical model, onedimensional and two-dimensional solitons are received and investigated, and various forms of nonlinear periodic fluctuations are presented. The dispersive and dissipative dependences connecting parameters of elastic waves can find application when developing methods of calculation of elements of designs on strength and stability.

Keywords: membrane, refined model, transverse vibrations, solitons, layered structure.

pp. 176-183.

**APPLICATION OF THE PATTERN RECOGNITION METHODS TO THE PROBLEM OF DAMPING VIBRATIONS OF HIGH-RISE BUILDINGS**

**D.V. Balandin, I.V. Kotel’nikov, L.G. Teklina**

**Нижегородский государственный университет им. Н.И.Лобачевского, Институт ****информационных технологий, математики и механики**

The capabilities and specific features of application of the pattern recognition methods to the problem of vibration damping for the high-rise buildings are discussed in this paper. A new statistical approach to the synthesis of non-fragile robust control systems with given properties is based on the formulation of the synthesis problem as a problem of pattern recognition. The problems of parametric synthesis that are not extreme and different by non-standard formulation are solved with use of this approach. The possibilities of this approach are illustrated by examples of synthesis of the quasi-invariant control system, of control with a given degree of vibration damping and of the hybrid system with a dynamic damper.

Keywords: vibration damping, control system with given properties, pattern recognition.

pp. 184-193.

**ROTATIONAL WAVES IN BLOCK ROTATING ENVIRONMENTS (THE CASE OF GEOMEDIUM)**

**A.****V. ****Vikulin**

**Институт вулканологии и сейсмологии ДВО РАН**

Properties of the Earth’s «solid» crust on the assumption of its block structure are researched. Motion of such a medium (geological environment) within rotational model submits to the law of conservation of momentum and can be described within the classical theory of elasticity with a symmetric stress tensor. Two types of rotational waves with close- and long-range action are typical for motion of a geological environment (geomedium). Slow solitons and fast excitons. The possibility of «collective» wave motion of a geomedium can determine its rheidity property. Superfluid motion of quantum liquid can be physical analog of such motion of a geomedium.

Keywords: mesodefect, block, rotation, wave-particle mechanism, symmetric stress tensor, rheidity, superfluidity.

pp. 194-206.

**EVOLUTION OF ELASTIC AND THERMOELASTIC NONLINEAR LONGITUDINALLY ROTATIONAL WAVES IN THE COSSERAT MEDIUM**

**Yu.V. Vinogradova, V.I. Erofeev, A.V. Leontieva**

**Институт проблем машиностроения РАН**

In the real work operation, plane non-linear thermoelastic longitudinal waves and plane non-linear elastic rotation waves within model of a geometrically nonlinear micropolar continuum (Cosserat medium) are considered. The equation of longitudinal thermoelastic waves is studied in two limit cases. The environments with low and high heat conduction are considered. It is shown that in these cases the equation of longitudinal thermoelastic waves comes down to the known equations describing classical Riemann waves and Riemann wave with attenuation. Features of distribution of these waves are analyzed. The equation of the rotation wave, in absence of thermoelastic effects, comes down to a nonlinear ordinary differential equation of the second order for stationary waves. It is shown that the equation has decisions, in a hyperacoustic case, in the form of periodic waves. Dependence of a wave number on amplitude and the relative turning angle of a stationary rotation wave is received.

Keywords: Cosserat medium, micropolar environment, Riemann wave, Riemann wave with attenuation, deformation tensor, bending-torsion tensor, longitudinal thermoelastic wave, elastic rotational wave.

pp. 207-217.

**TSUNAMI WAVES SPECTRA AT THE BLACK SEA SHELF ZONE**

**S.F. Dotsenko, A.V. Ingerov**

**Морской гидрофизический институт РАН**

Nonlinear evolution model of long surface waves is applied to analyze the amplification of tsunami-type waves on the Black Sea shelf at different positions of the seismic source and earthquake magnitude. Time series of sea level oscillations in the shelf zone are calculated and the estimate of the frequency spectra is obtained. Spectra have 1–3 peaks. The periods of tsunami waves are in the range of 10–30 minutes and that agrees with the region-specific values. Spectrum, as a rule, depends weakly on the initial sea level displacement form at a fixed size of the seismic generation zone, but significantly depends on its position and magnitude of the earthquake. With increase of the source magnitude the energy is usually concentrated in the lower frequencies in the spectral maxima with periods of 15–30 min, and with its decrease, the energy is distributed across the spectrum more evenly, or concentrated in the area of high frequency peak. Qualitative spectrum changes at the decrease and increase of the seismic source offshore distance are similar to changes caused by increase and decrease of the earthquake magnitude respectively.

Keywords: tsunami waves, seismic generation, numerical experiment, frequency spectrum, Black Sea.

pp. 218-224.

**ON THE FEATURES OF THE FINITE VOLUME OF DENSE WATER PROPAGATION IN THE FRESHWATER ENVIRONMENT ALONG A BOTTOM SLOPE**

**I.A. Isachenko, V.A. Gritsenko**

**Атлантическое отделение Института океанологии им. ****П.П. Ширшова РАН**

The study discusses the features of density current from finite volume release of salt water on a slope in freshwater environment based on 2D nonlinear numerical simulation. The distinction between such current and finite volume density currents on a horizontal bottom was described. A transition from subcritical flow to supercritical is occurred.

Keywords: density inhomogeneity, patch collapse, sloping bottom, nonlinear model, mixing, inertial and viscous phases, coastal waters.

pp. 225-231.

**CAPILLARY WAVES ON THE SURFACE OF A FALLING LIQUID DROP**

**A.****V. ****Kistovich**

**ФГУП Всероссийский научно-исследовательский институт физико-технических и радиотехнических измерений, Институт проблем механики им. ****А.Ю. Ишлинского РАН**

The paper presents the results of investigations of standing capillary waves arising on the free surface of a liquid drop falling in the air with constant velocity. In approximation of small wave amplitude, in some special coordinate system connected to undisturbed surface form, the boundary problem under consideration is produced. The solutions for capillary perturbations, and equations for nodes and loops coordinates of investigated waves, are received for empirical form of undisturbed surface approximately corresponded to one observed in experiments. The calculations done on the base of received relations are in a good qualitative and quantitative agreement with experimental results.

Keywords: capillary waves, drop.

pp. 232-238.

**MAGNETOELASTIC WAVES IN A ROD**

**A.O. Malkhanov**

**Институт проблем машиностроения РАН**

We consider the formation of stationary waves in a rod which has been placed into external magnetic field. It has been shown that the type of wave studied depends on its velocity of propagation and on the magnitude of the external magnetic field. There are shown the dependencies of the waves on magnitude of external magnetic field.

Keywords: magnetic field, waves in rod, magnetoelasticity.

pp. 239-245.

**NON-CONTACT THERMAL-PHYSICAL PROPERTIES MEASUREMENTS OF ROCKS ON TC14 DEVICE**

**D.S. Nikitin, M.D. Khutorskoy, A.S. Nikitin**

**Геологический институт РАН**

**Воронежский государственный архитектурно-строительный университет**

A new device called TC14 was created for thermal-physical properties measurements of rocks by the optical scanning method. Compared with the earlier applied equipments, it has some constructive elements. A new software for received analog signal processing with the LabView technology was developed. The first experience of thermal conductivities measurements on this device is got for 111 rocks samples from sub-salt layers of the Central Astrakhan deep hole. It is shown that thermal conductivity of this complex is intermediate between the minimum values for oversalt rocks and the maximum ones for evaporate rocks.

Keywords: thermal conductivity, optical scanning method, LabView technology, rocks, Central Astrakhan borehole.

pp. 246-254.

**SYSTEMATIC APPROACH TO ADEQUATE EQUATION OF STATE SEARCH AND NON-STANDARD FIRST RESULTS**

**G.****G. ****Petrik**

**Институт проблем геотермии ДНЦ РАН**

The most important problem of thermal physics which is obtaining a simple adequate thermal equation of state (EOS) remains to be unsolved, despite a lot of works and equations proposed in them. The paper presents some results obtained in a systematic approach to the search of physically reasonable EOS, including a new three-parametrical EOS with all the parameters having the sense determined by attraction and repulsion forces; the control parameter of the thermodynamic level, transforming the new EOS in a one-parametrical family; connection of the new EOS with the one-parametrical corresponding states law. The structure of the control parameter for the model has been revealed associated with the presence of two degrees of freedom for the centers simulating the system. The main of the obtained results is that a large group of cubic EOS of VDV-type fits into the scope of the studied molecular model of interacting centers; it allows to eliminate their main disadvantage: poor connection with the micro-level. Moreover, the same unconventional results demonstrate new possibilities of cubic equations in solving the accumulated cognitive problems.

Keywords: simulation, system approach, equation of state, control parameter, interacting centers model, Van der Waals equation of state, intermolecular interaction.

pp. 255-266.

**LAWS AND PROPERTIES OF JOINT STATISTICAL DISTRIBUTIONS OF FIELDS OF TEMPERATURE AND SALINITY IN THE NORTH ATLANTIC AND THEIR USE IN OCEANOGRAPHIC PROBLEMS SOLUTION**

**V.A. Sokolov**

Laws of joint statistical distributions of fields of temperature Т and salinity S in the North Atlantic, corresponding to known properties of conservatism of water masses and consolidation of sea waters when mixing, are described. Examples of practical use of joint statistical T-S distributions in the solution of the problems concerned with filtration of arrays of observations of these fields from casual and regular errors, and in testing their calculated values are given. The algorithm of probabilistic correction of calculated values of T-S fields at desired level of confidence interval of probability, applied in the analysis and correction of interpolated climatic values of T-S fields at the front of the North Atlantic Current, is described.

Keywords: North Atlantic Current, statistical distribution, water masses.

pp. 267-277.

**ON APPLICATION OF MODELS OF PLASTIC FLOW TO DESCRIPTION OF INELASTIC BEHAVIOR OF ANISOTROPIC ROCKS**

**K.****B. ****Ustinov**

**Институт проблем механики им. ****А.Ю. Ишлинского РАН**

A model of deformation of rocks that is a generalization of Hill anisotropic plasticity on the one hand and Drucker–Prager model on the other hand is considered. The model is based on non-associated plastic flow rule with hardening for anisotropic media accounted for the influence of hydrostatic stresses. Rather general case of combination of isotropic and kinematic hardening is considered.

Keywords: rocks, strength anisotropy, plastic flow, nonassociated plasticity.

pp. 278-287.