The journal publishes original research on theoretical and applied mechanics, articles on theoretical mechanics, fluid and gas mechanics, solid mechanics.
Archive of scientific articles from the journal "Applied Mathematics and Mechanics"
- PARTICLE VELOCITY, SPEED EQUATION AND UNIVERSAL ASYMPTOTICS FOR EFFICIENT MODELING OF HYDRAULIC FRACTURING
Linkov A.M. - 2015
The theoretical rationale of the hydraulic fracture (HF) problem is revisited. It implies that the particle velocity is the primary physical quantity, using of which provides significant analytical and computational advantages conventionally over using the flux. The fundamental significance of the speed equation (SE) for proper tracing fracture propagation is emphasized. It appears that when neglecting the lag between the fracture contour and the fluid front, the asymptotic form of continuity equation (CE) identically meets SE for non-singular or weakly singular leak- off. For strongly singular leak-off of Carter's type, the asymptotic form of CE yields generalized speed equation. We show that for zero lag, the system, comprised of asymptotic CE, elasticity equation and fracture condition, defines the universal asymptotic solution (universal asymptotic umbrella) of the HF problem.
- THE DYNAMIC CHARACTERISTICS OF DAMAGE PROBABILITY OF A GRAVITY DAM
CHEN J.Y., LI J., XU Q., ZHANG C.B., ZHAO C.F. - 2015
An approximate first-order probabilistic method based on the pseudo-excitation method (PSM) is proposed for investigating damage to concrete gravity dams. Within the framework of the method, the stochastic stiffness is determined under the action of a stochastic source of perturbations of the second order of smallness. The method contains the following steps. First, the MFW and Mazar's damage model are used to analyze how to calculate the expected value and variation of dam damage initiated by a random load (earthquake) under a static initial load. Then, based on the perturbation theory, the evolution of the probability distribution of damage to the dam under tensile stress is investigated. Finally, to test the model and analyze the convergence and stability of the corresponding numerical calculation, a numerical example is given. The calculation results show that the expected damage probability distributions under the action of random disturbances are stable. Compared to MPV, characteristics A first-order approximate probabilistic analytical method to investigate the damage of concrete gravity dams, based on pseudo-excitation method (
- Automodel problems on the compression of an ideal gas and its expansion from a point
VALIEV H.F., KRAIKO A.N. - 2015
Self-similar solutions are considered that describe one-dimensional unsteady flows of an ideal (nonviscous and nonheat-conducting) perfect gas. If in the well-known problem of isentropic compression of a gas to a plane, axis or center of symmetry (hereinafter, to the center of symmetry - CS) with a self-similarity index of unity, the result of compression is a uniform flow moving towards the CS, then the well-known problem arises of the deceleration of such a flow by a continuous centered wave and by a shock wave adjoining it (in the plane case, by one shock wave). Behind the shock wave coming from the CS, the gas is at rest. The change in the signs of time and velocity in the solutions describing the isentropic finite compression of the gas gives an idea of the evolution of the flow in the case of a uniform expansion of the gas from the CS. Other well-known self-similar solutions with a self-similarity index of unity give an unbounded isentropic compression of a finite gas mass to the CS (“compression to a point”). With such compression, the density, pressure, internal energy and velocity of the compressed gas are infinite, and the entropy is finite. The entropy is also finite after the stoppage of the gas by the shock wave coming from the CS. A new self-similar problem of the “expansion from a point” (plane or CS) of a finite mass of a “hot” gas with infinite initial energy, zero velocity, and finite entropy is solved. In new solutions (with and without a void zone in the vicinity of the CS), by virtue of the “mass integral” (its role is similar to the role of the energy integral in the problem of a strong explosion), all trajectories of hot gas particles are lines of constancy of the self-similar variable with the self-similarity index found from the analysis of dimensions . The influence of the finite initial density of the cold gas surrounding the compressed gas on the solutions found, the resulting locally self-similar solution, and sometimes paradoxical features of self-similar solutions during expansion into a void are discussed.
- ANALYTICAL MODELS OF SPATIAL TRAJECTORIES FOR SOLVING NAVIGATION PROBLEMS
Sokolov S.V. - 2015
The synthesis of analytical spatial models of trajectories is considered, which allow minimizing the composition of the measuring complex and computational costs in solving navigation problems.
- ASYMPTOTIC SOLUTION OF THE ELECTROELASTICITY PROBLEM FOR THICKNESS POLARIZED PIEZOCERAMIC SHELLS
AGALOVYAN L.A., AGALOVYAN M.L., GEVORKYAN R.S. - 2015
By asymptotically integrating the equations of the three-dimensional problem of the theory of electroelasticity in curvilinear coordinates, recurrent formulas are derived for determining the components of the stress tensor, the displacement vector, and the electric potential of the piezoceramic shell. The shell is considered to be inhomogeneous in plan (physical and mechanical coefficients may depend on tangential coordinates, but are constant in thickness) and polarized in thickness. Cases are considered when the conditions of the first, second, or mixed boundary value problems of elasticity theory are specified on the outer and inner surfaces of the shell. For one relatively general variant dispersion equations for vibration frequencies are derived, resonance frequencies are calculated, and their dependence on the thickness and physicomechanical parameters of the shell is established.
- INFLUENCE OF A CRACK IN THE ICE COVER ON THE HYDRODYNAMIC CHARACTERISTICS OF A SUBMERSIBLE VIBLE CYLINDER
Sturova I.V. - 2015
The results of solving the linear problem of steady oscillations are presented. horizontal cylinder, immersed in a liquid, on the upper boundary of which there is an ice cover with an infinite rectilinear crack parallel to the axis of the cylinder. The ice cover is modeled by a thin elastic plate, and a partially frozen crack is modeled by a system of two springs: vertical and spiral. It is assumed that the properties of the plates can change abruptly when passing through a crack. The method of mass sources distributed along the contour of the body was used. The corresponding Green's function is constructed using expansions in vertical eigenfunctions. The calculations of the hydrodynamic load acting on the cylinder and the amplitudes of the vertical displacements of the ice cover are performed. It is shown that the wave motion essentially depends on the position of the cylinder relative to the crack and its properties. The relationship between the damping coefficients and the amplitudes of flexural-gravitational waves in the far field is given.
- FORCED VIBRATIONS OF ORTHOTROPIC SHELLS IN THE PRESENCE OF VISCOUS RESISTANCE
GULGAZARYAN L.G. - 2015
Forced vibrations of orthotropic shells are considered in the presence of viscous resistance, when two variants of spatial boundary conditions are specified on the upper front surface of the shell, and a displacement vector is specified on the lower one. The solution of the corresponding dynamic equations of the three-dimensional problem of elasticity theory is obtained by an asymptotic method. The amplitudes of forced oscillations are determined and it is established that the presence of viscous resistance leads to the fact that the amplitudes of forced oscillations in the range of natural oscillations increase, but remain finite. Functions of the boundary layer type are obtained, characteristic equations are established for determining the decay rate of boundary oscillations in the direction from the side surface into the shell
- DEFORMATION RELATIONS FOR AN ELASTIC HALF-PLANE WITH A WEAKLY CURVED BOUNDARY
SOLDATENKOV I.A. - 2015
Relations between boundary stresses and displacements are derived for an elastic half-plane with a slightly curved boundary. To do this, the stress-strain state of the half-plane is expressed in terms of two harmonic functions using the general Papkovich-Neiber solution, and a conformal mapping of the original half-plane onto the canonical (even) half-plane is performed. As a result, for harmonic functions, a system of boundary problems is obtained, from which the desired deformation relations follow using the Fourier transform. The case of Coulomb friction is considered. The influence of the roughness factor of the half-plane boundary on its deformation is analyzed.
- DYNAMICS OF A ROTATING SOLAR SAIL IN THE PROCESS OF ITS OPENING
A. V. Zykov, V. P. Legostaev, A. V. Subbotin, A. V. Sumarokov, and S. N. Timakov - 2015
The model of the release of the canvas of the solar sail is considered, within the framework of which the sail, opened from the laid state, is presented in the form of four released cables. At the initial stage of the solar sail deployment, taking into account the central symmetry of the structural arrangement of the coils with cables, the release of one of the cables is modeled under the assumption that all other cables are released synchronously and the release control system ensures the dynamic symmetry of the process. A differential equation is given for small transverse vibrations in the plane of rotation of a point mass on a weightless cable in the process of release from a rotating central block. An analytical solution of the linearized equation for the release of a point mass is obtained, expressed in terms of Bessel functions for a uniform release and in terms of hypergeometric functions for a uniformly slow release. Numerical simulation carried out for two cases: when the cable is represented as a set of material points connected in series by weightless inextensible threads, and in the form of a weightless inextensible thread with a weighty load at the free end, confirms the obtained analytical results.
- ADDITIONAL CONSERVATION LAWS, FUNCTIONAL RELATIONS BETWEEN CONSERVATION LAWS AND POTENTIALS OF DIVERGENT EQUATIONS OF GAS DYNAMICS
Rylov A.I. - 2015
The issues of constructing and revealing functional relationships between the laws of conservation and construction and identifying additional conservation laws for previously found conservation laws for three-dimensional unsteady flows (E.D. Terentiev and Yu.D. Shmyglevskii, 1975) and for an infinite set of conservation laws for plane potential flows (A.I. Rylov, 2002). The functional connection here means the zero sum of three or more left parts of divergent equations, taken with variable coefficients to be determined.
- REMARKS ON ARTICLE O.B. GUSKOVA "METHOD OF SELF-CONSISTENT FIELD AS APPLIED TO THE DYNAMICS OF VISCOUS SUSPENSIONS". PMM. 2013. Vol. 77. Issue. 4. S. 557-572
MARTYNOV S.I. - 2015
In the above article, the problem of the dynamics of interacting spherical particles in a viscous fluid is considered. A large number of works have been published on this problem, in which various methods for solving the problem are proposed. Since the purpose of the remarks is not to review the methods and approaches available in the literature on this topic, we note only some of them that have been actively used in recent years. In addition to numerical methods based on the finite element method, these are the Stokes dynamics method and the lattice Boltzmann equation method. The above methods have both advantages and disadvantages. The disadvantages include high computational costs in their software implementation on a computer to calculate the dynamics of a large number of particles. At the same time, it can be stated that at present there is no method equally suitable for solving a wide class of problems in the dynamics of disperse systems, and research in this area is still relevant.
- GAME PROBLEMS OF GUIDANCE FOR PROPERLY LINEAR INTEGRO-DIFFERENTIAL VOLTERRA SYSTEMS
PASIKOV V.L. - 2015
We consider game situations of pointing to the origin of coordinates for controlled objects, the evolution of which is described by proper linear integro-differential and Volterra integral systems. Some modification of N.N. Krasovsky at suitable choice position spaces. A model example is given.
- ON THE THEORY OF AXISYMMETRIC CONICAL FLOWS AND THEIR ONE-DIMENSIONAL NON-STATIONARY ANALOGUES
Valiev Kh.F., Krayko A.N., Tillyaeva N.I. - 2015
In the approximation of an ideal (non-viscous and non-thermal-conducting) perfect gas, axisymmetric conical flows (CT) without swirl and their unsteady cylindrically and spherically symmetric self-similar analogs with a self-similarity index of unity are considered. In the flows under consideration, along with shock waves within the classical model(instantaneous heat release, on both sides of a gap of zero thickness - a perfect gas in the general case with different adiabatic indices) Chapman-Jouguet detonation waves (DWj) are allowed. The main new elements associated with QDs are the introduction to the known DWj flows and the combination of several QDs into one. The unification of non-stationary self-similar analogs of QDs is preceded by the construction and analysis of a number of new solutions. All associations of non-stationary analogues are also original. The systematization of the approaches used and the theoretical analysis based on them are illustrated by examples of numerical construction of the studied flows in the planes of their independent variables. Illustrations include streamlines (for CT), particle trajectories (for transient analogs), C+- and C-characteristics and their envelopes, shock waves and DW J.
- CONTACT PROBLEM OF MATHEMATICAL THEORY OF ELASTICITY WITH ZONES OF COUPLING AND SLIDING. ROLLING THEORY AND TRIBOLOGY
CHEREPANOV G.P. - 2015
In this paper, the contact problem of the mathematical theory of elasticity, taking into account adhesion on the contact, is considered as a subject of fracture mechanics. An exact solution is given to the general contact problem of fracture mechanics under plane deformation conditions with adhesion and slip zones of two different elastic half-spaces. In fact, this task is the basis of theoretical tribology. For one class of inhomogeneous materials, the solution is obtained in a closed form. The problem of the pressure of absolutely rigid stamps on an elastic body under plane deformation conditions, taking into account adhesion in the areas of adhesion and sliding, is also solved in a closed form, when Poisson's ratio is equal to 1/2. The original mathematical problem also covers the problems of fracture mechanics of composites on the propagation of cracks along the interface between two different elastic materials, taking into account the overlap/slip zones of crack edges. The method of analytic continuation is used to reduce problems to one generalized Riemann boundary value problem, the solution of which is found in a closed form. On the example of solving typical contact problems of fracture mechanics, a rigorous quantitative theory of the main rolling modes and the stick-slip phenomenon is given and analyzed. It is shown that in the absence of slippage and adhesion, the coefficient of rolling friction in Coulomb's law is directly proportional to (NRP) 1/2 for wheels and cylinders, and (NRP) 1/3 for balls, where N is the normal force (ball weight or linear weight of the cylinder) , R is the radius of the wheel or ball, P is the elastic compliance of the system. The influence of adhesion and roughness of materials on rolling, as well as the wear of materials during rolling, are characterized by two material constants of fracture mechanics. By decision of the editorial board of the PMM, the last section was added as a response to critical comments on the article published after this work.
- MAXIMUM LYAPUNOV EXPONENTS AND STABILITY CRITERIA FOR LINEAR SYSTEMS WITH VARIABLE DELAY
ZEVIN A.A. - 2015
The Myshkis problem of the maximum Lyapunov exponent of a linear differential equation of the first order with an arbitrary bounded delay. The result obtained is generalized to a system of equations of arbitrary order, the matrix of which has real eigenvalues. For a system with complex eigenvalues, a sufficient condition for exponential stability is obtained.
- MATHEMATICAL MODELING OF RECOVERY OF MECHANICAL PROPERTIES OF BONE CALL
Maslov L.B. - 2015
Presented mathematical model and a computational algorithm for bone tissue regeneration controlled by the law of cell differentiation and the action of an external mechanical stimulus of a periodic nature. The calculation of the restoration of the elastic properties of bone tissue is based on the generalized dynamic model of a changing poroelastic continuous medium and the finite element method in a three-dimensional formulation. Developed software makes it possible to study the processes of restoration of damaged bone elements of the human musculoskeletal system in the presence of a stationary dynamic load and to theoretically substantiate the choice of the optimal periodic effect on damaged tissues with the aim of their speedy and sustainable healing.
- ASYMMETRIC TANGENT LOAD AT THE BOUNDARY OF ELASTIC HALF-SPACE
M. V. DOLOTOV, I. D. KILL, Y. G. LIMONCHENKO - 2015
A dynamic problem is considered for an elastic half-space with a distributed asymmetric tangential load acting on its boundary. Simple expressions are obtained for the stress tensor components in the form of series converging at small times and having asymptotic properties. The errors of the approximate solution determined by the partial sums of the series are estimated.
- ABOUT ROLLING A BODY WITH A ROTOR ON A MOVABLE SUPPORT SPHERE
Yu.P. BYCHKOV - 2015
The problem of rolling without slipping of a body with a rotor on a movable support sphere in a uniform gravity field is considered. The boundary of the body in the area of contact with the support is a part of the spherical surface. The central ellipsoid of inertia of the system (body + rotor) is an ellipsoid of revolution, the axis of which passes through the geometric center of the sphere, which, generally speaking, does not coincide with the center of mass of the system. The support sphere arbitrarily translates and rotates around a vertical axis. Received complete system equations of motion of the carrier body and the rotor. In the case of a body of revolution, two integrals of the equations of motion are obtained. In the case when the body is a homogeneous ball, four integrals of the equations of motion are found, and the coordinates of the contact point of the ball with the support sphere are determined by quadratures, and all possible trajectories of the contact point of the ball with the sphere are indicated.
- ON THE EQUILIBRIUM OF SYSTEMS WITH DRY FRICTION
IVANOV A.P. - 2015
The properties of equilibrium positions of mechanical systems with Coulomb friction are discussed. A comparative analysis of various definitions of the concept of equilibrium is carried out. It is shown that the principles of virtual displacements and least constraint can be generalized to problems of statics with friction. The definitions of stability according to Lyapunov and Hill are considered; The second approach has certain advantages in these problems. To illustrate the results and conclusions obtained, a number of mechanical examples are considered.
SOLDATENKOV I.A. - 2015
Josephine, who had been sympathetic to engineering since childhood, studied at a private school for several years, and in 1858 married 27-year-old William Cochran. The young family settled in Shelbyville, Illinois, where William became one of the leaders of the local branch of the Democratic Party (he was even predicted to be governor of the state).
Josephine ran the household and played the role of socialite, helping to organize soirees where guests were usually served food on antique family china. Over time, chips appeared on the porcelain - the servants did not wash the dishes too carefully. The owner had to take care of the matter herself. How she hated him! And then Josephine decided to invent a dishwashing machine.
Sometime in the early 1880s, while drinking tea, she remembered how strong the pressure of a water jet can be. Literally half an hour later, the idea formed in her head to wash the dishes in a metal mesh basket with a powerful jet of soapy water (modern dishwashers use exactly this principle). Her friends and husband supported her idea, but William died in 1883. Left alone, Josephine spent days on end in the barn behind the house, attaching metal parts to a copper boiler. She hired an Illinois mechanic to help. railway George Butters.
March 8, 2009 marks the 170th birthday of Josephine Cochran (née Garis), the inventor of the dishwasher who freed women from hard work dishwashers.
The first model looked like a miniature sawmill, but still it was a real miracle. One of the local businessmen gave the inventor advice: “Try to offer this car to big hotels. They need a lot of clean dishes and they can save on dishwashers.”
On December 28, 1886, Josephine received a patent for her invention and went to Chicago, where she sold a pair of Garis-Cochran cars to two large hotels: Palmer House and Sherman House. Cars (and hotels) immediately became famous, they went to look at how museum exhibits. But the real triumph for the young company was in 1893, when nine Garis-Cochran machines almost continuously washed dishes for numerous visitors to the Chicago World's Fair. The car received the prize "For optimal design and reliability" and aroused particular interest among the female audience of the exhibition. Since 1898, cars began to be mass-produced - restaurants and hotels were willing to buy an industrial model (it paid off in a few months), the demand for a household one, priced at $ 350, was lower. Household machines gained popularity after the death of Josephine (she died in 1913), in the 1940s, when Garis-Cochran, as a result of a series of mergers and renamings, became part of KitchenAid (now part of Whirlpool Corporation).
PMM
pneumomechanical machine
Dictionary: S. Fadeev. Dictionary of abbreviations of the modern Russian language. - S.-Pb.: Polytechnic, 1997. - 527 p.
watering machine
Dictionary: S. Fadeev. Dictionary of abbreviations of the modern Russian language. - S.-Pb.: Polytechnic, 1997. - 527 p.
PMM
"Applied Mathematics and Mechanics"
edition, mat.
PMM
ferry-bridge machine
Dictionary: Dictionary of abbreviations and abbreviations of the army and special services. Comp. A. A. Shchelokov. - M .: AST Publishing House LLC, Geleos Publishing House CJSC, 2003. - 318 p.
PMM
mobile mechanical workshop
PMM
modernized makarov pistol
PMM
production management and marketing
Source: http://www.neic.nsk.su/faculties/ief/pmm/
Usage example
Department of PMM
PMM
Dishwasher
Dictionary of abbreviations and abbreviations. Academician. 2015 .
See what "PMM" is in other dictionaries:
PMM-2M- ... Wikipedia
PMM-2- ferry bridge machine. Ferry bridge vehicle PMM 2 is designed to cross water barriers of tanks, self-propelled artillery mounts and other equipment made on the basis of the tank. A modification of PMM 2 is PMM 2M. Contents 1 ... ... Wikipedia
PMM 12- Type: 9 mm Makarov pistol modernized PMM 12 9 mm Makarov pistol modernized PMM 8 Index GRAU 56 A 125M In the early 90s, they tried to improve the quality of the PM primarily by introducing a new, reinforced ... ... Wikipedia
PMM- Makarov pistol Makarov pistol Type: Pistol Country: USSR ... Wikipedia
PMM- pneumomechanical machine mobile mechanical workshop watering machine Applied Mathematics and Mechanics (journal) ... Dictionary of abbreviations of the Russian language
PMM "Wave"- Ferry bridge machine PMM Manufacturer ... Wikipedia
Makarov PM (PMM)- Makarov pistol PM / PMM / IZH 71 (USSR / Russia) Standard pistol PM Soviet production Pistol Makarov Modified (PMM). next to it is a new magazine for 12 rounds; a sectional view of the PM device. Caliber: 9x18mm; 9x18 PMM Length: 161 mm… … Small arms encyclopedia Wikipedia
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