Showing papers in "Doklady Physics in 2010"
TL;DR: In this article, the effect of surface effects on the elastic properties of a linear elastic rectilinear rod has been analyzed and a complex model combining both the presence of surface stresses and the surface layer with the properties that differ from those of the matrix has been proposed.
Abstract: 279 Many nanomaterials have abnormal physical prop� erties, which differ considerably from the properties of bulk materials. One of the explanations for these dif� ferences consists in the presence of surface effects, the role of which can be extremely large for nanodimen� sional structures in comparison with those in classical mechanics [1]. The purpose of this work is analysis of the influence of surface effects on the elastic characteristics of nan� oporous materials. Two models are considered. The first one is based on taking into account the surface stresses [1–4]. The surface stresses τ are the generali� zation of the surface tension known in the theory of capillarity for the case of solids. As is shown in [1, 5], taking into account surface stresses results in increas� ing stiffness of nanoporous materials. This phenome� non is similar to increasing flexural stiffness of nano� plates in comparison with the plates of macroscopic sizes [6, 7]. The second model uses the approach of the theory of composite materials [8–10]. In this approach, the surface effects are taken into account due to the surface layer of finite thickness with elastic moduli differing from those of the basic material (the matrix). Here the increase or decrease in the rod stiff� ness depends on the relation between the elastic mod� uli of the surface layer and the matrix. The effective stiffness can both decrease and increase with decreas� ing pore radius. On the basis of these two approaches, we proposed a complex model combining both the presence of surface stresses and the surface layer with the properties that differ from those of the matrix. PROBLEM FORMULATION We consider the problem on the tension–compres� sion of a linear elastic rectilinear rod. Let the rod have a circular cross section of radius R. We consider that n cylindrical pores with identical radii r (Fig. 1) are located in parallel to the rod axis. We designate the area occupied with pores in the rod cross section as S = πnr 2 . We assume also that the rod cross section is symmetric so that it is not subjected to bending under tension. A regularly distributed load, which is stati� cally equivalent to forces P, acts on the rod end faces. We designate the Young’s modulus of the rod mate� rial as E. For a large number (n � 1) of pores, the rod can be considered as a homogeneous cylinder made of transversally isotropic material. We designate the cor� responding effective longitudinal Young’s modulus
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TL;DR: In this article, the authors proposed a numerical-analytical method of determining the contact pressure distribution and an unknown contact area for the smooth indenter sliding with a constant velocity with zero shear stress at the boundary of the viscoelastic half-space.
Abstract: Imperfect elasticity of materials of interacting sol� ids results in hysteresis losses during their deforma� tion, which, in particular, is the cause of the appear� ance of forces of sliding and rolling friction. One of the most widespread models of an imperfectly elastic material is the viscoelastic solid. The contact problems of the sliding and rolling of linearly viscoelastic solids in the 2�D formulation are considered in (1-8). In these studies, the contact pres� sure distribution, its motionvelocity dependence, and the force of resistance to the motion caused by the relaxation properties of a viscoelastic solid are deter� mined. The class of 3�D contact problems is presented mainly by problems about pressing a stamp (indenter) in a viscoelastic halfspace (9-12). In this study, we proposed a numerical-analytical method of determining the contact pressure distribu� tion and an unknown contact area for the smooth indenter sliding with a constant velocity with zero shear stress at the boundary of the viscoelastic half� space. The problem is solved in the quasistatic formu� lation by constructing the Green's function for the vis� coelastic halfspace (the analogue of the Boussinesq function) for sliding of a concentrated force along it with a constant velocity. The material properties are characterized by the spectrum of relaxation of times. 1. The smooth indenter is loaded by a vertical force Q and moves with a constant velocity V over the vis� coelastic halfspace in the direction of the axis 0x (Fig. 1). The halfspace is described by the coordi� nates |x| < ∞, |y| < ∞, and z ≤ 0. In the mobile Cartesian system of coordinates (
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TL;DR: In this article, the authors studied the integrability of a rigid body in a resistant medium with non-standard properties, such as the integrals were neither analytical nor smooth, and for certain sets, they were even discontinuous.
Abstract: The results of this work appeared due to investigation of a certain problem on the motion of a rigid bodyin a resistant medium [1, 2], where it was necessary todeal with first integrals of dynamic systems with nonstandard properties. Specifically, the integrals wereneither analytical nor smooth, and for certain sets,they were even discontinuous. The last circumstancesallowed us to completely analyze all phase trajectoriesand to indicate their properties, which possessed“roughness” and were retained for the systems of amore general form with certain nontrivial encapsulatedtype symmetries. Therefore, it is of interest toinvestigate sufficiently wider classes of systems withsimilar properties, specifically, those taken from thedynamics of a rigid body interacting with a medium.New cases of integrability in the problem of spatialmotion of the rigid body in the resistant medium willbe presented.SYSTEMS WITH SYMMETRIES AND VARIABLE DISSIPATIONWITH A ZERO MEANWe studied the systems of ordinary differentialequations having at least one periodic phase coordinate. The systems under study possess symmetry properties such that their phase volume is retained on average for the period by the periodic coordinate. Forexample, the pendulum system with a smooth andperiodic righthand partα
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TL;DR: A.A. Fedotov, A.M. Shatalov, E.D. Polyanin, M.Yu. Tenkam as mentioned in this paper, 2010, published in Doklady Akademii Nauk, 2010, Vol. 435(5) pp.
Abstract: Doklady Physics, 2010, Vol. 55(12) pp 609–614. Copyright: Pleiades Publishing Ltd. 2010. Original Russian Text Copyright: I.A. Fedotov, A.D. Polyanin, M.Yu. Shatalov, E.M. Tenkam, 2010, published in Doklady Akademii Nauk, 2010, Vol. 435(5) pp. 613–618. [ABSTRACT ONLY]
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TL;DR: In this article, the authors derived the vibratory energy of a system with an arbitrary number of degrees of freedom and the dependence of the vibration energy on the geodesic coordinates and vibratory law.
Abstract: 203 The motion of a conservative mechanical system with holonomic bonds with a finite number of degrees of freedom under the effect of vibrations, the fre� quency of which considerably exceeds the frequencies of selfinduced vibrations of the system, is considered. For the averaged motion, the effect of vibration leads to the appearance of an additional summand of the potential energy (vibratory energy). The term "vibra� tory energy" was presented in the wellknown mono� graph Mechanics by Landau and Lifshits (1), and its derivation was performed only for systems with one degree of freedom. In this work, for a system with an arbitrary number of degrees of freedom, the derivation of the dependence of the vibratory energy on the gen� eralized coordinates and vibratory law is presented and its difference from (1) is shown. The minimum of the effective potential energy corresponds to stable steadystate motion. An example of determination of stable steadystate motions of a spherical pendulum with the arbitrary threedimensional vibration of the suspension center is presented.
11 citations
TL;DR: The problem of increasing the pulsed electrical strength of water is topical for the development of capacitive energy storage systems as mentioned in this paper, and increased values of the breakdown strength of the water were previously attained by a decrease in the electric field intensity near the electrodes.
Abstract: The problem of increasing the pulsed electrical strength of water is topical for the development of capacitive energy storage systems [1]. Increased values of the breakdown strength of water were previously attained by a decrease in the electric field intensity near the electrodes [2]. This was realized by different ways, namely, via injection of the charges by electrode materials, via introduction of bipolar ions of amino
TL;DR: In this article, the authors considered the hula! hoop excita! tion along two axes corresponding to an elliptic trajec! tory of the motion of the athlete's waist.
Abstract: A hula! hoop is sports equipment, which became popular in the 1960s, and is a thin! walled hoop that goes around the athlete’s waist. For spinning a hula! hoop, the athlete’s waist makes periodic motions in the horizontal plane resulting in stable rotations. In [1] the periodic motion of the athlete’s waist along one axis was considered, and the hula! hoop problem was reduced to the problem of a pendulum with a vibrating suspension point in the absence of gravity. The stable mode of pendulum rotation with an average angular velocity equal to the excitation frequency was found approximately, and the conditions of stability of this mode were obtained. In [2] the same mode of rotation was found for this pendulum by the method of averag! ing in the second approximation, and its stability con! ditions were investigated. Stable hula! hoop rotation for the periodic excitation along two axes was studied by the method of direct separation of motion in [3]. In this study, we considered the hula! hoop excita! tion along two axes corresponding to an elliptic trajec! tory of the motion of the athlete’s waist. For identical excitation amplitudes, exact solutions corresponding to the hula! hoop rotation with a constant angular velocity equal to the excitation frequency are obtained. The stability of these solutions is investi! gated. The conditions of the inseparable hula! hoop rotation, both stable and unstable, are derived. The case of close excitation amplitudes corre! sponding to the motion of the athlete’s waist along an ellipse close to a circle is considered. The solutions of the problem on stable hula! hoop rotation in the first, second, and third approximation are obtained by the averaging method. The comparison with the numeri! cal solution obtained with high accuracy shows that the third approximation practically coincides with it. The conditions of coexistence of stable rotation modes with opposite directions are obtained. An interesting case when the athlete’s waist rotates oppositely to the rotation of the hula! hoop is investigated.
TL;DR: In this paper, the authors consider the Lagrangiandynamics model for a system of particles exhibiting random accelerations given by various probability distributions and show by numerical simulation of different distribution moments that the behavior of the system qualitatively coincides with the theoretical asymptotic behavior for the averaging ensemble for the number of particles already on the order of several tens.
Abstract: 1. Following A.M. Obukhov (1), we consider the Lagrangiandynamics model for a system of particles exhibiting random accelerations given by various probability distributions. In this paper, we show by numerical simulation of different distribution moments that the behavior of the system qualitatively coincides with the theoretical asymptotic behavior for the averaging ensemble for the number of particles already on the order of several tens. When we consider the Eulerian characteristics of motion, the moments of a particle's relative velocities turn out to be depen� dent on the value T of the averaging interval. In the case of finite values of T, the analogs of the 2/3 law for the second moments and 4/5 law for the third moments take place. Examples of actual natural pro� cesses are known that differ from hydrodynamic tur� bulence and whose statistical characteristics are simi� lar to Kolmogorov ones. In 1959, Obukhov (1) proposed to employ the approximation of the Markovian process to describe the particle's motion in a developed turbulent fluid flow. This hypothesis was based on the paper of A.M. Yaglom (2), who showed that, in the inertial interval of turbulence, the frequency spectrum of the acceleration field for a Lagrangian particle is repre� sented by white noise. Its spectral density e corre� sponded to the dissipation rate of the turbulence kinetic energy per unit mass. In this case, the correla� tion function for the accelerations is the Dirac delta� function of time. This approximation for the correla� tion function of random forces per unit mass, i.e., of the accelerations, can also be accepted in the case when the correlation time of a random force is sub� stantially shorter than the reaction time T of the entire system (in this case, of a liquid particle). The Markovian behavior of the motion of a fixed liquid particle for the Gaussian accelerationprobabil� ity distribution makes it possible to describe this motion by the Fokker-Planck equation. This equa� tion can also be obtained on the basis of the Langevin equation for particles residing in the field of random accelerations a(t) (3-5). This equation can include friction and interaction with external flows. The given random accelerations simulate the energy influx into the system of particles. We solved numerically the equations
TL;DR: In this article, the authors presented an analogy to the detona- tion initiation in the gasmixture flow in the channel of a special helical shape, where they considered the gas mixture flow inside and outside the rotating elliptic cylinder included in the circular cylinder.
Abstract: 308 For estimating the possibility of detonation initia� tion during rotation, we considered the gasmixture flow inside and outside the rotating elliptic cylinder included in the circular cylinder. The values of critical parameters at which the detonation is formed were determined. We presented the analogy to the detona� tion initiation in the gasmixture flow in the channel of a special helical shape. The investigation is carried out by the numerical method based on the scheme of S.K. Godunov with a mobile calculation grid within the framework of the singlephase kinetics of burning of a stoichiometric propane-air mixture. A detailed flow pattern is obtained enabling us to reveal the fea� tures of the detonation initiation during the motion of boundaries of the region containing the gas mixture. Attempts at practical use of detonation in engines and other various power devices placed a number of problems in front of researchers. The problem of det� onation initiation in a limited space seems to be the most important among them. At present, we know of no experimental and theoretical results on the detona� tion initiation due to the combustionchamber rota� tion. The onedimensional problem on the detonation initiation by a piston (1) has a certain relation to the case under consideration.
TL;DR: The shape of the ocean surface can be determined if the ideal incompressible fluid is rendered into the state ofthe solidstate rotation with angular velocity Ω in avertical cylindrical container with radius as discussed by the authors.
Abstract: Vortex flows in the fluid depth generate the pressurefields distorting the free surface [1]. Characteristic“dark spots” mark the depressions in the cores ofattached vortexes in river whirlpools. Floating piecesof ice in northern seas [2] and surface waves in straits[3] are collected into regular spiral branches. The distant measurements from sputniks [4] of the shape ofthe surface of the ocean are used for detection of largeocean vortexes and flows.Vortex flows in the cylindrical geometry are oftenused in applications (in the chambers of water passages, cyclones, separators, and other facilities). Thepressure drops in closed volumes can lead to the formation of gas and vapor–gas cavities, vibrations ofwhich form unsteady forces promoting destruction ofeven such large constructions as water passages ofhydroelectric power stations. The pressure distributionin the vortex, which is difficult to measure in complexunsteady flows [5], can be conveniently followed bythe shape of the free surface.The shape of the surface is easily determined if theideal incompressible fluid is rendered into the state ofthe solidstate rotation with angular velocity Ω in avertical cylindrical container with radius