S. N. Gavrilov

S. N. Gavrilov
Institute for Problems in Mechanical Engineering, St. Petersburg, Russia

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47
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345
Citations

Publications

Publications (47)
Article
In the recent paper by Sokolov et al. (Int. J. of Heat and Mass Transfer 176 (2021) 121442) ballistic heat propagation in a 1D harmonic crystal is considered and the properties of the exact discrete solution and the continuum solution of the ballistic heat equation are numerically compared. The aim of this note is to demonstrate that the continuum...
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In the paper we apply asymptotic technique based on the method of stationary phase and obtain the approximate analytical description of thermal motions caused by a source on an isotopic defect of an arbitrary mass in a 1D harmonic crystal. It is well known that localized oscillation is possible in this system in the case of a light defect. We consi...
Article
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In the paper, we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinit...
Article
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We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass–spring system non-uniformly moving at a given sub-critical speed. The speed of the mass–spring system is assumed to be a slowly time-varying function less than the critical speed. To describe a non-vani...
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We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a given sub-critical speed. The speed of the mass-spring system is assumed to be a slowly time-varying function less than the critical speed. To describe the non-va...
Article
In this work the energy transfer in a one-dimensional harmonic crystal is investigated. In particular, a comparison between the discrete approach presented by Klein, Prigogine, and Hemmer with the continuum approach presented by Krivtsov is made. In the pioneering work of Klein and Prigogine the transfer of thermal energy is considered. In particul...
Preprint
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In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinite...
Preprint
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The aim of this note is to demonstrate that the continuous solution describing ballistic heat propagation in 1D harmonic crystal suggested previously by Krivtsov can be formally obtained as a slow component of far-field asymptotics of the corresponding exact discrete solution.
Article
We consider a forced oscillation and passage through resonance for an infinite-length system, having time-varying parameters and possessing a single trapped mode. The system is a string, lying on the Winkler foundation and equipped with a discrete linear mass-spring oscillator of time-varying stiffness. We obtain the principal term of the asymptoti...
Article
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We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system of stochastic ordinary differential equations. We perform a continualization procedure and derive an infinite s...
Article
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The planar response of horizontal massive taut strings, travelled by a heavy point-mass, either driven by an assigned force, or moving with an assigned law, is studied. A kinematically exact model is derived for the free boundary problem via a variational approach, accounting for the singularity in the slope of the deflected string. Reactive forces...
Article
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The features for the unsteady process of thermal equilibration (“the fast motions”) in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements of all the particles are zero and the particle velocities are random quantities with zero mean and a constant v...
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We consider a forced oscillations of an infinite-length mechanical system, with time-varying parameters, possessing a single trapped mode characterized by frequency $\Omega_0(\epsilon t)$. The system is a string, lying on the Winkler foundation, and equipped with a discrete linear mass-spring oscillator of time-varying stiffness. The discrete oscil...
Preprint
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The features for the unsteady process of thermal equilibration (the "fast motions") in a one-dimensional harmonic crystal with nearest-neighbor interactions lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements of all the particles are zero and the particle velocities are random quantit...
Article
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We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative stiffness). In such a system with constant parameters (the string tension), under certain conditions a trapped mode of oscillation exists and is unique. Ther...
Preprint
Full-text available
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system of stochastic ordinary differential equations. We perform a continualization procedure and derive an infinite s...
Article
Full-text available
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear par...
Chapter
We compare large time behavior of an infinite system, with time-varying parameters, possessing a unique trapped mode (characterized by frequency \(\varOmega _0(\varepsilon \tau )\)), with the behavior of a single degree of freedom system \(\ddot{y}+\varOmega _0^2(\varepsilon \tau )y=0\) (a linear mass-spring oscillator with time-varying stiffness)....
Article
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with constant parameters (the spring stiffness), under certain conditions a trapped mode of oscillation exists and is...
Preprint
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We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with constant parameters (the spring stiffness), under certain conditions a trapped mode of oscillation exists and is...
Preprint
Full-text available
We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative stiffness). In such a system with constant parameters (the string tension), under certain conditions a trapped mode of oscillation exists and is unique. Th...
Article
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We deal with a new phase nucleation in a phase-transforming bar caused by a collision of two non-stationary waves. We consider an initial stage of dynamical process in the finite bar before the moment of time when the waves emerged due to new phase nucleation reach the ends of the bar. The model of a phase-transforming bar with trilinear stress–str...
Article
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A nonlinear extended regularized model of taut string carrying a moving point mass is proposed with the intent to contribute to the solution of the paradox of particle’s discontinuous trajectory. Introducing a coupling between transversal and longitudinal string displacements, an additional equation expressing the so-called wave pressure force aris...
Article
This paper deals with transverse oscillations of an infinite string on the Winkler foundation with a point inertial inclusion of variable mass.
Conference Paper
We suggest a mechanical model describing buckling of a tectonic plate due to non-stationary longitudinal wave of compression that propagates along the plate. For low frequencies the interaction of a tectonic plate with its environment can be approximately described by means of the Winkler elastic foundation. Introducing the inhomogeneous Winkler fo...
Article
New-phase nucleation due to the collision of two non-stationary waves in a one-dimensional body is considered from the viewpoint of modern mechanics of phase transformations. It is proven that the solution that corresponds to the proposed simplest scientific explanation of the phase transformation always occurs in the first two cases. In the last c...
Conference Paper
We deal with the 1D non-stationary wave propagation in an elastic phase-transforming bar. The stress in the bar σ is assumed to be a piecewise linear function of the strain e containing a “negative slope segment,” thus, the strain energy is a non-convex function of the strain. It is known that the problem of elastostatics for such a material can ha...
Article
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We revisit, from the standpoint of the modern theory of phase transitions, the classical problem of stretching of a strain-softening bar with rehardening, considered earlier by Belytschko et al. We show that the classical solution, which is based on an empiric condition motivated by finite-element simulations, is not always consistent with the seco...
Article
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We revisit, from the standpoint of the modern theory of phase transitions, the classical problem on stretching of a strain-softening bar, considered earlier by Bažant, Belytschko et al. The known solution is singular and predicts localization of deformations at a single point (an interval with zero length) of the bar. We use the model of a phase tr...
Article
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In this paper we deal with one-dimensional wave propagation in a material that reacts differently to compression and tension. A possible approach to describe such materials is the heteromodular (or bimodular) elastic theory: a piece-wise linear theory with different elastic moduli depending on the stress state. We consider a one-dimensional problem...
Article
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The dynamic processes in an elastic bar composed of a material, which is capable of undergoing phase transitions, are under consideration. We use a model of an elastic body with non-convex strain energy potential. The bar with variable cross-sectional area is considered. Propagation of the phase boundary along the bar loaded with time-dependent ten...
Article
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The paper considers the application of the method of direct separation of motions to the investigation of distributed systems. An approach is proposed which allows one to apply the method directly to the initial equation of motion and to satisfy all boundary conditions, arising for both slow and fast components of motion. The methodology is demonst...
Article
Dynamical processes of phase interface in an infinite elastic bar with variable cross section that can undergo phase transformations are studied. The model of the elastic body with nonconvex deformation energy is used. The material of the bar is ideally elastic, and temperature effects are disregarded and the stress is a piecewise linear function o...
Article
Full-text available
The dynamic processes in an elastic bar composed of a material, which is capable of undergoing phase transitions, are under consideration. We use a model of an elastic body with non-convex strain energy potential. The admissible motions of the phase boundary along the bar are sought for. It is assumed that the phase boundary moves at a variable spe...
Article
A simple in form and physically clear asymptotic solution of the problem of the motion (without friction) of a point mass acted upon by a specified external force on a string on a Winkler foundation is obtained, taking into account the wave drag on the motion. It is shown that the point mass moves along the string in the same way as a point with a...
Article
Rocks, soils, and oil and tar sands are complex materials containing pores, cracks, and other defects. If this is the case, their constitutive behaviour can be nonlinear and stress-dependent, which implies that loading changes the properties of the material. If materials react differently to compression and tension, this can have a strong influence...
Article
We consider 1D nonstationary essentially nonlinear dynamic problem for heteromodular elastic medium. Heteromodular medium reacts differently to the tension and compression and therefore presents strongly nonlinear behaviour at infinitisemal deformations. It is subjected to the harmonic force which was "switched on" at zero moment of time. We consid...
Article
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The contact problem concerning oscillation of a circular rigid punch, moving uniformly at sub-Rayleigh speed along the surface of an elastic half space, is investigated using a three-dimensional formulation. Slow motion of the punch is considered, which implies that the characteristic time for the external loading is much larger than the time inter...
Article
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It is shown that natural vibrations, localized around the inclusion, are possible in a system consisting of an “infinite string on an elastic foundation-concentrated inertial inclusion which moves at a constant, subcritical velocity”. The evolution of the trapped mode of oscillations is described analytically for the case of a slowly accelerating i...
Article
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The paper is devoted to the investigation of a possibility of overcoming the critical speed by a moving concentrated load on a string. It is known that exceeding the critical speed is impossible in the framework of the linear statement for this problem. The general geometrically nonlinear statement for the problem is suggested. It allows one to tak...
Article
Phenomena that accompany the transonic transition experienced by a load moving along a string on a deformed base are studied. A solution in the form convenient for a qualitative analysis of the wave processes is proposed. The cases of the acceleration and deceleration of the load are considered.
Article
The passage through the critical velocity by an accelerating load moving along a string on an elastic foundation is considered. We obtain the inclination of the string and the internal force in the string before the load to be infinite at the moment of overcoming the critical velocity. Due to this an infinitely large driving force is necessary to o...
Article
The dynamics of an infinite string on an elastic foundation subjected to a moving load is under investigation in this paper. The load is modelled by a moving concentrated force. Both analytical and numerical methods are used. Non-stationary problems are analyzed. In particular the wave process caused by the accelerating load passing through the son...
Article
The paper is devoted to non-stationary problems in dynamics of elastic systems with moving loads. We deal with the simplest type of an elastic waveguide – a string on an elastic foundation. The moving load is modelled by the Dirac function. We consider the case when the load moves with an acceleration and passes through the sonic speed. Both analyt...

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