https://www.elibrary.ru/title_about_new.asp?i
1605-8119
Materials physics and mechanics
35
1
2018
1-189
RAR
RUS
1-9
Aero
Institute of Problems of Mechanical Engineering RAS
St.Petersburg, Russia
Bulygin
Institute of Problems of Mechanical Engineering RAS
St.Petersburg, Russia
Pavlov
Institute of Problems of Mechanical Engineering RAS
St.Petersburg, Russia
The solutions of nonlinear equations of plane deformation of the crystal media allowing martensitic transformations: complex representation for macrofield equations
Mathematical methods of the solution of the equations of statics of plane nonlinear deformation of the crystal media with a complex lattice allowing martensitic transformations are developed. The equations of a statics represent system of four connected nonlinear equations. The vector of macroshifts is looked in the Papkovish-Neuber form. The system of the connected nonlinear equations is reduced to system of the separate equations. The vector of microshifts can be found from the sine-Gordon equation with variable coefficient (amplitude) before the sine and Poisson equation. The class of doubly periodic solutions expressing in the Jacobi elliptic functions is found for a case of constant amplitude. It is shown that the nonlinear theory possesses a set of solutions which describe fragmentation of the crystal medium, emergence of defects of structure of different types, phase transformations and other topological features of the deformation which are implemented under the influence of intensive power loadings and which can't be described by classical mechanics of the continuous medium. Features of the found solutions are discussed.
10.18720/MPM.3512018_1
complex lattice; nonlinear model; plane deformation; complex representation of solution; nonautonomous sine-Gordon equation
https://mpm.spbstu.ru/article/2018.59.1/
MPM135_01_aero(1).pdf
RAR
RUS
10-15
Aizikovich
Don State Technical University
Rostov-on-Don, Russia
Erofeev
Lobachevsky State University of Nizhni Novgorod
Nizhny Novgorod, Russia
Leonteva
Don State Technical University
Rostov-on-Don, Russia
Plane longitudinal waves in a liquid saturated porous geometrically nonlinear medium
This paper considers the propagation of plane longitudinal waves in a liquid-saturated porous medium with allowance for the nonlinear relationship between deformations and displacements of the solid phase. This porous liquid-saturated medium is examined herein within the framework of the classical Biot’s theory. It is shown that a mathematical model allowing for a geometric nonlinearity may be reduced to a system of evolutionary equations with respect to displacements of the medium skeleton and liquid in pores. The system of evolutionary equations, in its turn, depending on the availability of viscosity, is reduced to asimple wave equation or the generalized Burgers equation. The solution of the Riemann equation is obtained for a bell-shaped initial profile. The solution for the generalized Burgers equation has been found in the form of a stationary shock wave. The relationship between the amplitude and width of the shock wave front is established.
10.18720/MPM.3512018_2
porous medium (Biot’s medium); geometrical nonlinearity; evolutionary equation; the Riemann wave; stationary shock wave
https://mpm.spbstu.ru/article/2018.59.2/
MPM135_02_aizikovich.pdf
RAR
RUS
16-20
Velarde
Universidad Complutense
Madrid, Spain
Chetverikov
Saratov National Research State University
Saratov, Russia
Dmitriev
Institute for Metals Superplasticity Problems
Ufa, Russia
Ebeling
Humboldt-University Berlin
Berlin, Germany
Korznikova
Institute for Metals Superplasticity Problems of the Russian Academy of Sciences
Ufa, Russia
Localized lump-soliton-like excitations in triangular Morse lattices
Localized supersonic long-living nonlinear modes excited in triangular lattices of point particles interacting via potential Morse bonds are studied in a frame of a model with appropriately chosen bonds to rule out redundancy bonds. Numerical simulations on a base of Newtonian equations are performed to define configurations (coordinates and velocities of all particles) of steady-state (meta-stable) modes and their characteristics including in particular excitations being lump soliton-like.
10.18720/MPM.3512018_3
2D Morse lattice; solitons in adjacent rows; meta-stable states; track length; life time
https://mpm.spbstu.ru/article/2018.59.3/
MPM135_03_chetverikov.pdf
RAR
RUS
21-27
Christov
Purdue University
West Lafayette, Indiana, USA
On the numerical solution of a variable-coefficient Burgers equation arising in granular segregation
We study a variable-coefficient Burgers equation arising in the modelling of segregation of dry bidisperse granular mixtures. The equation is subject to nonlinear boundary conditions for the particle flux. We construct a strongly implicit Crank–Nicolson type of numerical scheme for the latter equation. The scheme is benchmarked against a standard exact solution of kink type, showing second-order of accuracy and good discrete conservation properties. Two segregation problems considered in the literature are then solved and discussed. The first is the case of a linear kinetic stress profile, which renders the governing equation of constant-coefficient type, while the second is the case of a variable kinetic stress profile based on an expression fit to particle dynamics simulation data.
10.18720/MPM.3512018_4
Burgers equation; implicit finite-difference scheme; granular segregation
https://mpm.spbstu.ru/article/2018.59.4/
MPM135_04_christov.pdf
RAR
RUS
28-43
Dwivedi
Banaras Hindu University
India
Lal
Madan Mohan Malaviya University of Technology
India
Tiwari
Banaras Hindu University
India
Effect of imperfect bonding on the axisymmetric stresses in buried thick orthotropic cylindrical shells due to incident longitudinal wave (p-wave)
This paper is concerned with the estimation of axisymmetric stresses induced in an imperfectly bonded thick orthotropic buried pipeline due to seismic excitation (p-wave) travelling in the surrounding medium. The shell has been assumed to be imperfectly bonded to the surrounding medium. Particular attention has been focused on the analysis of the effect of stiffness and damping of the surrounding ground on the axial and hoop stresses. A thick shell theory formulation has been used and only axisymmetric behaviour of the shell has been investigated. The relative influence of the variation of orthotropic parameters on the stresses in the shell has also been studied for different angles of incidence of the p- wave. Results have been obtained for different soil conditions - hard (rocky), medium hard and soft. It is observed that both the stiffness and damping parameters in axial as well as radial direction reduce the axial stresses of the shell, significantly. On the other hand, the stiffness and damping parameters in radial direction reduce the hoop stresses of the shell significantly, while those in the axial direction give no variation in the hoop stresses.
10.18720/MPM.3512018_5
thick orthotropic cylindrical shell; seismic excitation; imperfect bonding
https://mpm.spbstu.ru/article/2018.59.5/
MPM135_05_dwivedi.pdf
RAR
RUS
44-52
Erofeev
Lobachevsky State University of Nizhni Novgorod
Nizhny Novgorod, Russia
Leonteva
Don State Technical University
Rostov-on-Don, Russia
Malkhanov
Mechanical Engineering Research Institute of Russian Academy of Sciences
Nizhny Novgorod, Russia
Shekoyan
Institute of Mechanics, National Academy of Sciences of the Republic of Armenia
Yerevan, Armenia
Nonlinear longitudinal magnetoelastic waves in a rod with account of damage in its material)
In this paper we study the propagation of longitudinal magnetoelastic waves in a rod with damage. It is shown that for a stationary magnetic field the system of equations of magnetoelasticity can be reduced to one evolution equation with respect to the function of longitudinal deformation. The equation comprises variants of generalized unperturbed Burgers equations, when the medium does not have conductivity. For these equations, solutions have been found in the form of stationary shock waves. The connection between the main parameters (amplitude, width of the front) of the shock wave and the parameters of the system have been established. The influence of the damage parameters and the elastic nonlinearity of the material on the width of the front of the shock wave is determined. The evolutionary equation of magnetoelasticity has been investigated by an approximate method, when the medium is conductive. The influence of the conductivity parameters of the medium and material damage on the amplitudes of the first and second harmonics of the decomposition has been analyzed.
10.18720/MPM.3512018_6
longitudinal deformation; nonlinearly elastic rod; material damage; magnetic field; evolutionary equation; asymptotic solution.
https://mpm.spbstu.ru/article/2018.59.6/
MPM135_06_erofeev.pdf
RAR
RUS
53-58
Erofeev
Lobachevsky State University of Nizhni Novgorod
Nizhny Novgorod, Russia
Pavlov
Lobachevsky State University of Nizhni Novgorod
Nizhni Novgorod, Russia
Vikulin
Institute of Volcanology and Seismology of Far Eastern Branch of Russian Academy of Sciences
Petropavlovsk-Kamchatsky, Russia
Do rotational waves really exist?
A review of theoretical representations and experimental data on rotational motions of elements of a continuous medium is given. Description of wave rotational motions is impossible in the framework of the classical theory of elasticity, but it is allowed within the scope of generalized continua models (the Cosserat microspolar model, moment and gradient models, etc.), as well as in the framework of A.V. Vikulin’s model, in which the stresses are described by a symmetric tensor. Physical, geological and geophysical data are given that confirm both rotational approaches to describing the blocks and plates composing a geomedium and the existence of rotational waves.
10.18720/MPM.3512018_7
microstructured media; the Cosserat theory; rotational waves;geodynamics
https://mpm.spbstu.ru/article/2018.59.7/
MPM135_07_erofeev.pdf
RAR
RUS
59-65
Igumnov
Lobachevsky State University of Nizhni Novgorod
Nizhni Novgorod, Russia
Metrikin
Lobachevsky State University of Nizhni Novgorod
Nizhny Novgorod, Russia
On the theory of a non-autonomous vibro-impact system with memory in the frictional force
The dynamics of a non-autonomous vibro-impact system is investigated in this work. The system is composed of two vibrating bodies, which experience frictional resistance that is described with the help of a modified Coulomb friction model with memory. The mathematical model that describes the dynamics of the vibro-impact system can be classified as a dynamical system with variable structure. It consists of a system of ordinary differential equations and some functional relations. The model is analyzed by means of application of the point mapping technique. This technique allows to study the structure of the phase space of the system and its dependence on (i) the varying in time static coefficient of friction, (ii) the parameters of a harmonic force that acts on the system, and (iii) the position of a stopper that limits the system displacement. Numerical study of the system dynamics allowed for identification of the main regimes of the system motion and their intermittency. For example, periodical regimes of high complexity were found as well as the transition to chaos through the period doubling bifurcation. Additionally, the use of symbolic computations helped to uniquely interpret the obtained bifurcation diagrams.
10.18720/MPM.3512018_8
frictional vibrations; friction with memory; point mapping; bifurcation diagram; symbolic dynamics
https://mpm.spbstu.ru/article/2018.59.8/
MPM135_08_igumnov.pdf
RAR
RUS
66-70
Vavilov
Institute for problems in Mechanical Engineering RAS
St.Petersburg, Russia
Indeitsev
Institute of Problems of Mechanical Engineering RAS
St.Petersburg, Russia
Porubov
porubov@math.ioffe.ru
Skubov
Peter the Great St. Petersburg Polytechnic University
St.Petersburg, Russia
Lukin
Peter the Great St. Petersburg Polytechnic University
St.Petersburg, Russia
On the influence of the microstructure on the stress-strain state of material
The present paper is devoted to the problem of describing materials capable of structural transformations. Basing on two-component model of material with nonlinear internal force, we investigate the existence of non-stable constitutive curve containing a decreasing segment. For this purpose a kinematic loading of two-component rod is considered. The main goal is to determine the influence of the relative displacement on the stress-strain dependence and to establish the expression, connecting the position of the critical point on the diagram with the parameters of the microstructure.
10.18720/MPM.3512018_9
non-monotone constitutive curve; two-component model; structural transformations
https://mpm.spbstu.ru/article/2018.59.9/
MPM135_09_indeitsev.pdf
RAR
RUS
71-79
Dmitriev
Institute for Metals Superplasticity Problems
Ufa, Russia
Zhou
K.
Nanyang Technological University
Singapore
Korznikova
Institute for Metals Superplasticity Problems of the Russian Academy of Sciences
Ufa, Russia
Baimova
Institute for Metals Superplasticity Problems of the Russian Academy of Sciences
Ufa, Russia
Lobzenko
Ufa Research Center of Russian Academy of Sciences
Ufa, Russia
Liu
Nanyang Technological University
Singapore
Graphane: discrete breathers for dehydrogenation
Clusters of discrete breathers in fully hydrogenated graphene (also called gr aphane) are studied by means of molecular dynamics simulation. The energy exchange between gapdiscrete breathers is studied for clusters composed of two and three discrete breathers. It is shown that difference in the initial amplitude or in the initial vibration phase of discrete breathers affect the energyexchange between them. It is shown that the life time of single discrete breather in thermal equilibrium at 50 K is of order of 10 ps.
10.18720/MPM.3512018_10
nonlinear dynamics; discrete breather; intrinsic localized mode; graphene; graphane; dehydrogenation
https://mpm.spbstu.ru/article/2018.59.10/
MPM135_10_korznikova.pdf
RAR
RUS
80-86
Kovaleva
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Moscow, Russia
Smirnov
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Moscow, Russia
Manevitch
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Moscow, Russia
The nonlinear model of the librational dynamics of the paraffin crystal
In our work we consider the librational dynamics of the chains in paraffin crystals. We consider the paraffin chains being completely rigid and only inter-chain potential is taken into account. To study the possible change in the dynamics with the increase of the temperature, i.e. when the system achieves the vicinity of the rotation phase transition we consider the model without restrictions on the amplitudes of the rotational angles. The nonlinear spectra of the system are studied.
10.18720/MPM.3512018_11
librational dynamics; oscillatory chains; nonlinear normal modes; dispersion relation
https://mpm.spbstu.ru/article/2018.59.11/
MPM135_11_kovaleva.pdf
RAR
RUS
87-100
Kumar
Kurukshetra University Kurukshetra
Kurukshetra, India
Propagation of Stoneley waves at the boundary surface of thermoelastic diffusion solid and microstretch thermoelastic diffusion solid
This present investigation is focus on the propagation of Stoneley waves at the interface of thermoelastic diffusion solid half space and microstretch thermoelastic diffusion solid half space. The secular equation of Stoneley waves is derived in the compact form by using the appropriate boundary conditions. Phase velocity and attenuation coefficients are obtained numerically. Also the components of normal displacement, normal stress and temperature distribution are obtained. The effect of diffusion and relaxation times on the phase velocity, attenuation coefficient, normal displacement, stress components and temperature distribution are depicted graphically for a particular model. Some particular cases of interest are also deduced.
10.18720/MPM.3512018_12
microstretch; thermoelastic diffusion; Stoneley waves
phase velocity; attenuation coefficient
https://mpm.spbstu.ru/article/2018.59.12/
MPM135_12_kumar.pdf
RAR
RUS
101-114
Kumar
Kurukshetra University Kurukshetra
Kurukshetra, India
Kumar
Govt. Degree College Chowari (Chamba)
India
Gourla
Himachal Pradesh University
India
Plane wave and fundamental solution in thermoporoelastic medium
The present article deals with the study of propagation of plane wave and fundamental solution in the thermoporoelastic medium. It is found that for two dimensional model, their exist three longitudinal waves, namely P1-wave, P2-wave and T-wave in addition to transverse wave. Characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and depicted graphically. The representation of the fundamental solution of the system of equations in the thermoporoelastic medium in case of steady oscillations is considered in term of elementary functions. Some basic properties of the fundamental solution are established. Some special cases are also deduced.
10.18720/MPM.3512018_13
plane wave; fundamental solution; thermoporoelastic medium; steady oscillations
https://mpm.spbstu.ru/article/2018.59.13/
MPM135_13_kumar.pdf
RAR
RUS
115-125
Kumar
Kurukshetra University Kurukshetra
Kurukshetra, India
Singh
Lovely Professional University
India
Pathania
Guru Nanak Dev Engineering College
India
Propagation of Rayleigh waves in a micropolar thermoelastic half-space with impedance boundary conditions
This paper deals with the propagation of Rayleigh waves in a micropolar thermoelastic half space with impedance boundary conditions. The boundary of the half spaceis thermally insulated / isothermal and it is assumed that normal traction, shear traction and shear couple traction at the surface, varies linearly with normal, tangential components of displacement and microrotation respectively. The secular equation for Rayleigh wave with impedance boundary conditions is obtained and this equation is in agreement with the classical secular equation for elastic solid with traction free boundary conditions when micropolar, thermal and impedance parameters are removed. The non-dimensional speed of Rayleigh wave is computed as a function of impedance parameters and presented graphically for a particular micropolar thermoelastic material
10.18720/MPM.3512018_14
micropolar thermoelasticity; Rayleigh waves; i mpedance boundary conditions; secular equation
https://mpm.spbstu.ru/article/2018.59.14/
MPM135_14_kumar.pdf
RAR
RUS
126-138
Kumar
Kurukshetra University Kurukshetra
Kurukshetra, India
Vashisth
Kurukshetra University
Haryana, India
Ghangas
Kurukshetra University
Haryana, India
Waves in anisotropic thermoelastic medium with phase lag, two-temperature and void
This paper presents a study of propagation of plane waves in an anisotropic thermoelastic medium with void and two-temperature in the context of three-phase-lag theory of thermoelasticity. The existence of waves namely, quasi-longitudinal wave (
10.18720/MPM.3512018_15
anisotropic; thermoelastic; void; two-temperature; three-phase-lag; phase velocity; attenuation factor
https://mpm.spbstu.ru/article/2018.59.15/
MPM135_15_kumar.pdf
RAR
RUS
139-144
Porubov
porubov@math.ioffe.ru
Osokina
Peter the Great St. Petersburg Polytechnic University
St.Petersburg, Russia
Michelitch
Universite Pierre et Marie Curie
Paris, France
Operator approach to square lattice nonlinear dynamics
Two dimensional square lattice is considered when the forces between the lattice particles are expressed both linearly and quadratically dependent on the spring elongations. The shift operator approach, firstly developed by [1] and applied to the one-dimensional linear problem, is extended on the two-dimensional nonlinear case. The discrete strain energy and the discrete governing nonlinear equations of motion are obtained. Also, the continuum nonlinear equation for the plane longitudinal waves propagation is obtained in a weakly nonlinear case.
10.18720/MPM.3512018_16
lattice; nonlinear modeling; strain wave
https://mpm.spbstu.ru/article/2018.59.16/
MPM135_16_porubov.pdf
RAR
RUS
145-154
Sargsyan
Shirak State University
Armenia
Zhamakochyan
Shirak State University
Armenia
Applied theory of micropolar elastic thin plates with constrained rotation and the finite element method
In the present paper boundary value problems of three-dimensional micropolar theory of elasticity with constrained rotation are considered in thin region of the plate. On the basis of the previously developed hypotheses an applied theory of micropolar thin plates with constrained rotation is constructed, where transverse shear strains are taken into account. The energy balance equation is obtained and the corresponding variation functional is constructed. The finite element method is developed for the boundary problems (statics and natural oscillation) of micropolar plates with constrained rotation. On the basis of the analysis of the corresponding numerical results main properties of the micropolarity of the material are established.
In the present paper boundary value problems of three-dimensional micropolar theory of elasticity with constrained rotation are considered in thin region of the plate. On the basis of the previously developed hypotheses an applied theory of micropolar thin plates with constrained rotation is constructed, where transverse shear strains are taken into account. The energy balance equation is obtained and the corresponding variation functional is constructed. The finite element method is developed for the boundary problems (statics and natural oscillation) of micropolar plates with constrained rotation. On the basis of the analysis of the corresponding numerical results main properties of the micropolarity of the material are established.
10.18720/MPM.3512018_17
micropolar elasticity; constrained rotation; thin plate; applied theory; finite element method
https://mpm.spbstu.ru/article/2018.59.17/
MPM135_17_sargsyan.pdf
RAR
RUS
155-166
Savin
Institute of Physical Chemistry, RAS
Moscow, Russia
Dmitriev
Institute for Metals Superplasticity Problems
Ufa, Russia
Korznikova
Institute for Metals Superplasticity Problems of the Russian Academy of Sciences
Ufa, Russia
Kistanov
Nanyang Technological University
Singapore
Multilayered scrolls of carbon nanoribbons
Possible equilibrium states of multilayered carbon nanoribbons are found using the chain model moving on a plane previously proposed by the authors. For very short nanoribbons only flat multilayered structures are possible, while for sufficiently long nanoribbons the lowes energy have nanoscrolls with folded structures having intermediate value of energy. Dependencies of the internal and external radii of the scrolls, as well as the number of coils on the nanoribbon length are calculated. It is found that the radial thermal espansion coefficient of nanoscrolls is two or even three orders of magnitude larger than the linear thermal expansion coefficient of diamond. Thus, carbon nanoscrolls can be used to make very sensitive temperature sensors.
10.18720/MPM.3512018_18
graphene; chain model; scrolls; thermal expansion
https://mpm.spbstu.ru/article/2018.59.18/
MPM135_18_savin.pdf
RAR
RUS
167-174
Smirnov
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Moscow, Russia
Manevitch
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Moscow, Russia
Nonlinear torsion dynamics of the n-paraffin crystal
The nonlinear dynamical equations, which describe the torsion oscillations of the n-paraffin (alkanes) crystal have been derived in the framework of the coarse-grain model. The essentially nonlinear discrete equations reflect the influence of the internal multi-well conformation potential of the paraffin chain as well as the symmetry of the molecular field of the chain environment at the arbitrary large oscillation amplitudes.
10.18720/MPM.3512018_19
n-paraffin; torsion oscillations; nonlinear dynamics; coarse-grain mode
https://mpm.spbstu.ru/article/2018.59.19/
MPM135_19_smirnov.pdf
RAR
RUS
175-180
Vasiliev
Don State Technical University
Rostov-on-Don, Russia
Volkov
Don State Technical University
Rostov-on-Don, Russia
Aizikovich
Don State Technical University
Rostov-on-Don, Russia
Approximated analytical solution of contact problem on indentation of elastic half-space with coating reinforced with inhomogeneous interlayer
Axisymmetric contact problem on indentation of linearly elastic half-space with coating reinforced with inhomogeneous in depth interlayer is considered. Elastic moduli of the interlayer vary with depth according to arbitrary continuously differentiable independent functions. Construction of the compliance functions is reduced to the solution of Cauchy problems for a system of ordinary differential equations with variable coefficients. Contact problem is reduced to the solution of an integral equation which is solved using the bilateral asymptotic method. Approximated analytical expressions for contact stresses and indentation force are provided. Stresses and displacements inside the half-space and coating are obtained in the form of quadratures.
10.18720/MPM.3512018_20
contact; indentation; two-layered coating; functionally graded materials; analytical methods
https://mpm.spbstu.ru/article/2018.59.20/
MPM135_20_vasiliev.pdf
RAR
RUS
181-189
Zemlyanukhin
Yuri Gagarin Saratov State Technical University
Saratov, Russia
Bochkarev
Yuri Gagarin Saratov State Technical University
Saratov, Russia
Perturbation method, Padé approximants and exact solutions of nonlinear mechanics equationsr pages 181-189
In this article we are suggesting a method for finding exact solutions to integrable and non-integrable nonlinear mechanics equations that is based on the perturbation method. The criterion of equality of sequential diagonal Padé approximants whose minimum order is determined by the pole order of the equation’s solution is used for summation of the perturbation series. When the criterion is satisfied, the Padé approximants are the sought exact solutions.
10.18720/MPM.3512018_21
perturbation method; Padé approximants; nonlinear evolution equations; exact solutions
https://mpm.spbstu.ru/article/2018.59.21/
MPM135_21_zemlyanukhin.pdf