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Porubov A.V.,Institute of Problems in Mechanical Engineering | Maugin G.A.,University Pierre and Marie Curie
International Journal of Non-Linear Mechanics | Year: 2011

A non-linear dynamic model is developed to account for material inhomogeneities in a growth plate in long bones. The governing equations are obtained to account for non-linear dispersive, viscoelastic and inhomogeneous features of the growth plate. The evolution of non-linear strain waves over the material inhomogeneities is obtained via the asymptotic solutions. It is shown that variations in the amplitude and the width of both the bell-shaped and kink-shaped waves reflect the position and the size of the inhomogeneity. This may be used for a detection of the growing plate features and in the development of the reactiondiffusion equation for the stimulus of the growth of long bones. © 2010 Elsevier Ltd. All rights reserved.

Porubov A.V.,Institute of Problems in Mechanical Engineering | Maugin G.A.,University Pierre and Marie Curie | Andrievsky B.R.,Institute of Problems in Mechanical Engineering
Wave Motion | Year: 2011

The interaction of the components of composite solitary waves governed by nonlinear coupled equations is studied numerically. It is shown how predictions of the known exact traveling wave solutions may help in understanding and explaining the process of reshaping seen as head-on and take-over collisions of individual solitary waves. The most interesting results concern the switch in the sign or the periodic modulation of the amplitude of the solitary wave and the direction of its propagation due to collisions. © 2011 Elsevier B.V..

News Article | November 22, 2016
Site: www.eurekalert.org

WASHINGTON, D.C., Nov. 22, 2016 -- This month, Samsung recalled 2.8 million top-loading washing machines due to excessive vibrations that could cause the top to break off -- a problem that led to at least nine reported injuries. The vibrations happen when the normal oscillations of the washing machine become trapped in resonance, causing it to shake harder and harder at the resonant frequency. It's a problem that doesn't just afflict washing machines. It can be an issue with all kinds of machines that rely on vibrations and oscillations, such as industrial shaking devices used to separate different-sized gravel and other raw materials, or riddling machines that loosen the sediment stuck on the insides of a champagne bottle and make the debris easier to remove. But now researchers have developed an algorithm that could help machines avoid getting trapped in this resonant motion. Using a combination of computer simulations and experiments, the researchers found that by carefully increasing and decreasing the speed of a rotor, they could nudge it past its resonant frequency. The rotor doesn't get stuck in resonance like the faulty washing machine. "Our method is analogous to pushing a car back and forth in order to get it out of a ditch," said Alexander Fradkov of the Institute of Problems in Mechanical Engineering, Russian Academy of Sciences. He and his colleagues describe their new research this week in Chaos, from AIP Publishing. Their method applies particularly when turning on a machine and the rotor speeds up. As it accelerates, depending on the design of the rest of the machine, it might reach a resonant frequency. The rotor might then become trapped operating at this frequency, which could cause damage or simply mean the machine doesn't work as designed. Boosting the power of the rotor could push it over the hump, but that requires more energy and a bigger, unwieldy motor. Instead, the researchers found that by increasing or lowering the rotor's speed by small amounts, they could control its frequency and get it past resonance. They used a computer to model a system in which two vibrational rotors are coupled together. Their model results matched those from a two-rotor machine designed for these kinds of experiments. The researchers also used specific mathematical analysis to show that by controlling a system with arbitrarily small intensities, they could move it from one state of motion to any other state. This theoretical scenario, involving a system with only one degree of freedom and assuming no friction, is important for better understanding cybernetical physics -- the study of how to control a physical system, Fradkov explained. "This result allows us to be more optimistic in practical applications since it provides an algorithm for how to move from one position to another with little effort," he said. The next step, the researchers say, is to see how you could control a system near resonances at higher frequencies (and therefor energies) and to explore the effects of different initial conditions. The article, "Control of oscillations in vibration machines: start up and passage through resonance," is authored by Alexander L. Fradkov, Dmitrii Gorlatov, Olga Tomchina and Dmitrii Tomchin. The article will appear in the journal Chaos Nov. 22, 2016 [DOI: 10.1063/1.4966632]. After that date, it can be accessed at http://scitation. . Chaos is devoted to increasing the understanding of nonlinear phenomena in all disciplines and describing their manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines. See http://chaos. .

Aero E.L.,Institute of Problems in Mechanical Engineering | Bulygin A.N.,Institute of Problems in Mechanical Engineering
Continuum Mechanics and Thermodynamics | Year: 2011

This article analyses the propagation of nonlinear periodic and localized waves. It examines crystals whose lattice consists of two periodic sub-lattices. Arbitrary large displacements of sub-lattices u are assumed. This theory takes into account the additional element of translational symmetry. The relative displacement in a sub-lattice for one period (and even for a whole number of periods) does not alter the structure of the whole complex lattice. This means that its energy does not vary under such a relatively rigid translation of sub-lattices and should represent the periodic function of micro-displacement. The energy also depends on the gradients of macroscopic displacement describing alterations in the elementary cells of a crystal. The variational equations of macro- and micro-displacements are shown to be a nonlinear generalization of the well-known linear equations of acoustic and optical modes of Karman, Born, and Huang Kun. Exact solutions to these equations are obtained in the one-dimensional case-localized and periodic. Criteria are established for their mutual transmutations. © 2010 Springer-Verlag.

Porubov A.V.,Institute of Problems in Mechanical Engineering | Andrianov I.V.,RWTH Aachen
Wave Motion | Year: 2013

A possible improvement of a continuum model for diatomic crystals is examined using continuum limit of a discrete diatomic model. For this purpose, various discrete models of diatomic lattice are compared at the linearized and weakly nonlinear levels. The suitable numbering of the atoms in the lattice is found which is better adopted for continualization than the familiar pair numbering introducing two sub-lattices. The coupled governing partial nonlinear differential equations for longitudinal strain and relative distance between the atoms are obtained in the continuum limit that allows us to describe localization of the strains due to the presence of the atoms of two kinds. It is found, that the equations obtained possess two kinds of localized wave solutions, one related to the acoustical branch and the other one related to the optical branch. © 2013 Elsevier B.V.

Filippenko G.V.,Institute of Problems in Mechanical Engineering
Proceedings of the International Conference Days on Diffraction, DD 2012 | Year: 2012

The problem of forced oscillations of the empty semi-infinite cylindrical shell partially submerged into a layer of liquid and rigidly fixed to the bottom is considered in the rigorous mathematical statement. The source of vibration and acoustical field in the system shell-liquid is external force acting on the shell. The stationary problem is considered. The exact analytical solution of the problem is constructed. © 2012 IEEE.

Abramian A.K.,Institute of Problems in Mechanical Engineering | Vakulenko S.A.,Institute of Problems in Mechanical Engineering
COMPDYN 2015 - 5th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering | Year: 2015

The present paper is devoted to an issue of possible localization of waves propagating within a structure that consists of a film connected to a backing material through a substrate. The substrate is initially damaged. In the first approximation the film model in the present paper is assumed to be a string on an elastic foundation with a coefficient depending on the substrate damage degree. The elastic foundation imitates the substrate and backing material effects on the film. Initiation of a string delamination resulted from the structure damaged at localized oscillations caused by a periodic impact load has been considered. At loading the initial damage of the substrate is changing in time and space according to the proposed law of the damage growth. It has been shown that at impact the cause of the string substrate material damage increase can be localized oscillation modes. The localized mode existence depends on relation between the initial substrate rigidity and the main material rigidity. There is also possible a passage through a sequence of resonances under the action of a periodic impact force.

Porubov A.V.,Institute of Problems in Mechanical Engineering | Andrianov I.V.,RWTH Aachen | Danishevs'Kyy V.V.,PrydniprovSka State Academy of Civil Engineering and Architecture
International Journal of Solids and Structures | Year: 2012

Nonlinear strain wave propagation along the lamina of a periodic two-component composite was studied. A nonlinear model was developed to describe the strain dynamics. The model asymptotically satisfies the boundary conditions between the lamina, in contrast to previously developed models. Our model reduces an initial two-dimensional problem into a single one-dimensional nonlinear governing equation for longitudinal strains in the form of the Boussinesq equation. The width of the lamina may control the propagation of either compression or tensile localized strain waves, independent of the elastic constants of the materials of the composite.© 2012 Elsevier Ltd. All rights reserved.

Filippenko G.V.,Institute of Problems in Mechanical Engineering
Proceedings of the International Conference Days on Diffraction 2011, DD 2011 | Year: 2011

Shells are the elements of various constructions, partially submerged into the liquid. It is important to estimate the level of vibration fields in these composite systems and analyze energy and energy flow in them. The results represented here are based on the formulas obtained in [1], [2], [3]. © 2011 IEEE.

Porubov A.V.,Institute of Problems in Mechanical Engineering | Andrievsky B.R.,Institute of Problems in Mechanical Engineering
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

It is shown numerically that kink-shaped and bell-shaped localized moving defects may coexist in a biatomic crystalline lattice. The shape and velocity of these waves are defined from a corresponding single wave exact traveling wave solution to the governing coupled nonlinear equations. The features of the initial conditions, or an external loading, are found that provide simultaneous propagation of these nonlinear moving defects, inputs, and their amplitudes. © 2012 American Physical Society.

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