Oleg Gendelman - Academia.edu (original) (raw)
Papers by Oleg Gendelman
Journal of Sound and Vibration, 2008
Journal of Sound and Vibration, 2015
Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003
ABSTRACT We study the dynamics of a semi-infinite linear chain of particles that is weakly couple... more ABSTRACT We study the dynamics of a semi-infinite linear chain of particles that is weakly coupled to a strongly nonlinear oscillator at its free end. We analyze families of localized standing waves situated inside the lower or upper attenuation zones of the linear chain, corresponding to energy predominantly confined in the nonlinear oscillator. These families of standing waves are generated due to resonant interactions between the chain and the nonlinear attachment. A scenario for the realization of energy pumping phenomena in the system under consideration is discussed, and is confirmed by direct numerical simulations of the chain-attachment dynamic interaction.
Journal of Vibration and Acoustics, 2004
Normal Modes and Localization in Nonlinear Systems, 2001
Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly non... more Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly nonlinear damped oscillators isinvestigated. Special attention is paid to the excitation of a nonlinearnormal mode while the energy is initially stored in other modes of thesystem. The transition proceeds via the mechanism of subharmonicresonance which is possible because of the strong nonlinearity of thesystem. The conditions of
Foundations of Engineering Mechanics, 2010
ABSTRACT Discrete systems comprising an infinite number of particles are rather challenging for a... more ABSTRACT Discrete systems comprising an infinite number of particles are rather challenging for a formulation of tractable models. The simplifications related to a low number of the degrees of freedom or normal modes cannot normally be implemented directly. Transition to a continuum and to a description in terms of partial differential equations may be involved and normally requires a number of assumptions; each of them should be carefully checked. In particular, for different regimes of motion of the discrete system one can obtain rather different continuous approximations. On the other side, such systems are extremely important both in mechanics (for modeling arrays of structural elements etc.) and in physics. For the study of the relationship between macroscopic properties and the microscopic structure in classical physics, the models of this sort are the best possible.
Foundations of Engineering Mechanics, 2010
The necessary precondition for the formulation of tractable models of mechanics is an adequate un... more The necessary precondition for the formulation of tractable models of mechanics is an adequate understanding of the main notions and concepts involved in the theoretical considerations. The lack of such understanding jeopardizes efficient scientific development. This is clearly seen in the historical context – the way to formation of mechanics was rather tortuous.
Foundations of Engineering Mechanics, 2010
ABSTRACT An asymptotic approach is rather efficient when dealing with the theory of oscillations,... more ABSTRACT An asymptotic approach is rather efficient when dealing with the theory of oscillations, since one often can figure out a number of relatively simple limit cases which can be efficiently treated and completely understood. Such an approach allows the deepest possible simplification but preserves the most significant features of dynamical behavior. At the same time, one can use the expansions by small parameters characterizing the deviation of the system from the tractable limit case.
EPL (Europhysics Letters), 2014
Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B, 2011
ABSTRACT We introduce a novel type of the nonlinear energy sink (NES) designed as an eccentric ma... more ABSTRACT We introduce a novel type of the nonlinear energy sink (NES) designed as an eccentric mass rotating within a horizontal plane. The gravity is not a factor here, therefore such a rotator has no eigenfrequency and can inertially couple and resonate with any mode of the primary system. The dynamics of the system consisting of a primary linear oscillator and the eccentric rotator is rich beyond expectations and features multiple resonances and chaotic modes. A numerical study shows that the system, when subject to high impulsive loads, inevitably enters a 1:1 resonance that enables highly efficient targeted energy transfer from the primary mass to the NES. The results of an experimental investigation are in good agreement with the analytical and numerical estimates.
We consider a propagation of exotermic transition front in a discrete conservative oscillatory ch... more We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and topochemical reactions. Due to constant energy supply, the transition front can propagate with high velocities, precluding any continuum-based considerations. Stationary propagation of the front is accompanied by formation of a non-stationary oscillatory tail with complicated internal structure. We demonstrate that the structure of the oscillatory tail is related to a relationship between phase and group velocities of the oscillations. We suggest also an approximate analytic procedure, which allows one to determine all basic characteristics of the propagation process: velocity and width of the front, frequency and amplitude of the after-front oscillations, as well as the structure of the oscillatory tail. As an example, we consider a simple case of bihar...
The determination of the normal and transverse (frictional) inter-particle forces within a granul... more The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, taunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external forces and the orientations of contacts between particles (of any given sizes), to compute all the inter-particle forces. Having solved this problem we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.
EPL (Europhysics Letters)
We focus on the observed reduction in shear modulus when the stress on an amorphous solid is incr... more We focus on the observed reduction in shear modulus when the stress on an amorphous solid is increased beyond the initial linear region. Careful numerical quasi-static simulations reveal an intimate relation between plastic failure and the reduction in shear modulus. The attainment of the smallest value of the shear modulus is identified with spreading of the regions that underwent a plastic event. We present an elementary “two-state” model that interpolates between failed and virgin regions and provides a simple and effective characterization of the phenomenon.
Abstract: Two-dimensional structural defects in a polyethylene crystal (twist domain walls) are i... more Abstract: Two-dimensional structural defects in a polyethylene crystal (twist domain walls) are investigated by means of analytic treatment and molecular dynamics simulation. The formation of the domain wall as a result of relaxation of the crystal from different initial states is studied and parameters of this type of defects are calculated.
The paper considers heat conductivity in a set of one-dimensional lattice models, which contain p... more The paper considers heat conductivity in a set of one-dimensional lattice models, which contain particles with two different masses. First of all, we address recent findings concerning peculiar heat transport in a diatomic billiard close to the integrable limit. Our simulations demonstrate that the heat transport in this case remains superdiffusive, and the heat conductivity therefore is abnormal. Then, the effect of mass disorder on the heat transport in the diatomic system is explored both for systems with abnormal and normal heat conductivity. Two main characteristics of the disorder are addressed -- internal correlations in the disordered structure, and concentration of the "impurities" with different mass. We show that the disorder does not modify the convergency properties of the heat conduction coefficient in the thermodynamical limit. However, as one would expect, the disorder strongly effects the quantitative properties of the heat transport. Moreover, we demonstr...
In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fro... more In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in dynamics of common and popular lattices. In this study, we address a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. The front propagation obeys the scaling law lsimt4/3l \sim t^{4/3}lsimt4/3. The frequency of the oscillatory tail remains constant, and the wavelength scales as lambdasimt1/3\lambda \sim t^{1/3}lambdasimt1/3. These scaling laws result from the nonlocal effects; we derive them analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initi...
International Journal of Non-Linear Mechanics, 2014
ABSTRACT Multi-scale vibratory energy exchange between a main oscillator including Saint-Venant t... more ABSTRACT Multi-scale vibratory energy exchange between a main oscillator including Saint-Venant term and a cubic nonlinear energy sink is studied. Analytically obtained invariant manifold of the system at fast time scale and detected fixed points and/or fold singularities at first slow time scale let us predict and explain different regimes that the system may face during the energy exchange process. The paper will be accompanied by some numerical results confirming our analytical predictions.
Journal of Sound and Vibration, 2008
Journal of Sound and Vibration, 2015
Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003
ABSTRACT We study the dynamics of a semi-infinite linear chain of particles that is weakly couple... more ABSTRACT We study the dynamics of a semi-infinite linear chain of particles that is weakly coupled to a strongly nonlinear oscillator at its free end. We analyze families of localized standing waves situated inside the lower or upper attenuation zones of the linear chain, corresponding to energy predominantly confined in the nonlinear oscillator. These families of standing waves are generated due to resonant interactions between the chain and the nonlinear attachment. A scenario for the realization of energy pumping phenomena in the system under consideration is discussed, and is confirmed by direct numerical simulations of the chain-attachment dynamic interaction.
Journal of Vibration and Acoustics, 2004
Normal Modes and Localization in Nonlinear Systems, 2001
Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly non... more Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly nonlinear damped oscillators isinvestigated. Special attention is paid to the excitation of a nonlinearnormal mode while the energy is initially stored in other modes of thesystem. The transition proceeds via the mechanism of subharmonicresonance which is possible because of the strong nonlinearity of thesystem. The conditions of
Foundations of Engineering Mechanics, 2010
ABSTRACT Discrete systems comprising an infinite number of particles are rather challenging for a... more ABSTRACT Discrete systems comprising an infinite number of particles are rather challenging for a formulation of tractable models. The simplifications related to a low number of the degrees of freedom or normal modes cannot normally be implemented directly. Transition to a continuum and to a description in terms of partial differential equations may be involved and normally requires a number of assumptions; each of them should be carefully checked. In particular, for different regimes of motion of the discrete system one can obtain rather different continuous approximations. On the other side, such systems are extremely important both in mechanics (for modeling arrays of structural elements etc.) and in physics. For the study of the relationship between macroscopic properties and the microscopic structure in classical physics, the models of this sort are the best possible.
Foundations of Engineering Mechanics, 2010
The necessary precondition for the formulation of tractable models of mechanics is an adequate un... more The necessary precondition for the formulation of tractable models of mechanics is an adequate understanding of the main notions and concepts involved in the theoretical considerations. The lack of such understanding jeopardizes efficient scientific development. This is clearly seen in the historical context – the way to formation of mechanics was rather tortuous.
Foundations of Engineering Mechanics, 2010
ABSTRACT An asymptotic approach is rather efficient when dealing with the theory of oscillations,... more ABSTRACT An asymptotic approach is rather efficient when dealing with the theory of oscillations, since one often can figure out a number of relatively simple limit cases which can be efficiently treated and completely understood. Such an approach allows the deepest possible simplification but preserves the most significant features of dynamical behavior. At the same time, one can use the expansions by small parameters characterizing the deviation of the system from the tractable limit case.
EPL (Europhysics Letters), 2014
Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B, 2011
ABSTRACT We introduce a novel type of the nonlinear energy sink (NES) designed as an eccentric ma... more ABSTRACT We introduce a novel type of the nonlinear energy sink (NES) designed as an eccentric mass rotating within a horizontal plane. The gravity is not a factor here, therefore such a rotator has no eigenfrequency and can inertially couple and resonate with any mode of the primary system. The dynamics of the system consisting of a primary linear oscillator and the eccentric rotator is rich beyond expectations and features multiple resonances and chaotic modes. A numerical study shows that the system, when subject to high impulsive loads, inevitably enters a 1:1 resonance that enables highly efficient targeted energy transfer from the primary mass to the NES. The results of an experimental investigation are in good agreement with the analytical and numerical estimates.
We consider a propagation of exotermic transition front in a discrete conservative oscillatory ch... more We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and topochemical reactions. Due to constant energy supply, the transition front can propagate with high velocities, precluding any continuum-based considerations. Stationary propagation of the front is accompanied by formation of a non-stationary oscillatory tail with complicated internal structure. We demonstrate that the structure of the oscillatory tail is related to a relationship between phase and group velocities of the oscillations. We suggest also an approximate analytic procedure, which allows one to determine all basic characteristics of the propagation process: velocity and width of the front, frequency and amplitude of the after-front oscillations, as well as the structure of the oscillatory tail. As an example, we consider a simple case of bihar...
The determination of the normal and transverse (frictional) inter-particle forces within a granul... more The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, taunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external forces and the orientations of contacts between particles (of any given sizes), to compute all the inter-particle forces. Having solved this problem we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.
EPL (Europhysics Letters)
We focus on the observed reduction in shear modulus when the stress on an amorphous solid is incr... more We focus on the observed reduction in shear modulus when the stress on an amorphous solid is increased beyond the initial linear region. Careful numerical quasi-static simulations reveal an intimate relation between plastic failure and the reduction in shear modulus. The attainment of the smallest value of the shear modulus is identified with spreading of the regions that underwent a plastic event. We present an elementary “two-state” model that interpolates between failed and virgin regions and provides a simple and effective characterization of the phenomenon.
Abstract: Two-dimensional structural defects in a polyethylene crystal (twist domain walls) are i... more Abstract: Two-dimensional structural defects in a polyethylene crystal (twist domain walls) are investigated by means of analytic treatment and molecular dynamics simulation. The formation of the domain wall as a result of relaxation of the crystal from different initial states is studied and parameters of this type of defects are calculated.
The paper considers heat conductivity in a set of one-dimensional lattice models, which contain p... more The paper considers heat conductivity in a set of one-dimensional lattice models, which contain particles with two different masses. First of all, we address recent findings concerning peculiar heat transport in a diatomic billiard close to the integrable limit. Our simulations demonstrate that the heat transport in this case remains superdiffusive, and the heat conductivity therefore is abnormal. Then, the effect of mass disorder on the heat transport in the diatomic system is explored both for systems with abnormal and normal heat conductivity. Two main characteristics of the disorder are addressed -- internal correlations in the disordered structure, and concentration of the "impurities" with different mass. We show that the disorder does not modify the convergency properties of the heat conduction coefficient in the thermodynamical limit. However, as one would expect, the disorder strongly effects the quantitative properties of the heat transport. Moreover, we demonstr...
In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fro... more In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in dynamics of common and popular lattices. In this study, we address a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. The front propagation obeys the scaling law lsimt4/3l \sim t^{4/3}lsimt4/3. The frequency of the oscillatory tail remains constant, and the wavelength scales as lambdasimt1/3\lambda \sim t^{1/3}lambdasimt1/3. These scaling laws result from the nonlocal effects; we derive them analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initi...
International Journal of Non-Linear Mechanics, 2014
ABSTRACT Multi-scale vibratory energy exchange between a main oscillator including Saint-Venant t... more ABSTRACT Multi-scale vibratory energy exchange between a main oscillator including Saint-Venant term and a cubic nonlinear energy sink is studied. Analytically obtained invariant manifold of the system at fast time scale and detected fixed points and/or fold singularities at first slow time scale let us predict and explain different regimes that the system may face during the energy exchange process. The paper will be accompanied by some numerical results confirming our analytical predictions.