Vibration of string placed between extended and point limiters

Krupenin, V. L.

doi:10.3103/s105261881702008x

Cited by 3 publications

(9 citation statements)

References 3 publications

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“…1, a ). The introduction of generalized functions is necessary in view of the discontinuities arising from shocks [1,3,4].…”

Section: Forced Flat Oscillations Of a String With A Double Limiter 2mentioning

confidence: 99%

“…The case of a conservative system ( 0 ε = ) was considered in the article [3]. The form of the strength of the interaction force with a point limiter Ф∆1 (u) was determined from the following considerations.…”

Section: Forced Flat Oscillations Of a String With A Double Limiter 2mentioning

confidence: 99%

“…Relations 3define a generalized function Ф∆(и). For some n-th approach of the string to the limiter [3]…”

Section: Forced Flat Oscillations Of a String With A Double Limiter 2mentioning

confidence: 99%

“…In the first case, the modeling should be carried out by describing the shock process in the structures themselves. Models of distributed strongly nonlinear systems of simple structure can be used here [3]. In the second case, it may be expedient to conduct some idealization ("smearing" the equipment over space) and use models of highly nonlinear continuous media of complex structure [2,[4][5][6].…”

Section: Introductionmentioning

confidence: 99%

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Distributed impact elements and their use in modelling vibration fields in machines structures

Krupenin¹

2018

MATEC Web Conf.

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To model the vibration fields established in composite multidimensional machine structures, distributed impact elements are used, which take into account the wave processes occurring in colliding subsystems (shock pairs), which, in turn, quite often determine the structure of these fields. Two types of corresponding models are considered: with simple and complex structures. Specific examples of dynamic models are given. The results of the analysis are given.

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“…1, a ). The introduction of generalized functions is necessary in view of the discontinuities arising from shocks [1,3,4].…”

Section: Forced Flat Oscillations Of a String With A Double Limiter 2mentioning

confidence: 99%

Section: Forced Flat Oscillations Of a String With A Double Limiter 2mentioning

confidence: 99%

“…Relations 3define a generalized function Ф∆(и). For some n-th approach of the string to the limiter [3]…”

Section: Forced Flat Oscillations Of a String With A Double Limiter 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Distributed impact elements and their use in modelling vibration fields in machines structures

Krupenin¹

2018

MATEC Web Conf.

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“…In addition, several analytical approaches have been used to obtain time-periodic solutions formally for different types of piecewiselinear dynamical systems with rigid impacts. One can mention Fourier and Green function methods [4,5,8,17,18,19,23,24,25,31,37], modal decomposition [27,38] and sawtooth time transformations [32]. Most of the results obtained for discrete systems concern impacts localized on a single particle, and different types of waves have been constructed.…”

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confidence: 99%

Periodic Motions of Coupled Impact Oscillators

James

Acary

Pérignon

2018

Advanced Topics in Nonsmooth Dynamics

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We study the existence and stability of time-periodic oscillations in a chain of coupled impact oscillators, for rigid impacts without energy dissipation. We formulate the search of periodic solutions as a boundary value problem incorporating unilateral constraints. This problem is solved analytically in the vicinity of the uncoupled limit and numerically for larger coupling constants. Different solution branches corresponding to nonlinear localized modes (breathers) and normal modes are computed.

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Localization in Finite Asymmetric Vibro-Impact Chains

Grinberg¹,

Gendelman²

2018

SIAM J. Appl. Dyn. Syst.

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We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with asymmetric rigid constraints (the displacement domain of each particle is finite), and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an impact (not necessarily elastic), that satisfies Newton impact law. Nonlinearity of the system stems from the impacts; their possible non-elasticity is the sole source of damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the asymmetric discrete breathers, both in conservative and forced-damped settings. The asymmetry makes two types of breathers possible: breathers that impact both or only one constraint. Transition between these two types of the breathers corresponds to a grazing bifurcation. Special character of the nonlinearity permits explicit derivation of a monodromy matrix. Therefore, the stability of the obtained breather solutions can be exactly studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. All three generic scenarios of the loss of stability (pitchfork, Neimark-Sacker and period doubling bifurcations) are observed.

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Vibration of string placed between extended and point limiters

Cited by 3 publications

References 3 publications

Distributed impact elements and their use in modelling vibration fields in machines structures

Distributed impact elements and their use in modelling vibration fields in machines structures

Periodic Motions of Coupled Impact Oscillators

Localization in Finite Asymmetric Vibro-Impact Chains

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