Complex fluctuations of flexible plates under longitudinal loads with account for white noise

Krylova, E. Yu.; Папкова, И. В.; Ерофеев, Н. П.; Захаров, В. М.; Кrysko, V.А.

doi:10.1134/s0021894416040167

Cited by 9 publications

(2 citation statements)

References 7 publications

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“…Visualization behavior of elements of microelectromechanical systems (MEMS) in the form of beams, plates and shells under the action of various kinds of loads currently is an actual scientific problem [1,2,7,8,9,18]. One of the ways of MEMS evolution is to reduce their mechanical components to the nanoscale and to reduce their mass.…”

Section: Introductionmentioning

confidence: 99%

Visualization of Transition's Scenarios from Harmonic to Chaotic Flexible Nonlinear-elastic Nano Beam's Oscillations

Krysko¹,

Папкова²,

Krylova³

et al. 2019

GraphiCon'2019 Proceedings. Volume 2

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In this study, a mathematical model of the nonlinear vibrations of a nano-beam under the action of a sign-variable load and an additive white noise was constructed and visualized. The beam is heterogeneous, isotropic, elastic. The physical nonlinearity of the nano-beam was taken into account. The dependence of stress intensity on deformations intensity for aluminum was taken into account. Geometric non-linearity according to Theodore von Karman’s theory was applied. The equations of motion, the boundary and initial conditions of the Hamilton-Ostrogradski principle with regard to the modified couple stress theory were obtained. The system of nonlinear partial differential equations to the Cauchy problem by the method of finite differences was reduced. The Cauchy problem by the finite-difference method in the time coordinate was solved. The Birger variable method was used. Data visualization is carried out from the standpoint of the qualitative theory of differential equations and nonlinear dynamics were carried out. Using a wide range of tools visualization allowed to established that the transition from ordered vibrations to chaos is carried out according to the scenario of Ruelle-Takens-Newhouse. With an increase of the size-dependent parameter, the zone of steady and regular vibrations increases. The transition from regular to chaotic vibrations is accompanied by a tough dynamic loss of stability. The proposed method is universal and can be extended to solve a wide class of various problems of mechanics of shells.

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Section: Introductionmentioning

confidence: 99%

Visualization of Transition's Scenarios from Harmonic to Chaotic Flexible Nonlinear-elastic Nano Beam's Oscillations

Krysko¹,

Папкова²,

Krylova³

et al. 2019

GraphiCon'2019 Proceedings. Volume 2

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show abstract

“…Progress in micro-and nano-technologies leads to the interest of scientists not only to the behavior of full-size mechanical systems in the form of plates and shells [13,14,16], but also the need to create mathematical models that take into account the scale effects at the micro and nano level [10,12,19]. In most works on this subject linear models are used for numerical analysis [15,17,18,21,22].…”

Section: Introductionmentioning

confidence: 99%

Visualization of Scenarios for the Transition of Oscillations from Harmonic to Chaotic for a Micropolar Kirchhoff-Love Cylindrical Meshed Panel

Krylova¹,

Папкова²,

Салтыкова³

et al. 2019

GraphiCon'2019 Proceedings. Volume 2

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On the basis of the kinematic hypotheses of the Kirchhoff-Love built a mathematical model of micropolar cylindrical meshed panels vibrations under the action of a normal distributed load. In order to take into account the size-dependent behavior, the panel material is considered as a Cosser’s pseudocontinuum with constrained particle rotation. The mesh structure is taken into account by the phenomenological continuum model of G. I. Pshenichnov. For a cylindrical panel consisting of two systems of mutually perpendicular edges, a scenario of transition of oscillations from harmonic to chaotic is constructed. It is shown that in the study of the behavior of cylindrical micropolar meshed panels it is necessary to study the nature of the oscillations of longitudinal waves.

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Nonlinear Dynamics of Flexible Meshed Cylindrical Panels in the White Noise’s Field

Awrejcewicz

Krylova

Папкова

et al. 2022

Springer Proceedings in Mathematics &Amp; Statistics

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Complex fluctuations of flexible plates under longitudinal loads with account for white noise

Cited by 9 publications

References 7 publications

Visualization of Transition's Scenarios from Harmonic to Chaotic Flexible Nonlinear-elastic Nano Beam's Oscillations

Visualization of Transition's Scenarios from Harmonic to Chaotic Flexible Nonlinear-elastic Nano Beam's Oscillations

Visualization of Scenarios for the Transition of Oscillations from Harmonic to Chaotic for a Micropolar Kirchhoff-Love Cylindrical Meshed Panel

Nonlinear Dynamics of Flexible Meshed Cylindrical Panels in the White Noise’s Field

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