Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members

A. V. Krysko, J. Awrejcewicz, O. A. Saltykova, S. S. Vetsel, V. A. Krysko

Результат исследований: Материалы для журналаСтатья

8 Цитирования (Scopus)

Выдержка

Nonlinear beam-beam and beam-cylindrical shell contact interactions, where a beam is subjected to harmonic uniform load, are studied. First, the nonlinear dynamics governed by four nonlinear PDEs including a switch function controlling the contact pressure between the mentioned structural members are presented. Relations between dimensional and dimensionless quantities are derived, and the original problem of infinite dimension has been reduced to that of oscillator chains via the FDM (Finite Difference Method). Time histories, FFT (Fast Fourier Transform), phase portraits, Poincaré maps, and Morlet wavelets are applied to discover novel nonlinear chaotic and synchronization phenomena of the interacting structural members. Numerous bifurcations, full-phase synchronization of the beam-shell vibrations, the evolution of energy of the vibrating members, damped vibrations of the analyzed conservative system of the beam and the shell surface deformations for various time instants, as well as the buckling of the shell induced by impacts are illustrated and discussed, among others. In addition, we have detected that in all studied cases, in spite of analyzing a large set of nonlinear ODEs approximating the behavior of interacting structural members, the scenario of transition from regular to chaotic dynamics follows the Ruelle-Takens-Newhouse scenario.

Язык оригиналаАнглийский
Страницы (с-по)622-638
Число страниц17
ЖурналChaos, Solitons and Fractals
Том91
DOI
СостояниеОпубликовано - 1 окт 2016

Отпечаток

Cylindrical Shell
Nonlinear Dynamics
Contact
Closed
Interaction
Shell
Vibration
Nonlinear ODE
Scenarios
Conservative System
Phase Synchronization
Nonlinear PDE
Infinite Dimensions
Phase Portrait
Chaotic Dynamics
Fast Fourier transform
Buckling
Dimensionless
Large Set
Instant

ASJC Scopus subject areas

  • Mathematics(all)

Цитировать

Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members. / Krysko, A. V.; Awrejcewicz, J.; Saltykova, O. A.; Vetsel, S. S.; Krysko, V. A.

В: Chaos, Solitons and Fractals, Том 91, 01.10.2016, стр. 622-638.

Результат исследований: Материалы для журналаСтатья

Krysko, A. V. ; Awrejcewicz, J. ; Saltykova, O. A. ; Vetsel, S. S. ; Krysko, V. A. / Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members. В: Chaos, Solitons and Fractals. 2016 ; Том 91. стр. 622-638.
@article{05b679bbffc841f9b5c3d66508b9d068,
title = "Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members",
abstract = "Nonlinear beam-beam and beam-cylindrical shell contact interactions, where a beam is subjected to harmonic uniform load, are studied. First, the nonlinear dynamics governed by four nonlinear PDEs including a switch function controlling the contact pressure between the mentioned structural members are presented. Relations between dimensional and dimensionless quantities are derived, and the original problem of infinite dimension has been reduced to that of oscillator chains via the FDM (Finite Difference Method). Time histories, FFT (Fast Fourier Transform), phase portraits, Poincar{\'e} maps, and Morlet wavelets are applied to discover novel nonlinear chaotic and synchronization phenomena of the interacting structural members. Numerous bifurcations, full-phase synchronization of the beam-shell vibrations, the evolution of energy of the vibrating members, damped vibrations of the analyzed conservative system of the beam and the shell surface deformations for various time instants, as well as the buckling of the shell induced by impacts are illustrated and discussed, among others. In addition, we have detected that in all studied cases, in spite of analyzing a large set of nonlinear ODEs approximating the behavior of interacting structural members, the scenario of transition from regular to chaotic dynamics follows the Ruelle-Takens-Newhouse scenario.",
keywords = "Beam, Chaos, Dynamics, Impact, Shell, Wavelet",
author = "Krysko, {A. V.} and J. Awrejcewicz and Saltykova, {O. A.} and Vetsel, {S. S.} and Krysko, {V. A.}",
year = "2016",
month = "10",
day = "1",
doi = "10.1016/j.chaos.2016.09.001",
language = "English",
volume = "91",
pages = "622--638",
journal = "Chaos, Solitons and Fractals",
issn = "0960-0779",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members

AU - Krysko, A. V.

AU - Awrejcewicz, J.

AU - Saltykova, O. A.

AU - Vetsel, S. S.

AU - Krysko, V. A.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - Nonlinear beam-beam and beam-cylindrical shell contact interactions, where a beam is subjected to harmonic uniform load, are studied. First, the nonlinear dynamics governed by four nonlinear PDEs including a switch function controlling the contact pressure between the mentioned structural members are presented. Relations between dimensional and dimensionless quantities are derived, and the original problem of infinite dimension has been reduced to that of oscillator chains via the FDM (Finite Difference Method). Time histories, FFT (Fast Fourier Transform), phase portraits, Poincaré maps, and Morlet wavelets are applied to discover novel nonlinear chaotic and synchronization phenomena of the interacting structural members. Numerous bifurcations, full-phase synchronization of the beam-shell vibrations, the evolution of energy of the vibrating members, damped vibrations of the analyzed conservative system of the beam and the shell surface deformations for various time instants, as well as the buckling of the shell induced by impacts are illustrated and discussed, among others. In addition, we have detected that in all studied cases, in spite of analyzing a large set of nonlinear ODEs approximating the behavior of interacting structural members, the scenario of transition from regular to chaotic dynamics follows the Ruelle-Takens-Newhouse scenario.

AB - Nonlinear beam-beam and beam-cylindrical shell contact interactions, where a beam is subjected to harmonic uniform load, are studied. First, the nonlinear dynamics governed by four nonlinear PDEs including a switch function controlling the contact pressure between the mentioned structural members are presented. Relations between dimensional and dimensionless quantities are derived, and the original problem of infinite dimension has been reduced to that of oscillator chains via the FDM (Finite Difference Method). Time histories, FFT (Fast Fourier Transform), phase portraits, Poincaré maps, and Morlet wavelets are applied to discover novel nonlinear chaotic and synchronization phenomena of the interacting structural members. Numerous bifurcations, full-phase synchronization of the beam-shell vibrations, the evolution of energy of the vibrating members, damped vibrations of the analyzed conservative system of the beam and the shell surface deformations for various time instants, as well as the buckling of the shell induced by impacts are illustrated and discussed, among others. In addition, we have detected that in all studied cases, in spite of analyzing a large set of nonlinear ODEs approximating the behavior of interacting structural members, the scenario of transition from regular to chaotic dynamics follows the Ruelle-Takens-Newhouse scenario.

KW - Beam

KW - Chaos

KW - Dynamics

KW - Impact

KW - Shell

KW - Wavelet

UR - http://www.scopus.com/inward/record.url?scp=84985906169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84985906169&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2016.09.001

DO - 10.1016/j.chaos.2016.09.001

M3 - Article

AN - SCOPUS:84985906169

VL - 91

SP - 622

EP - 638

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -