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, 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.
| Original language | English |
|---|---|
| Pages (from-to) | 622-638 |
| Number of pages | 17 |
| Journal | Chaos, Solitons and Fractals |
| Volume | 91 |
| DOIs | |
| Publication status | Published - 1 Oct 2016 |
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Keywords
- Beam
- Chaos
- Dynamics
- Impact
- Shell
- Wavelet
ASJC Scopus subject areas
- Mathematics(all)
Cite this
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.
In: Chaos, Solitons and Fractals, Vol. 91, 01.10.2016, p. 622-638.Research output: Contribution to journal › Article
}
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
VL - 91
SP - 622
EP - 638
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
ER -