Abstract
A closed cylindrical shell with circular cross-section having constant stiffness and density and subjected to sign changeable loading and embedded into a temperature field is analyzed. Both BubnovGalerkin (with a higher approximation) and Fourier methods are applied to solve the derived nonlinear nondimensional partial differential equations. Among others, the novel scenario of transition from shell harmonic to chaotic vibrations via the collapse of quasi-periodic vibrations with one independent frequency and Hopf bifurcation is detected, illustrated and discussed. In addition, it is shown how for various intensities of the temperature field (including its absence) the increase of the loading yields qualitative changes in the investigated shell dynamics, and how chaotic zones are transmitted into periodic ones and vice versa.
| Original language | English |
|---|---|
| Pages (from-to) | 1515-1529 |
| Number of pages | 15 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 18 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 Jan 2008 |
| Externally published | Yes |
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Keywords
- Bubnov-Galerkin method
- Chaos
- Cylindrical shell
- Fourier representation
- Partial differential equations
- Temperature field
- Vibrations
ASJC Scopus subject areas
- Modelling and Simulation
- Engineering (miscellaneous)
- General
- Applied Mathematics
Cite this
Chaotic vibrations of closed cylindrical shells in a temperature field. / Krysko, A. V.; Awrejcewicz, J.; Kuznetsova, E. S.; Krysko, V. A.
In: International Journal of Bifurcation and Chaos, Vol. 18, No. 5, 01.01.2008, p. 1515-1529.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Chaotic vibrations of closed cylindrical shells in a temperature field
AU - Krysko, A. V.
AU - Awrejcewicz, J.
AU - Kuznetsova, E. S.
AU - Krysko, V. A.
PY - 2008/1/1
Y1 - 2008/1/1
N2 - A closed cylindrical shell with circular cross-section having constant stiffness and density and subjected to sign changeable loading and embedded into a temperature field is analyzed. Both BubnovGalerkin (with a higher approximation) and Fourier methods are applied to solve the derived nonlinear nondimensional partial differential equations. Among others, the novel scenario of transition from shell harmonic to chaotic vibrations via the collapse of quasi-periodic vibrations with one independent frequency and Hopf bifurcation is detected, illustrated and discussed. In addition, it is shown how for various intensities of the temperature field (including its absence) the increase of the loading yields qualitative changes in the investigated shell dynamics, and how chaotic zones are transmitted into periodic ones and vice versa.
AB - A closed cylindrical shell with circular cross-section having constant stiffness and density and subjected to sign changeable loading and embedded into a temperature field is analyzed. Both BubnovGalerkin (with a higher approximation) and Fourier methods are applied to solve the derived nonlinear nondimensional partial differential equations. Among others, the novel scenario of transition from shell harmonic to chaotic vibrations via the collapse of quasi-periodic vibrations with one independent frequency and Hopf bifurcation is detected, illustrated and discussed. In addition, it is shown how for various intensities of the temperature field (including its absence) the increase of the loading yields qualitative changes in the investigated shell dynamics, and how chaotic zones are transmitted into periodic ones and vice versa.
KW - Bubnov-Galerkin method
KW - Chaos
KW - Cylindrical shell
KW - Fourier representation
KW - Partial differential equations
KW - Temperature field
KW - Vibrations
UR - http://www.scopus.com/inward/record.url?scp=47749125788&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=47749125788&partnerID=8YFLogxK
U2 - 10.1142/S0218127408021130
DO - 10.1142/S0218127408021130
M3 - Article
AN - SCOPUS:47749125788
VL - 18
SP - 1515
EP - 1529
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
SN - 0218-1274
IS - 5
ER -