Abstract
Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the BubnovGalerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 3347-3371 |
| Number of pages | 25 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 19 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 1 Jan 2009 |
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Keywords
- Chaos
- Plate strip
- Stability
- Wavelets
ASJC Scopus subject areas
- Modelling and Simulation
- Engineering (miscellaneous)
- General
- Applied Mathematics
Cite this
On the wavelet transform application to a study of chaotic vibrations of the infinite length flexible panels driven longitudinally. / Awrejcewicz, J.; Krysko, A. V.; Soldatov, V.
In: International Journal of Bifurcation and Chaos, Vol. 19, No. 10, 01.01.2009, p. 3347-3371.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the wavelet transform application to a study of chaotic vibrations of the infinite length flexible panels driven longitudinally
AU - Awrejcewicz, J.
AU - Krysko, A. V.
AU - Soldatov, V.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the BubnovGalerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.
AB - Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the BubnovGalerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.
KW - Chaos
KW - Plate strip
KW - Stability
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=73149103508&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=73149103508&partnerID=8YFLogxK
U2 - 10.1142/S0218127409024803
DO - 10.1142/S0218127409024803
M3 - Article
VL - 19
SP - 3347
EP - 3371
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 - 10
ER -