Abstract
In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton’s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity. The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincaré maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed. In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics.
| Original language | English |
|---|---|
| Title of host publication | Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers |
| Publisher | Springer Verlag |
| Pages | 25-32 |
| Number of pages | 8 |
| Volume | 10187 LNCS |
| ISBN (Print) | 9783319570983 |
| DOIs | |
| Publication status | Published - 2017 |
| Event | 6th International Conference on Numerical Analysis and Its Applications, NAA 2016 - Lozenetz, Bulgaria Duration: 15 Jun 2016 → 22 Jun 2016 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 10187 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Conference
| Conference | 6th International Conference on Numerical Analysis and Its Applications, NAA 2016 |
|---|---|
| Country | Bulgaria |
| City | Lozenetz |
| Period | 15.6.16 → 22.6.16 |
Fingerprint
Keywords
- Bifurcations
- Chaos
- Non-linear dynamics
- Timoshenko beam
- White Gauss noise
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
Cite this
Chaotic dynamics of structural members under regular periodic and white noise excitations. / Awrejcewicz, J.; Krysko, A. V.; Papkova, I. V.; Erofeev, N. P.; Krysko, V. A.
Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers. Vol. 10187 LNCS Springer Verlag, 2017. p. 25-32 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10187 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Chaotic dynamics of structural members under regular periodic and white noise excitations
AU - Awrejcewicz, J.
AU - Krysko, A. V.
AU - Papkova, I. V.
AU - Erofeev, N. P.
AU - Krysko, V. A.
PY - 2017
Y1 - 2017
N2 - In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton’s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity. The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincaré maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed. In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics.
AB - In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton’s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity. The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincaré maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed. In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics.
KW - Bifurcations
KW - Chaos
KW - Non-linear dynamics
KW - Timoshenko beam
KW - White Gauss noise
UR - http://www.scopus.com/inward/record.url?scp=85018389650&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018389650&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-57099-0_3
DO - 10.1007/978-3-319-57099-0_3
M3 - Conference contribution
SN - 9783319570983
VL - 10187 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 25
EP - 32
BT - Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers
PB - Springer Verlag
ER -