Abstract
We propose a procedure for predicting the stability loss and transition into chaos of a network of oscillators lying on a curve, where each of the oscillators can move in two perpendicular directions. Dynamics of the coupled oscillators are governed by the sixth-order PDE, which is directly derived using the classical hypotheses of a curvilinear flexible beam movement theory. We apply FDM (Finite Difference Method) to reduce PDEs into ODEs, and the used number of spatial coordinate positions defines the number of involved oscillators approximating the dynamics of our continuous structural member (beam). Our procedure has a few advantages over the classical approaches, which has been illustrated and discussed. The proposed method has been validated for non-linear dynamical regimes by using the classical vibrational analysis (time histories, frequency power spectra and Poincaré maps).
| Original language | English |
|---|---|
| Pages (from-to) | 81-92 |
| Number of pages | 12 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 27 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - 1 Jan 2015 |
| Externally published | Yes |
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Keywords
- Beam
- Chaos
- Elasticity
- Network of oscillators
- Stability
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics
Cite this
Quantifying chaos of curvilinear beams via exponents. / Awrejcewicz, J.; Krysko, V. A.; Kutepov, I. E.; Vygodchikova, I. Yu; Krysko, A. V.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 27, No. 1-3, 01.01.2015, p. 81-92.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Quantifying chaos of curvilinear beams via exponents
AU - Awrejcewicz, J.
AU - Krysko, V. A.
AU - Kutepov, I. E.
AU - Vygodchikova, I. Yu
AU - Krysko, A. V.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We propose a procedure for predicting the stability loss and transition into chaos of a network of oscillators lying on a curve, where each of the oscillators can move in two perpendicular directions. Dynamics of the coupled oscillators are governed by the sixth-order PDE, which is directly derived using the classical hypotheses of a curvilinear flexible beam movement theory. We apply FDM (Finite Difference Method) to reduce PDEs into ODEs, and the used number of spatial coordinate positions defines the number of involved oscillators approximating the dynamics of our continuous structural member (beam). Our procedure has a few advantages over the classical approaches, which has been illustrated and discussed. The proposed method has been validated for non-linear dynamical regimes by using the classical vibrational analysis (time histories, frequency power spectra and Poincaré maps).
AB - We propose a procedure for predicting the stability loss and transition into chaos of a network of oscillators lying on a curve, where each of the oscillators can move in two perpendicular directions. Dynamics of the coupled oscillators are governed by the sixth-order PDE, which is directly derived using the classical hypotheses of a curvilinear flexible beam movement theory. We apply FDM (Finite Difference Method) to reduce PDEs into ODEs, and the used number of spatial coordinate positions defines the number of involved oscillators approximating the dynamics of our continuous structural member (beam). Our procedure has a few advantages over the classical approaches, which has been illustrated and discussed. The proposed method has been validated for non-linear dynamical regimes by using the classical vibrational analysis (time histories, frequency power spectra and Poincaré maps).
KW - Beam
KW - Chaos
KW - Elasticity
KW - Network of oscillators
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84928689525&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84928689525&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2015.02.016
DO - 10.1016/j.cnsns.2015.02.016
M3 - Review article
AN - SCOPUS:84928689525
VL - 27
SP - 81
EP - 92
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 1-3
ER -