Abstract
We propose a novel mathematical model of a vibrating multi-layer Timoshenko-type beam. We show that the introduced model essentially changes the type of partial differential equations allowing inclusion of rotational inertial effects. We illustrate and discuss the influence of boundary conditions, the beam layers and parameters of the external load on the non-linear dynamics of this composite beam including a study of its regular, bifurcation and chaotic behavior.The originally derived infinite problem is reduced to the finite one using either Finite Difference Method (FDM) or Finite Element Method (FEM) which guarantees validity and reliability of the obtained numerical results. In addition, a comparative study is carried out aiming at a proper choice of the efficient wavelet transform. In particular, scenarios of transition into chaos are studied putting emphasis on novel phenomena. Charts of the system dynamical regimes are also constructed with respect to the control parameters regarding thickness and composition of the beam layers.
| Original language | English |
|---|---|
| Pages (from-to) | 2568-2589 |
| Number of pages | 22 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 19 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 1 Aug 2014 |
| Externally published | Yes |
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Keywords
- Bifurcation
- Chaos
- Multi-layer Timoshenko beams
- Wavelets
ASJC Scopus subject areas
- Modelling and Simulation
- Numerical Analysis
- Applied Mathematics
Cite this
Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects. / Krysko, A. V.; Awrejcewicz, J.; Saltykova, O. A.; Zhigalov, M. V.; Krysko, V. A.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 8, 01.08.2014, p. 2568-2589.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects
AU - Krysko, A. V.
AU - Awrejcewicz, J.
AU - Saltykova, O. A.
AU - Zhigalov, M. V.
AU - Krysko, V. A.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - We propose a novel mathematical model of a vibrating multi-layer Timoshenko-type beam. We show that the introduced model essentially changes the type of partial differential equations allowing inclusion of rotational inertial effects. We illustrate and discuss the influence of boundary conditions, the beam layers and parameters of the external load on the non-linear dynamics of this composite beam including a study of its regular, bifurcation and chaotic behavior.The originally derived infinite problem is reduced to the finite one using either Finite Difference Method (FDM) or Finite Element Method (FEM) which guarantees validity and reliability of the obtained numerical results. In addition, a comparative study is carried out aiming at a proper choice of the efficient wavelet transform. In particular, scenarios of transition into chaos are studied putting emphasis on novel phenomena. Charts of the system dynamical regimes are also constructed with respect to the control parameters regarding thickness and composition of the beam layers.
AB - We propose a novel mathematical model of a vibrating multi-layer Timoshenko-type beam. We show that the introduced model essentially changes the type of partial differential equations allowing inclusion of rotational inertial effects. We illustrate and discuss the influence of boundary conditions, the beam layers and parameters of the external load on the non-linear dynamics of this composite beam including a study of its regular, bifurcation and chaotic behavior.The originally derived infinite problem is reduced to the finite one using either Finite Difference Method (FDM) or Finite Element Method (FEM) which guarantees validity and reliability of the obtained numerical results. In addition, a comparative study is carried out aiming at a proper choice of the efficient wavelet transform. In particular, scenarios of transition into chaos are studied putting emphasis on novel phenomena. Charts of the system dynamical regimes are also constructed with respect to the control parameters regarding thickness and composition of the beam layers.
KW - Bifurcation
KW - Chaos
KW - Multi-layer Timoshenko beams
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=84894321761&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84894321761&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2013.12.013
DO - 10.1016/j.cnsns.2013.12.013
M3 - Review article
AN - SCOPUS:84894321761
VL - 19
SP - 2568
EP - 2589
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 8
ER -