Abstract
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω p, q 0} is reported, and scenarios of the system transition into chaos are illustrated.
| Original language | English |
|---|---|
| Pages (from-to) | 36-43 |
| Number of pages | 8 |
| Journal | Acta Mechanica Sinica/Lixue Xuebao |
| Volume | 27 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2011 |
| Externally published | Yes |
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Keywords
- Chaos
- Euler-Bernoulli beams
- Finite difference method
- Finite element method
ASJC Scopus subject areas
- Computational Mechanics
- Mechanical Engineering
Cite this
Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods. / Awrejcewicz, J.; Krysko, A. V.; Mrozowski, J.; Saltykova, O. A.; Zhigalov, M. V.
In: Acta Mechanica Sinica/Lixue Xuebao, Vol. 27, No. 1, 01.02.2011, p. 36-43.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods
AU - Awrejcewicz, J.
AU - Krysko, A. V.
AU - Mrozowski, J.
AU - Saltykova, O. A.
AU - Zhigalov, M. V.
PY - 2011/2/1
Y1 - 2011/2/1
N2 - Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω p, q 0} is reported, and scenarios of the system transition into chaos are illustrated.
AB - Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω p, q 0} is reported, and scenarios of the system transition into chaos are illustrated.
KW - Chaos
KW - Euler-Bernoulli beams
KW - Finite difference method
KW - Finite element method
UR - http://www.scopus.com/inward/record.url?scp=79952847277&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952847277&partnerID=8YFLogxK
U2 - 10.1007/s10409-011-0412-5
DO - 10.1007/s10409-011-0412-5
M3 - Article
VL - 27
SP - 36
EP - 43
JO - Acta Mechanica Sinica/Lixue Xuebao
JF - Acta Mechanica Sinica/Lixue Xuebao
SN - 0567-7718
IS - 1
ER -