Abstract
In the present part of the paper various problems of non-linear dynamics of nano-beams within the modified couple stress theory as well as the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson models are studied taking into account the geometric non-linearity. Different characteristics of the vibrational process, including Fourier spectra, wavelet spectra, phase portraits, Poincaré maps as well as the largest Lyapunov exponents, are studied for the same physical-geometric parameter with and without consideration of the size-dependent behaviour. Vibration graphs are constructed and analysed, and scenarios of transition from regular to chaotic vibrations are illustrated and discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 106-121 |
| Number of pages | 16 |
| Journal | International Journal of Non-Linear Mechanics |
| Volume | 93 |
| DOIs | |
| Publication status | Published - 1 Jul 2017 |
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Keywords
- Beam models
- Chaos
- Nano-mechanics
- Vibrations
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
Cite this
Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams. / Krysko, A. V.; Awrejcewicz, J.; Zhigalov, M. V.; Pavlov, S. P.; Krysko, V. A.
In: International Journal of Non-Linear Mechanics, Vol. 93, 01.07.2017, p. 106-121.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams
AU - Krysko, A. V.
AU - Awrejcewicz, J.
AU - Zhigalov, M. V.
AU - Pavlov, S. P.
AU - Krysko, V. A.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - In the present part of the paper various problems of non-linear dynamics of nano-beams within the modified couple stress theory as well as the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson models are studied taking into account the geometric non-linearity. Different characteristics of the vibrational process, including Fourier spectra, wavelet spectra, phase portraits, Poincaré maps as well as the largest Lyapunov exponents, are studied for the same physical-geometric parameter with and without consideration of the size-dependent behaviour. Vibration graphs are constructed and analysed, and scenarios of transition from regular to chaotic vibrations are illustrated and discussed.
AB - In the present part of the paper various problems of non-linear dynamics of nano-beams within the modified couple stress theory as well as the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson models are studied taking into account the geometric non-linearity. Different characteristics of the vibrational process, including Fourier spectra, wavelet spectra, phase portraits, Poincaré maps as well as the largest Lyapunov exponents, are studied for the same physical-geometric parameter with and without consideration of the size-dependent behaviour. Vibration graphs are constructed and analysed, and scenarios of transition from regular to chaotic vibrations are illustrated and discussed.
KW - Beam models
KW - Chaos
KW - Nano-mechanics
KW - Vibrations
UR - http://www.scopus.com/inward/record.url?scp=85015628571&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85015628571&partnerID=8YFLogxK
U2 - 10.1016/j.ijnonlinmec.2017.03.006
DO - 10.1016/j.ijnonlinmec.2017.03.006
M3 - Article
AN - SCOPUS:85015628571
VL - 93
SP - 106
EP - 121
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
SN - 0020-7462
ER -