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 |
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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 |
Keywords
- Beam models
- Chaos
- Nano-mechanics
- Vibrations
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics