Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams

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	https://doi.org/10.1016/j.ijnonlinmec.2017.03.006
Publication status	Published - 1 Jul 2017

Keywords

Beam models
Chaos
Nano-mechanics
Vibrations

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Applied Mathematics

Access to Document

10.1016/j.ijnonlinmec.2017.03.006

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Krysko, A. V., Awrejcewicz, J., Zhigalov, M. V., Pavlov, S. P., & Krysko, V. A. (2017). Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams. International Journal of Non-Linear Mechanics, 93, 106-121. https://doi.org/10.1016/j.ijnonlinmec.2017.03.006

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

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