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Open AccessFeature PaperArticle

Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli–Euler Beam Subjected to Periodic and Colored Noise

1
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland
2
Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russia
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Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politechnicheskaya, 410054 Saratov, Russia
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Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya, 410054 Saratov, Russia
5
Precision Mechanics and Control Institute, Russian Academy of Science, 24 Rabochaya Str., 410028 Saratov, Russia
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(3), 170; https://doi.org/10.3390/e20030170
Received: 17 January 2018 / Revised: 16 February 2018 / Accepted: 1 March 2018 / Published: 5 March 2018
(This article belongs to the Special Issue Entropy in Dynamic Systems)
In this part of the paper, the theory of nonlinear dynamics of flexible Euler–Bernoulli beams (the kinematic model of the first-order approximation) under transverse harmonic load and colored noise has been proposed. It has been shown that the introduced concept of phase transition allows for further generalization of the problem. The concept has been extended to a so-called noise-induced transition, which is a novel transition type exhibited by nonequilibrium systems embedded in a stochastic fluctuated medium, the properties of which depend on time and are influenced by external noise. Colored noise excitation of a structural system treated as a system with an infinite number of degrees of freedom has been studied. View Full-Text
Keywords: geometric nonlinearity; Bernoulli–Euler beam; colored noise; noise induced transitions; true chaos; Lyapunov exponents; wavelets geometric nonlinearity; Bernoulli–Euler beam; colored noise; noise induced transitions; true chaos; Lyapunov exponents; wavelets
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MDPI and ACS Style

Awrejcewicz, J.; Krysko, A.V.; Erofeev, N.P.; Dobriyan, V.; Barulina, M.A.; Krysko, V.A. Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli–Euler Beam Subjected to Periodic and Colored Noise. Entropy 2018, 20, 170. https://doi.org/10.3390/e20030170

AMA Style

Awrejcewicz J, Krysko AV, Erofeev NP, Dobriyan V, Barulina MA, Krysko VA. Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli–Euler Beam Subjected to Periodic and Colored Noise. Entropy. 2018; 20(3):170. https://doi.org/10.3390/e20030170

Chicago/Turabian Style

Awrejcewicz, Jan; Krysko, Anton V.; Erofeev, Nikolay P.; Dobriyan, Vitalyi; Barulina, Marina A.; Krysko, Vadim A. 2018. "Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli–Euler Beam Subjected to Periodic and Colored Noise" Entropy 20, no. 3: 170. https://doi.org/10.3390/e20030170

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