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

Entropy

Anton V. Krysko¹  Vadim A. Krysko²  Jan Awrejcewicz³  Vitalyi Dobriyan⁴  Nikolay P. Erofeev⁴  Marina A. Barulina⁵ 

[1] Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russia;Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politechnicheskaya Str., 410054 Saratov, Russia;Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054 Saratov, Russia;Precision Mechanics and Control Institute, Russian Academy of Science, 24 Rabochaya Str., 410028 Saratov, Russia;

关键词: geometric nonlinearity;    Bernoulli–Euler beam;    colored noise;    noise induced transitions;    true chaos;    Lyapunov exponents;    wavelets;   

DOI  :  10.3390/e20030170

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown