Quantifying chaos by various computational methods. Part 2

Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise

Jan Awrejcewicz, Anton V. Krysko, Nikolay P. Erofeev, Vitalyi Dobriyan, Marina A. Barulina, Vadim A. Krysko

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number170
JournalEntropy
Volume20
Issue number3
DOIs
Publication statusPublished - 1 Mar 2018

Fingerprint

Euler-Bernoulli beams
chaos
vibration
kinematics
degrees of freedom
harmonics
approximation
excitation

Keywords

  • Bernoulli-Euler beam
  • Colored noise
  • Geometric nonlinearity
  • Lyapunov exponents
  • Noise induced transitions
  • True chaos
  • Wavelets

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Quantifying chaos by various computational methods. Part 2 : Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise. / Awrejcewicz, Jan; Krysko, Anton V.; Erofeev, Nikolay P.; Dobriyan, Vitalyi; Barulina, Marina A.; Krysko, Vadim A.

In: Entropy, Vol. 20, No. 3, 170, 01.03.2018.

Research output: Contribution to journalArticle

Awrejcewicz, Jan ; Krysko, Anton V. ; Erofeev, Nikolay P. ; Dobriyan, Vitalyi ; Barulina, Marina A. ; Krysko, Vadim A. / Quantifying chaos by various computational methods. Part 2 : Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise. In: Entropy. 2018 ; Vol. 20, No. 3.
@article{e244316bf4684d6e97cb0b093e462981,
title = "Quantifying chaos by various computational methods. Part 2: Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise",
abstract = "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.",
keywords = "Bernoulli-Euler beam, Colored noise, Geometric nonlinearity, Lyapunov exponents, Noise induced transitions, True chaos, Wavelets",
author = "Jan Awrejcewicz and Krysko, {Anton V.} and Erofeev, {Nikolay P.} and Vitalyi Dobriyan and Barulina, {Marina A.} and Krysko, {Vadim A.}",
year = "2018",
month = "3",
day = "1",
doi = "10.3390/e20030170",
language = "English",
volume = "20",
journal = "Entropy",
issn = "1099-4300",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "3",

}

TY - JOUR

T1 - Quantifying chaos by various computational methods. Part 2

T2 - Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise

AU - Awrejcewicz, Jan

AU - Krysko, Anton V.

AU - Erofeev, Nikolay P.

AU - Dobriyan, Vitalyi

AU - Barulina, Marina A.

AU - Krysko, Vadim A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - Bernoulli-Euler beam

KW - Colored noise

KW - Geometric nonlinearity

KW - Lyapunov exponents

KW - Noise induced transitions

KW - True chaos

KW - Wavelets

UR - http://www.scopus.com/inward/record.url?scp=85044211980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044211980&partnerID=8YFLogxK

U2 - 10.3390/e20030170

DO - 10.3390/e20030170

M3 - Article

VL - 20

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 3

M1 - 170

ER -