Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Abstract

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω _p, q ₀} is reported, and scenarios of the system transition into chaos are illustrated.

Original language	English
Pages (from-to)	36-43
Number of pages	8
Journal	Acta Mechanica Sinica/Lixue Xuebao
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s10409-011-0412-5
Publication status	Published - 1 Feb 2011
Externally published	Yes

Keywords

Chaos
Euler-Bernoulli beams
Finite difference method
Finite element method

ASJC Scopus subject areas

Computational Mechanics
Mechanical Engineering

Access to Document

10.1007/s10409-011-0412-5

Fingerprint Dive into the research topics of 'Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods'. Together they form a unique fingerprint.

Cite this

@article{9bf99009dd474b42b45334806cf4389c,

title = "Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods",

abstract = "Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω p, q 0} is reported, and scenarios of the system transition into chaos are illustrated.",

keywords = "Chaos, Euler-Bernoulli beams, Finite difference method, Finite element method",

author = "J. Awrejcewicz and Krysko, {A. V.} and J. Mrozowski and Saltykova, {O. A.} and Zhigalov, {M. V.}",

year = "2011",

month = feb,

day = "1",

doi = "10.1007/s10409-011-0412-5",

language = "English",

volume = "27",

pages = "36--43",

journal = "Acta Mechanica Sinica/Lixue Xuebao",

issn = "0567-7718",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

AU - Awrejcewicz, J.

AU - Krysko, A. V.

AU - Mrozowski, J.

AU - Saltykova, O. A.

AU - Zhigalov, M. V.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω p, q 0} is reported, and scenarios of the system transition into chaos are illustrated.

AB - Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ω p, q 0} is reported, and scenarios of the system transition into chaos are illustrated.

KW - Chaos

KW - Euler-Bernoulli beams

KW - Finite difference method

KW - Finite element method

UR - http://www.scopus.com/inward/record.url?scp=79952847277&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952847277&partnerID=8YFLogxK

U2 - 10.1007/s10409-011-0412-5

DO - 10.1007/s10409-011-0412-5

M3 - Article

AN - SCOPUS:79952847277

VL - 27

SP - 36

EP - 43

JO - Acta Mechanica Sinica/Lixue Xuebao

JF - Acta Mechanica Sinica/Lixue Xuebao

SN - 0567-7718

IS - 1

ER -