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

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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.}",

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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

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