Effect of transverse shears on complex nonlinear vibrations of elastic beams

Abstract

Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h²) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ≤ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.

Original language	English
Pages (from-to)	834-840
Number of pages	7
Journal	Journal of Applied Mechanics and Technical Physics
Volume	52
Issue number	5
DOIs	https://doi.org/10.1134/S0021894411050191
Publication status	Published - 1 Sep 2011
Externally published	Yes

Keywords

chaos
elastic beams
finite difference method
finite element method
mathematical modeling
nonlinear dynamics

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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title = "Effect of transverse shears on complex nonlinear vibrations of elastic beams",

abstract = "Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ≤ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.",

keywords = "chaos, elastic beams, finite difference method, finite element method, mathematical modeling, nonlinear dynamics",

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

year = "2011",

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doi = "10.1134/S0021894411050191",

language = "English",

volume = "52",

pages = "834--840",

journal = "Journal of Applied Mechanics and Technical Physics",

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number = "5",

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T1 - Effect of transverse shears on complex nonlinear vibrations of elastic beams

AU - Krysko, V. A.

AU - Zhigalov, M. V.

AU - Saltykova, O. A.

AU - Krysko, A. V.

PY - 2011/9/1

Y1 - 2011/9/1

N2 - Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ≤ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.

AB - Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ≤ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.

KW - chaos

KW - elastic beams

KW - finite difference method

KW - finite element method

KW - mathematical modeling

KW - nonlinear dynamics

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EP - 840

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

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