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 | |
| Publication status | Published - 1 Sep 2011 |
| Externally published | Yes |
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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
Cite this
Effect of transverse shears on complex nonlinear vibrations of elastic beams. / Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.
In: Journal of Applied Mechanics and Technical Physics, Vol. 52, No. 5, 01.09.2011, p. 834-840.Research output: Contribution to journal › Article
}
TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=80155133894&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80155133894&partnerID=8YFLogxK
U2 - 10.1134/S0021894411050191
DO - 10.1134/S0021894411050191
M3 - Article
VL - 52
SP - 834
EP - 840
JO - Journal of Applied Mechanics and Technical Physics
JF - Journal of Applied Mechanics and Technical Physics
SN - 0021-8944
IS - 5
ER -