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 |
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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Cite this
Krysko, V. A., Zhigalov, M. V., Saltykova, O. A., & Krysko, A. V. (2011). Effect of transverse shears on complex nonlinear vibrations of elastic beams. Journal of Applied Mechanics and Technical Physics, 52(5), 834-840. https://doi.org/10.1134/S0021894411050191