Comparison of the Von Kármán and Kirchhoff models for the post-buckling and vibrations of elastic beams
Résumé
We compare different models describing the buckling, post-buckling and vibrations of elastic beams in the plane. Focus is put on the first buckled equilibrium solution and the first two vibration modes around it. In the incipient post-buckling regime, the classic Woinowsky-Krieger model is known to grasp the behavior of the system. It is based on the von Kármán approximation, a 2nd order expansion in the strains of the buckled beam. But as the curvature of the beam becomes larger, the Woinowsky-Krieger model starts to show limitations and we introduce a 3rd order model, derived from the geometrically-exact Kirchhoff model. We discuss and quantify the shortcomings of the Woinowsky-Krieger model and the contributions of the 3rd order terms in the new model, and we compare them both to the Kirchhoff model. Different ways to nondi-mensionalize the models are compared and we believe that, although this study is performed for specific boundary conditions, the present results have a general scope and can be used as abacuses to estimate the validity range of the simplified models.
| Origine | Fichiers éditeurs autorisés sur une archive ouverte |
|---|---|
| Licence |
![]()
Cite 10.5281/zenodo.4766972 Rapport Vetyukov, Y., & Popp, A. (2021). Review of ‘Comparison of the Von Kármán and Kirchhoff models for the post-buckling and vibrations of elastic beams’. Zenodo. https://doi.org/10.5281/ZENODO.4766972