Comparison of the Von Kármán and Kirchhoff models for the post-buckling and vibrations of elastic beams

We compare different models describing the buckling, post-buckling and vibrations of elastic beams in plane. Focus is put on first buckled equilibrium solution two vibration modes around it. In incipient regime, classic Woinowsky-Krieger model known to grasp behavior system. It based von Kármán approximation, a 2nd order expansion strains beam. But as curvature beam becomes larger, starts show limitations we introduce 3rd model, derived from geometrically-exact Kirchhoff model. discuss quantify shortcomings contributions terms new them both Different ways nondi-mensionalize are compared believe that, although this study performed for specific boundary conditions, present results have general scope can be used abacuses estimate validity range simplified models.