chapter
Vibration and Load Interaction in Post-Buckling Analyses of Thin-Walled Elements
WithF. Mohri, L. Azrar, M. Potier-Ferry
Pages 8

This work deals with vibration and load interactions in thin-walled elements with open cross sections. The vibration analysis is investigated under two types of static pre-loadings: pure compression and lateral bending forces. A non-linear model which accounts for non-linear warping, bending-bending and torsion-bending couplings is used for the analysis. Based on this model and on the Galerkin’s approach, dynamic equations are formulated. The equilibrium solutions in the pre-buckling and post-buckling ranges are computed using iterative methods. Using the tangent stiffness matrix derived around the static solution, the small vibration analysis is carried out and load-frequency curves are presented and discussed in both the pre-buckling and post-buckling zones. Sometimes, these response curves are linear according to the famous Southwell plot, especially for bisymmetric sections under compressive loads, in which case, they are also linear in the post-buckling range. Closed-form solutions are then formulated. In other load cases, such as in lateral buckling behaviour, the load-frequency curves are load height dependent and are never linear. In the post-buckling range, the load-frequency curve depends on the nature of the equilibrium path. The lowest eigenvalue Ω2 is positive when the solution is stable and negative when it is unstable.