Frequency and mode change in the large deflection and post-buckling of compact and thin-walled beams

This paper deals with the investigation of normal modes change of metallic structures, when subjected to geometrical nonlinearities in the large displacement/rotations field. Namely, a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach are employed to formulate higher order beam theories including geometric nonlinearities. Thus, a finite element approximation is used along with a path-following method to perform nonlinear analyses. Linearized vibration modes around equilibrium states and along the whole equilibrium path of structures subjected to bending and compression loadings are evaluated by solving a classical eigenvalue problem. In order to show the capabilities of the proposed methodology, both solid and thin-walled cross-section beams are considered. The analyses demonstrate that, with some differences depending on the geometry and both boundary and loading conditions, natural frequencies and modal shapes may change significantly as the structure is subjected to large displacements and rotations.