Numerical and experimental determination of natural frequencies and critical loads for compressed open thin-walled beams

As is well known, thin-walled open profiles have an appreciable bending stiffness at least about one of the principal axes of inertia, but a low torsional stiffness. In addition, boundary effects do not have rapid extinction, and the contribution of warping stiffness may be crucial. Due to the widespread application of open thin-walled beams in engineering, vibration and stability analyses are of prime interest for this kind of elements. Since strain modes of thin-walled beams can be coupled according to the cross-section geometry, the pre-buckling equilibrium path can affect both the critical load and the natural frequencies. We have investigated on the effects of non-trivial equilibrium paths and warping constraints in thin-walled open profiles by a numerical in-house code based on a finite difference procedure, where stability is analyzed in a dynamic setting. This has provided interesting results when coupled with a direct one-dimensional model of standard beam enriched with a coarse descriptor of warping. Thus, we have undertaken an experimental campaign to verify these results, starting from the most simple cases to prepare and measure, i.e., beams with two axes of symmetry. In this contribution, we present some numerical and experimental results in terms of natural frequencies and critical loads for compressed thin-walled beams, having cruciform cross-sections with a vanishing or a remarkable warping stiffness. The specimens were subject to axial loads by means of a universal testing machine, and the natural frequencies were extracted, using piezoelectric pickups, for increasing values of the axial compressive force.