Fundamental frequency evolution in slender beams subjected to imposed axial displacements

The influence of applied axial loads on the fundamental vibration frequency is strictly connected with the stability analysis of elastic slender beams. For this reason, the correct evaluation of the fundamental frequency is of primary importance in designing new structures and components, as well as in monitoring existing ones. At the same time, if an internal axial load arises in a slender element as the consequence of an imposed (static) axial end displacement, then a different dynamic structural response is encountered respect to the case in which a beam end is free to slide, during transverse vibration, and a (constant) axial load is applied externally. This difference is due to the change in the axial boundary condition. Moreover, the presence of an initial curvature of the beam axis may significantly affect the aforesaid response. The experimental study proposed in the present paper investigates the dependence of the fundamental frequency on the axial load in slender beams subjected to imposed axial end displacements. The considered specimens presented different geometrical imperfections (initial curvatures), and were tested in two different constraint conditions (hinged-hinged and hinged-clamped). In addition, the behaviors observed during the experiments were reproduced by numerical simulations offering a valid confirmation for test results and contributing to understand the evolution of the fundamental frequency in the analyzed slender elements subjected to imposed axial end displacements.