On the axial force identification in Euler-Bernoulli beams with unknown boundary conditions

Identification of the tensile force in slender axially-loaded structural elements, such as stay cables, metallic bars and tie-rods, is of paramount importance for health mon- itoring and safety assessment purposes. Dynamic testing techniques provide the ground for quick and cheap identification strategies, based on the knowledge of: (a) a set of iden- tified natural frequencies, and (b) a structural model that relates natural frequencies to the axial-force value. Within this framework, reliability of the identified axial force values depends, among other factors, on the predictive capabilities of the underlying structural model. Errors may arise, in particular, from the modeling of boundary conditions. The present paper analytically investigates the effect of boundary conditions on the modal prop- erties of axially loaded Euler-Bernoulli beam elements. Starting from theoretical results obtained on this archetypal structural model, a numerical procedure for the identification of the axial force in beam elements with unknown bending stiffness and boundary condi- tions is then presented. Parametric analyses are carried out to quantitatively assess the accuracy of the proposed identification algorithm in the case of frequencies contaminated by measurement errors.