Minimal requirements for the vibration-based identification of the axial force, the bending stiffness and the flexural boundary conditions in cables

This paper aims at presenting the guidelines to follow in order to set up an identification procedure which is able to determine the axial force, the flexural rigidity and the rotational end stiffnesses of slender and tensioned structural elements, based on measurements of their natural frequencies and mode shapes. First of all, when such an element is slightly affected by bending stiffness effects, perturbation methods can be applied to get a composite approximation for its natural frequencies and an asymptotic expression for its mode shapes. These simple analytical formulas allow to understand the role played by each model parameter in the modal response and show that the axial force, the flexural rigidity and the rotational end stiffnesses can be correctly identified under some conditions, which are established and provided in this document. Among others, it is necessary that the identification procedure relies on the first few natural frequencies and mode shapes, which are measured near each extremity of the element, as well as some natural frequencies associated with higher modes.