On the identification of axial force in stay cables anchored to flexible supports

This paper analytically investigates the effect of flexible restraints on the modal properties of a shallow cable with small bending stiffness. An asymptotic second-order accurate closed form equation for the natural frequencies of the cable is presented. This expression generalizes a well-known result of the literature, valid in the particular case of perfectly clamped end sections, and allows one to define a single parameter that globally describes the flexibility of the cable restraints. The identifiability of this parameter within a frequency-based identification procedure is then critically discussed and a simple yet effective procedure to simultaneously identify the axial force and the bending stiffness of the cable is presented. A numerical example illustrates the performance of the proposed identification procedure in the case of modal frequencies contaminated by measurement errors.