Cable tension estimation by means of vibration response andmoving mass technique

Abstract

This paper approaches a novel technique to estimate cable tension simply based on itsvibration response. The vibration response has been quite extensively adopted in the pastdue to its simplicity and, mainly, because the inverse approach allows the tensionestimation with the cable in its original site. A first tentative approach consists inusing a certain number of experimentally measured natural frequencies to be introduced inthe theoretical vibration formula; this formula, however, involves also the cable length,the cable mass per unit length and its flexural rigidity. Unfortunately, some problemsarise in its application to real structures, such as the case of suspended andcable-stayed bridges, because the exact cable length cannot be measured (it appears at thefourth exponent in the vibration formula); moreover section and weight can be estimatedwithin a certain degree of accuracy, whilst the boundary conditions are often defined withdifficulty. A novel extension of the method is here proposed, which takes advantage from amoving mass travelling on the cable. This is the case occurring when cables are verifiedwith magnetic-based technology to detect rope faults and cross section reduction. In thisway, the extracted natural frequencies are varying with time due to the moving load, andhence they have to be extracted adopting a time-varying approach. Although someapproximation linked to the shape modification must be introduced, a simple iterativeprocedure can be settled, by considering the cable length as an unknown. An estimation ofthe equivalent length is given, and successively this value is used to obtain anestimation of the cable tension.