Cable tension estimation by means of vibration response and moving mass technique

Abstract

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