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.