Free linear vibrations of cables under thermal stress

This paper aims at investigating the effect of thermal stress on free linear vibrations of cables. An analytical model extending Irvine's theory to thermoelasticity is proposed. In addition to the sag-extensibility parameter, this model yields a second dimensionless independent parameter related to the temperature change. Some general two-dimensional contour plots are presented giving the relative change in natural frequencies due to temperature with respect to the only two independent parameters of the problem. Depending on their values, this change can be quite significant. For in-plane symmetric modes, it is shown that a positive (resp. negative) temperature change does not necessarily decrease (resp. increase) natural frequencies and that thermoelastic effects can lead to cross-over due to the modification of the initial sag.