The linear theory of free vibrations of a suspended cable

A linear theory is developed for the free vibrations of a uniform suspended cable in which the ratio of sag to span is about 1:8, or less. Both in-plane and out-of-plane motion is considered. It is shown that the analysis of the symmetric in-plane modes is heavily dependent on a parameter which allows for the effects of cable geometry and elasticity. The results of simple experiments are reported which establish the validity of the theory.