The problem of vibration control of overhead line conductors subjected to laminar transverse wind, inducing stationary vibrations by Karmán effect is of high importance due to consequences upon these structures lifetime and service. We consider the cable model as Euler-Bernoulli beam that include the influence of cable rigidity and that respect the author condition which detaches the suspended cable model of the beam model with viscous, hysteretic or dry friction internal damping hypothesis. The original analytical expression of the free vibration modes and the resonance frequencies equation for the cable with clamped extremities has produced. Some experimental aspects are underlined in the paper
