Planar oscillations of a cable-supported beam with feedback controlled actions

Active tendon control for slender and flexible structural systems such as guyed mast and cable-stayed bridge, is an innovative methodology to contain their oscillations. In this paper, a simple cable-supported cantilever beam is controlled by means of an imposed longitudinal displacement at the grounded end of the cable aiming to stabilize planar oscillation amplitudes of both cable and beam. The equations of motion of this system are obtained including cable elasticity through finite strain. Analytical eigensolutions of the linearized equations are used to investigate influences of mechanical characteristics on a family of structural systems and to derive a nonlinear discrete model by classical Galerkin method. A one mode model is used to design linear and nonlinear feedback control laws. Comparisons on the effectiveness of different strategies are made on the basis of both control intensity and system response amplitudes.