NONLINEAR OSCILLATIONS OF A NONRESONANT CABLE UNDER INPLANE EXCITATION WITH A LONGITUDINAL CONTROL

The nonlinear oscillations of a controlled suspended elastic cable und er in-plane excitation are considered. Active control realized by long itudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadra tic enhanced velocity feedback control laws are chosen and their effec ts on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane st eady-state solutions and their stability under an out-of-plane disturb ance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence o f the control effectiveness on the system parameters is investigated i n the case of the first symmetric mode and the range of oscillation am plitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quant ities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered whe n the motion is characterized by two comparable components.