Bearing Movement Caused By The Unstable Vibration Control Of Stay Cables

The instability and control of an inclined taut cable under support-motion excitations are studied in this paper. A direct approach to the instability of a parametrically excited cable system with multi-degree-of-freedom (MDOF) and an optimal control strategy for the system have been proposed. First, differential equations of motion of the inclined taut cable is derived and converted into equations for the parametrically excited vibration of MDOF system by using the Galerkin method. Second, the problem of parametrically excited instability of the MDOF system is converted into an eigenvalue problem based on the Floquet theory, Fourier series and generalized eigenvalue analysis, by which the instability is determined directly. Third, parametrically excited vibration equations for the controlled cable are derived and an approach to the instability is determined similarly. Furthermore, the optimal active control law is determined according to the dynamical programming principle and its implementable conditions for the cable are obtained. Then the optimal active control force is determined in terms of the mode control. The active control of the parametrically excited instability of the cable is studied. Finally, a large number of numerical results are obtained and analyzed according to the above method. It is investigated for the instable regions and their comparison with numerical simulation, the effects of supports motion, cable length, inclined angle, tension and stiffness on instability, and the effectiveness of the passive control and optimal active control. The results illustrate that in general, the parametrically excited instability of inclined taut cables is increased with excitation amplitude and frequency; the effectiveness of the passive control is not so good, but the effectiveness of the optimal active control is remarkable for the cable instability.