Cable Bearing Periodic And Random Movement Of The Stability And Control

The instability and control of an inclined stay cable under periodic and stochasticsupport-motion are studied in this thesis. First, differential equations of motioncontaining stochastic perturbation of the inclined stay cable is derived and convertedinto equations for the parametrically excited vibration of multi-degree-of-freedomsystem by using the Galerkin method. Stochastic parametrically excited vibration ofmain modes is considered. The Ito equation and its moment equation are derived.Perturbation solutions are expressed as the product of periodic component andexponent characteristics component by the Floquet theory. The period component andperiod coefficients are expanded into Fourier series. A series of algebraic equationsare derived and a eigenvalue problem is established according to the existence ofperturbation solution. The behavior of the perturbation solution is determined by thesign of eigenvalues. The instability of the parametrically excited system is directlydetermined by the solution of eigenvalues. Unstable regions of the cable are obtainedthrough the numerical computation, and verified by time-history response. The effectsof many factors on the cable instability are analyzed by large numbers of numericalresults.Stochastic parametrically excited vibration equations for the controlled cable arederived similarly and an approach to the instability is determined. The effectiveness ofpassive control using the isolator and damper is analyzed for the instability of thestochastic parametrically excited vibration. Furthermore, the optimal active controllaw is determined according to the dynamical programming principle and itsimplementable conditions for the cable are obtained. Then the optimal active controlforce is determined in terms of the mode control. The active control of theparametrically excited instability of the cable is studied. Finally, a large number ofnumerical results are obtained and analyzed according to the above method. It isinvestigated for the unstable regions and their comparison with numerical simulation, the effects of stochastic excitation intensity, supports motion, cable length, inclinedangle, tension and stiffness on instability, and the effectiveness of the optimal activecontrol.