document: Vibration control of the rotating flexible-shaft/multi-flexible-disk system with the eddy-current damper In this paper , the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by applying the assumed-mode method into the kinetic and strain energies , and the virtual work done by the eddy-current damper . From Lagrange 's equations , the resulting discretized equations of motion can be simplified as a bilinear system -LRB- BLS -RRB- . Introducing the control laws , including the quadratic , nonlinear and optimal feedback control laws , into the BLS , it is found that the eddy-current damper can be used to suppress flexible and shear vibrations simultaneously , and the system is globally asymptotically stable . Numerical results are provided to validate the theoretical analysis
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extractive_keyphrases: virtual work discretized equations of motion bilinear system optimal feedback control laws shear vibrations
abstractive_keyphrases: rotating flexible-shaft/multi-flexible-disk system eddy-current damper rotating flexible-timoshenko-shaft/flexible-disk coupling system assumed-mode method lagrange's equations quadratic feedback control laws nonlinear feedback control laws flexible vibrations