Vibration Control of the Rotating Flexible-Shaft/Multi-Flexible-Disk System With the Eddy-Current Damper

Abstract

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 (BLS). 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.