Active vibration control of elastically restrained rotating beams with piezoelectric patches placement optimization

This paper establishes a dynamic model of an elastically restrained rotating beam equipped with piezoelectric sensors/actuators, and the ability to actively control vibrations of this beam subjected to mixed excitation with optimization of the placement of piezoelectric patches is investigated. The elastic boundary conditions are simulated via the artificial spring technique, and the stiffening effect resulting from rotation motion is considered by adding potential energy due to the centrifugal force. The displacement field is expanded using the modified Fourier series method, and the system governing equations are derived through the Lagrange equations. On the basis of the controllability Gramian matrix, the placement of piezoelectric sensors/actuators is optimized for the first two flapwise modal vibrations and their combination, and the effects of boundary stiffness and rotational speed on the optimization results and corresponding control performance are studied. The results indicate that the linear spring stiffness significantly influences the optimization results, whereas the torsional spring stiffness and rotational speed have little effect on the optimization results. Finally, a vibration control experiment was conducted on a rotating beam to verify the correctness and effectiveness of the proposed control system.