Three-dimensional vibration suppression of flexible beams under multi-directional excitations via piezoelectric actuators: Theoretical and experimental investigations

In this paper, we propose a control strategy that uses piezoelectric actuators to suppress three-dimensional (3D) vibrations in flexible beams. Three control strategies for suppressing 3D vibrations of a beam under y direction excitation and combined y and z direction excitations are studied theoretically and experimentally. The influences of actuator arrangement on 3D vibration suppression performance are analyzed. In addition, the effectiveness of the proposed control strategy under combined y and z direction excitations with random disturbances is also investigated. Finally, the proposed algorithm is compared with the traditional PID algorithm. Results indicate that single-direction transverse excitation induces vibrations in multiple directions of the beam. While a single piezoelectric actuator can effectively suppress vibrations along the excitation direction, its influence on adjacent directions is limited and may even exacerbate the vibration. In contrast, employing two independently controlled piezoelectric actuators positioned at adjacent beam roots significantly enhances 3D vibration suppression under various excitations compared to a single actuator. Furthermore, an equidistant arrangement of actuators at the beam root achieves superior vibration suppression performance and requires lower voltage than a non-equidistant configuration. Additionally, the proposed control strategy exhibits strong disturbance rejection and outperforms the traditional PID algorithm in 3D vibration suppression.