Multi-mode Vibration Averagely Control for Cylindrical Shells by Optimally Distributed Piezoelectric Sensors and Actuators

Purpose Multi-modal vibration control often causes modal peaks' reductions unevenly, which makes the active vibration suppression system less effective to the broadband disturbance. To this end, a multi-mode vibration average suppression method for cylindrical shells with optimally distributed piezoelectric sensors and actuators (S/As) is proposed in this paper. Methods Based on the equivalent homogenized parameters of the macro-fiber composite (MFC), the modal control force of MFC with a tilt angle is derived. Its form is similar to that of the modal sensing signal with a tilt angle. A modified S/As placement optimization criterion of maximum observability and controllability for average distribution of the control efficiencies of multi-mode is also proposed. Thus, an optimization model of considering the positions and orientations of orthotropic piezoelectric S/As for the cylindrical shell multi-mode vibration control is established. Result The proposed method is applied to optimize the S/As distribution of a cantilever cylindrical shell. The results of optimization placement show that the S/As are placed near the free ends, their tilt angles tend to π/2 rad. To valid the effectiveness of optimized S/As distribution, a linear quadratic Gaussian (LQG) controller with Kalman filter is applied to control the response of cylindrical shell under the harmonic and transient excitations. Conclusion The vibration control system with S/As distribution optimized by the modified criterion could suppress all the response peaks more averagely than that under the original criterion, and achieve better vibration control performance. In addition, including the tilt angle in the optimization problem, the efficiency and the uniformity of the multi-mode vibration suppression system could be improved.