Conical shell vibration optimal control with distributed piezoelectric sensor and actuator layers

In this study, conical shell vibration with distributed piezoelectric layers on the shell surface is controlled by a distributed optimal controller. Two piezoelectric layers are distributed on the conical shell surface with the same geometry and they are segmented into the same numbers of patches. One piezoelectric layer is considered to be a sensor layer and the other one is considered to be an actuator layer. An optimal controller with various constants for each piezoelectric patch is determined with an optimal input voltage. The conical shell electromechanical equations of motions with piezoelectric layers are extracted. The Galerkin method is used for obtaining the time domain equations and after that optimal constants of the controller are determined. Various kinds of distribution for the piezoelectric layer are considered and their effects on the conical shell vibration control are evaluated. For a better assessment, free vibration response, forced vibration response with concentrated and distributed force, and the frequency response of the considered system are computed and compared with the uncontrolled response. The results show the high impact of the optimal controller on the vibration mitigation of the conical shell and also the actuator applied voltage amplitude is considerably low. The applicability of the piezoelectric layer in the conical shell vibration mitigation is vividly determined by using an optimal controller which decreases the actuator applied voltage amplitude dramatically.