Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh–Ritz modes using genetic algorithm

In this study, the active vibration control and configurational optimization of a cylindrical shell are analyzed by using piezoelectric transducers. The piezoelectric patches are attached to the surface of the cylindrical shell. The Rayleigh–Ritz method is used for deriving dynamic modeling of cylindrical shell and piezoelectric sensors and actuators based on the Donnel–Mushtari shell theory. The major goal of this study is to find the optimal locations and orientations of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, in order to limit spillover effects, the residual modes are taken into consideration. The optimization variables are the positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. In this article, for improving the maximum power and capacity of actuators for amplitude depreciation of negative velocity feedback strategy, we have proposed a new control strategy, called “Saturated Negative Velocity Feedback Rule (SNVF)”. The numerical results show that the optimization procedure is effective for vibration reduction, and specifically, by locating actuators and sensors in their optimal locations and orientations, the vibrations of cylindrical shell are suppressed more quickly.