Configuration optimization of piezoelectric patches attached to functionally graded shear-deformable cylindrical shells considering spillover effects

In this article, the optimal configurations of piezo-transducers for active vibration control of a functionally graded cylindrical shell are analyzed. The first-order shear deformation theory is employed for kinematic formulation of functionally graded cylindrical shell and piezo-patches. The boundary conditions of functionally graded shear-deformable cylindrical shell are simply supported, and the piezo-patches are attached to its surface. The Rayleigh–Ritz technique is used for deriving dynamic formulation and discretizing functionally graded shear-deformable cylindrical shell as well as piezoelectric transducers. The major goal of this study is to find optimal locations and orientations of piezoelectric transducers. The optimization procedure is designed based on desired controllability and observability of contributing modes as well as undesirable modes. Furthermore, in order to limit spillover effect, the effects of residual modes are regarded. The optimization variables are positions and angular orientations of piezo-patches. Genetic algorithm is utilized to evaluate the optimal configurations. For active vibration control, a negative velocity feedback control algorithm is used. The numerical results show that the optimization procedure is effective for vibration reduction. Moreover, by locating transducers in their optimal locations and orientations, the undesirable vibrations of functionally graded shear-deformable cylindrical shell would be suppressed quickly.