Spatially Distributed Orthogonal Piezoelectric Shell Actuators: Theory And Applications

Abstract

The distributed structural control of elastic shell continua using spatially distributed orthogonal piezoelectric actuators is proposed and three generic distributed feedback algorithms with spatial feedback functions are formulated. In order to prevent spillovers from the modal couplings of feedback forces, the distributed actuators are spatially shaped to be orthogonal to those undesirable modes. Consequently, the distributed feedback functions evolve to modal feedback functions which can be represented as a gain factor and a spatially distributed mode shape (actuator) function. In practice, the actuator can be shaped and convolved based on the prescribed mode shape function and the gain factor can be treated as a weighting factor. To demonstrate the utilities of the generic theory, distributed orthogonal convolving modal actuators designed for a circular ring shell are proposed and their control effectiveness evaluated. Analyses suggested that the primary control action comes from the in-plane membrane control forces; the contribution from the electric bending moment is relatively insignificant for lower natural modes, i.e., n < 10. It was observed that the control effect increases as the structural stiffness decreases or the structural flexibility increases. Increasing the control moment arm (as the ring becomes thicker) of the actuator layer seems insignificant in the overall control effect for lower natural modes.