Active vibration control of composite sandwich beams with piezoelectric extension-bending and shear actuators

We have used quasi-static equations of piezoelectricity to derive a finite element formulation capable of modelling two different kinds of piezoelastically induced actuation in an adaptive composite sandwich beam. This formulation is made to couple certain piezoelectric constants to a transverse electric field to develop extension-bending actuation and shear-induced actuation. As an illustration, we present a sandwich model of three sublaminates: face/core/face. We develop a control scheme based on the linear quadratic regulator/independent modal space control (LQR/IMSC) method and use this to estimate the active stiffness and the active damping introduced by shear and extension-bending actuators. To assess the performance of each type of actuator, a dynamic response study is carried out in the modal domain. We observe that the shear actuator is more efficient in actively controlling the vibration than the extension-bending actuator for the same control effort.