Mechanics and control of coupled bending and twisting vibration of laminated beams

A shear-deformable beam theory is proposed to model the coupled bending and twisting vibration in laminated beams. Two types of coupling are considered: mass coupling and stiffness coupling. The control of the coupled vibration is accomplished by smart layers incorporated in the host structure. The capability of two different types of piezoelectric layers in detecting and supplying bending and twisting motion is addressed in this article. Traditional lead zirconate titanate (PZT) piezoelectric layers can detect and supply a twisting motion only indirectly, while a PZT/epoxy piezoelectric composite (PZT/Ep) has been shown to sense and actuate both bending and twisting motion. A modal cost and controllability analysis is discussed to compare the performance of the actuation configurations. In a series of examples, the PZT/Ep actuator has provided the best bending-twisting actuation for vibration damping.