Stabilizing higher-order equilibria of post-buckled beams using piezoelectric actuation

Abstract

The higher-order static equilibria of post-buckled structures are nominally unstable. Recently it has been shown that by actuating two piezoelectric patches bonded to a post-buckled beam, the second-order equilibria can be stabilized and the beam can stably transition from one first-order post-buckled shape to the other, thereby avoiding snap-through. This paper considers the extent to which third- or fourth-order equilibria of clamped–clamped post-buckled beams can be stabilized using actuation of three or four patches of piezoelectric actuators. Using a numerical modeling approach that is validated with experiments, it is shown that stabilization of third- and fourth-order equilibria is physically realizable. Two actuation strategies are considered: a symmetric one in which voltages of equal magnitude are applied to all patches, and an asymmetric strategy in which two different voltage magnitudes are used. Various actuator lengths are also considered. Using either actuation strategy, it is shown that both the third- and fourth-order equilibria can stabilize over certain regions of parameter space. Stabilized third- and fourth-order equilibria are demonstrated experimentally and correlate well with numerical predictions.