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.

后屈曲结构的高阶静态平衡名义上是不稳定的。最近的研究表明，通过致动两个与后屈曲梁结合的压电贴片，可以稳定二阶平衡，并且梁可以稳定地从一个一阶后屈曲形状过渡到另一阶，从而避免了卡扣现象。通过。本文考虑了通过使用三个或四个压电致动器片的致动，可以在多大程度上稳定被夹紧的后屈曲梁的三阶或四阶平衡。使用经过实验验证的数值建模方法，可以证明三阶和四阶平衡的稳定在物理上是可以实现的。考虑了两种驱动策略：一种对称策略，其中等幅电压施加到所有贴片，以及使用两个不同电压幅度的非对称策略。还考虑了各种致动器长度。使用任何一种激励策略，都表明三阶和四阶平衡都可以在参数空间的某些区域上保持稳定。实验证明了稳定的三阶和四阶平衡，并且与数值预测。