Post-buckled structures are prone to snap-through instabilities when external loading causes the structure to lose local stability and jump to a remote equilibrium. However, using piezoelectric actuation, structures can undergo entirely stable transitions between remote equilibria, thereby avoiding snap-through. This paper investigates the linearized vibrational properties of post-buckled beams along these stable transition paths. Numerical results are calculated using an elastica model with allowances for piezoelectric actuation. The model is non-dimensionalized to provide a general view of how the natural frequencies and corresponding mode shapes evolve during stable transitions. Results are presented for two types of stable transitions—one in which the transition is accomplished by changing the external load under a constant actuation level, and one in which the actuation levels are changed without external loading. Results show that the first four natural frequencies of the beam undergo complicated changes during a stable transition. Results also indicate that the first two mode shapes tend to be asymmetric and localized during the early and later stages of the transition. Yet, during the middle of the transition, when the static configuration of the beam is an anti-symmetric “S” shape, the first two mode shapes are symmetric and global. The natural frequencies and modes predicted by the numerical model are validated with a series of experiments.

当外部荷载导致结构失去局部稳定性并跳至远处的平衡状态时，后屈曲结构易于发生卡扣不稳定性。然而，使用压电致动，结构可以在远距离平衡之间经历完全稳定的过渡，从而避免了卡扣。本文研究了沿这些稳定过渡路径的后屈曲梁的线性振动特性。数值结果是使用具有压电驱动余量的弹性模型来计算的。该模型未进行尺寸标注，以提供自然频率和相应模式形状在稳定过渡期间如何演化的总体视图。给出了两种类型的稳定过渡的结果，其中一种是通过在恒定的驱动水平下改变外部负载来完成过渡的，一种是在没有外部负载的情况下改变致动水平的装置。结果表明，光束的前四个固有频率在稳定的过渡过程中会经历复杂的变化。结果还表明，在过渡的早期和后期，前两个模态形状趋于不对称且局部化。但是，在过渡过程中，当光束的静态构型为反对称的“ S”形时，前两个模态形状是对称且整体的。通过一系列实验验证了数值模型预测的固有频率和模式。结果还表明，在过渡的早期和后期，前两个模态形状趋于不对称且局部化。但是，在过渡过程中，当光束的静态构型为反对称的“ S”形时，前两个模态形状是对称且整体的。通过一系列实验验证了数值模型预测的固有频率和模式。结果还表明，在过渡的早期和后期，前两个模态形状趋于不对称且局部化。但是，在过渡过程中，当光束的静态构型为反对称的“ S”形时，前两个模态形状是对称且整体的。通过一系列实验验证了数值模型预测的固有频率和模式。