Theoretical modelling of arch-shaped carbon nanotube resonators exhibiting Euler-Bernoulli snap-through bi-stability

In this work, we present a detailed static and dynamic analysis of a recently reported electrically actuated buckled carbon nanotube (CNT) resonator, based on the Euler-Bernoulli beam theory. The system behavior is analyzed using the Galerkin reduced order model. We show that a simple single-modal analysis can already predict snap-through bi-stability in a buckled CNT resonator. However, we prove that the experimental data, in which the snap-through buckling occurs at a finite frequency, cannot be explained without taking into account out-of-plane motion. The buckled CNTs are the first type of buckled beams to exhibit out-of-plane static motion, resulting in a unique three-dimensional snap-through transition, never before predicted. In addition, we show the criteria under which these devices can also exhibit latching phenomena, meaning that they can maintain their buckle configuration when no force is applied, making these devices appealing for mechanical memory applications.