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 present a detailed two-dimensional analysis, which predicts static behavior similar to buckled micro-beams, despite the difference in the force dependency on the beam deflection. However, we show that buckled CNTs are the first type of buckled beams to exhibit out-of-plane static deflection, 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 buckled configuration when no force is applied, making these devices appealing for mechanical memory applications.