Stability analysis of multilayer graphene nano-sensors: a new stress-driven nonlocal shear beam model

The unique mechanical properties of graphene have made it a topic of enormous research interest over the last few years. Studying graphene’s pull-in instability is key for its application in nanoelectromechanical systems. Understanding the thresholds of this instability helps prevent failure in graphene-based nanoelectromechanical systems, such as sensors and actuators, maintaining device performance and lifespan. In this paper, based on stress-driven nonlocal elasticity, a new size-dependent multi-beam shear model was presented to investigate the pull-in instability of multilayer graphene/substrate nano-sensors. The sensor bends towards the graphene layer because of the thermomechanical mismatch during the fabrication process. Therefore, the curvature effect is included in the proposed model. Also, the impact of the Casimir force is considered in the modeling. A finite element method has been used to simulate the nano-sensor and to obtain the pull-in instability. For validation, the pull-in voltage values obtained from the presented methodology have been compared with the results of others. Finally, considering different numbers of graphene layers and geometrical parameters such as length, initial gap, and curvature, it can be seen how these parameters affect the instability voltage of this nano-sensor.