Transverse Vibration of Circular Double-Layer Graphene Sheets Using Nonlocal Elasticity Theory

Graphene possesses excellent physical and chemical properties and has potential applications in nanobiological devices and nanoelectromechanical systems such as actuators [1], optoelectronics [2], and biosensors [3]. In addition, the vibrational properties play an important role in structural stability of nanoelectromechanical systems used in dynamic environments. In the recent years, several researchers investigated the vibration behavior of graphene sheets using continuum models [4-5]. In order to avoid overestimating vibrational responses, it is necessary to consider the small scale effect in the analysis of nanostructures [6]. In this article, free transverse vibration of a circular double-layer graphene is studied based on nonlocal elasticity theory. The circular double-layer graphene sheets with the radius R is depicted in Fig. 1. The vibration equation for the nonlocal constitutive relations of the graphene is given by