Free Vibration of Heterostructures of Graphene and Boron Nitride in Thermal Environment via Aifantis Theory with Velocity Gradients and Ritz Method

This article aims to investigate the free vibration of mono-/ multi-layered hererostructures of graphene and boron nitride in thermal environment. To this end, at first, the nonlinear model of inter-layered interaction between different layers are estimated based on Lenard-Jones 6-12 potential, then two variable refined plate theory is used to model the vibrational behavior of in-plane heterostructures of graphnme/boron nitride or vertically stacked graphene/ boron nitride hybrid structures. To incorporate the size effect into two-variable refined plate hypothesis, Aifantis’s theory is used to derive potential energy. To formulate the kinetic energy, an additional length scale which adds gradient velocity to kinetic energy is also used. The eigen-frequency equations are obtained based on Hamilton principle and Ritz method. The results show that the layout of graphene and boron nitride layers only affect out-of-phase natural frequency of multilayered nano-plates. Also, the significant impact of number of boron nitride layers used in heterostructures on the reduction of natural frequency of hybrid structure is demostrated. By controlling the area occupied by boron nitride in mono-layered hybrid structures, one can enhance the natural frequency of nano-sheets. The effects of the value of length scale parameter and temperature change on natural frequencies are studied as well.