Vibration of a multilayer graphene sheet under layerwise tension forces

Abstract

The present work is inspired by the fact that tension enforced by external force applied directly to the outermost layers of a (usually incommensurate) multilayer graphene sheet cannot be effectively transferred to all inner layers due to interlayer sliding, and therefore tension force in inner layers can be much lower than the tension force in the outermost layers. In this paper, a three-beam model is presented to study vibration of a multilayer graphene sheet under layerwise tension forces. In contrast to the commonly used single-beam model which assumes that tension in all layers of a multilayer graphene sheet are identical, the present model treats the top and bottom layers as two beams, and all other inner layers together as another beam which has different tension force than the top and bottom beams. Our results indicate that actual tensile stress/strain in the outmost singlelayers of a multilayer graphene sheet can be much (for instance, almost ten times, for specific examples discussed here) higher than that estimated by the widely used single-beam model, and the latter can badly underestimate actual tensile stress/strain of multilayer graphene resonators. In addition, at least for typical examples discussed here, the present model shows that vibrational frequencies of a multilayer graphene sheet are largely determined by the total tension, and the distribution of the total tension over different layers does not make a huge impact to vibrational frequencies of multilayer graphene resonators. Based on this conclusion, an explicit formula is given for resonant frequencies of multilayer graphene sheets under layerwise tension forces although the actual maximum tension depends on how total tension is distributed over all layers.