Monolayer graphene resonators for mass detection: A structural mechanics feasibility study

This paper studies the vibrational behavior of a circular graphene sheet operating as resonance nanomechanical mass sensor. For this purpose a structural mechanics based technique is developed and utilized in order to simulate the dynamic response of individual graphene sheets and graphene-attached mass systems. Interatomic interactions are simulated by equivalent spring elements with stiffness derived by corresponding potential energies provided by molecular theory and expressing the resistance in relative movements between carbon atoms under deformation. The inertial effects of the system are approached using appropriate lumped masses in atomic positions. Assembling the global stiffness and mass matrices using common finite element procedures, the equation of free vibration is solved for sheets with and without a mass lying on it. The solution gives the natural frequencies and corresponding mode shapes of vibration of individual graphene sheets and graphene-attached mass systems providing their vibrational characteristics. Subsequently, assuming the geometric characteristics of graphene, support conditions as well as the weight, number and position of the attached masses as the global design parameters, a parametric study on mass sensing characteristics is presented in order to examine the potential behavior of a circular graphene monolayer sheet as mass sensor.