Vibration characteristics of wrinkled single-layered graphene sheets

A pseudo beam model with 3-node beam element is proposed to simulate the modal behavior of the wrinkled single-layered graphene sheets (SLGS) based on molecular structural mechanics (MSM) method. The wrinkling characteristics are simulated using a direct perturbed-force technique originated from the continuum theory. The primary bifurcation and the secondary wrinkling behaviors are investigated so as to obtain the characteristics of the formation and the evolution of the wrinkles. The wrinkled shape, stress and effective mass are introduced into the modal model using the updated geometry technique. The effects of the wrinkles on the vibration characteristics of the SLGS are then interpreted by comparing with the unwrinkled case. The effects of the aspect ratio on the modal behavior of wrinkled SLGS are further studied. Based on the MSM simulation results and the continuum thin plate model, a prediction model is proposed to obtain the natural frequency of wrinkled SLGS. The predictions agree well with the MSM simulations. The results and observations are good references to design a wrinkled highly frequency nano-devices.