Wave Analysis of Thick Rectangular Graphene Sheets: Thickness and Small-Scale Effects on Natural and Bifurcation Frequencies

Free vibration and wave analysis of thick rectangular graphene are studied by employing the propagation method. To consider small-scale effects thickness a plate in nanoscales, equations motions represented Eringen nonlocal theory coupled with Mindlin plates. solve governing motion technique, reflection matrices derived. These combined to obtain exact natural frequencies sheets for all six possible boundary conditions. check accuracy reliability method, compared results literature, excellent agreement is observed. Additionally, sheet performed different types waves captured. Deriving dispersion relation sheet, bifurcation (cut-off escape frequencies) analytically found. Finally, parameter on investigated. It observed that highly dependent sheet’s parameter. More importantly, number order depend these two parameters as well. Our findings valuable sustainable design fabrication graphene-based sensors, which structural health monitoring embedded great importance.