Study on wave propagation characteristics of double-layer graphene sheets via nonlocal Mindlin–Reissner plate theory

• Wave propagation in DLGSs is investigated using nonlocal plate theory.
• Vibrational modes are divided into in-phase and anti-phase modes in the study.
• Escape frequencies are less than that obtained from nonlocal beam theory.
• Escape frequencies are different between the in-phase and anti-phase modes.

In this work, wave propagation characteristics of double-layer graphene sheets (DLGSs) are investigated using nonlocal Mindlin–Reissner plate theory. The vibrational modes are divided into in-phase mode and anti-phase mode, which is a special feature of DLGSs. The wave propagation behaviors in DLGSs in the in-phase mode and anti-phase mode are different. Cutoff frequency and escape frequency are analyzed in this study. In particular, the escape frequencies with different nonlocal parameters are less than that obtained from nonlocal Timoshenko beam theory and different between the in-phase mode and anti-phase mode. This is because shear forces consider the nonlocal effects in nonlocal Mindlin–Reissner plate theory, but do not consider the nonlocal effects in nonlocal Timoshenko beam theory. Thus, the present work will provide a better representation of wave propagation in DLGSs and will have implications in their application as electromechanical oscillators.