▎ 摘　　要

Graphene nanoribbons (GNRs) are potential nanomaterial electromechanical oscillators because of their outstanding mechanical and electronic properties. Double-layer GNRs (DLGNRs), which are two-layer finite-wide counterparts of crystalline graphene sheets coupled to each other via van der Waals interaction forces, present two kinds of vibrational modes in flexural wave propagation. These two modes are defined as the in-phase mode and anti-phase mode. In this study, based on the nonlocal Timoshenko beam theory and Winkler spring model, the wave propagation characteristics of DLGNRs embedded in an elastic matrix are investigated by dividing the vibrational mode into the in-phase mode and anti-phase mode. This will provide more accurate guidance for the application of DLGNRs. When the nonlocal effects and elastic matrix are considered, three critical frequencies are found. These are defined as the cutoff, escape, and low-cutoff frequencies. Moreover, the results show that the wave propagation characteristics of embedded DLGNRs are significantly influenced by nonlocal parameters and the Winkler foundation modulus. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653827]