▎ 摘　　要

This paper contains a nonlocal strain gradient-based theory to survey viscoelastic wave dispersion characteristics of axially loaded double-layered graphene sheets (DLGSs) resting on the viscoelastic substrate. Actually, a comprehensive size-dependent analysis is performed in which both amplifying and minimizing effects are covered. Also, the kinematic relations have been derived by the means of a one-variable classical plate theory. Besides, the final nonlocal governing equations can be developed using the Hamilton's principle. These equations will be finally solved utilizing an analytical solution to obtain wave frequency, phase velocity and escape frequency of DLGSs. Last section is allocated to study the effects of various terms including wave number, nonlocal parameter, length scale parameter, structural damping coefficient, Winkler coefficient, Pasternak coefficient, damping coefficient and axial load on the wave propagation behaviors of DLGSs.