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.

本文包含基于非局部应变梯度的理论，以研究位于粘弹性基底上的轴向加载双层石墨烯片（DLGS）的粘弹性波色散特性。实际上，会进行全面的尺寸相关分析，其中涵盖了放大效果和最小化效果。而且，运动关系已经通过一变量经典板理论推导。此外，最终的非局部控制方程可以使用汉密尔顿原理来发展。这些方程式将最终通过解析解决方案求解，以获得DLGS的波频率，相速度和逃逸频率。最后一部分是研究各种术语的影响，包括波数，非局部参数，长度尺度参数，结构阻尼系数，