Wave dispersion of mounted graphene with initial stress

This paper is focused on the initial stress affected wave dispersion in mounted graphene. To capture the size-dependent and shear deformation effects, the second-order shear deformation theory (SSDT) and nonlocal strain gradient elasticity theory are used to model the graphene. A size-dependent shear deformation plate model is established on the basis of the orthotropic constitutive equations, the nonlocal strain gradient theory as well as the SSDT. Analytical solutions are developed for the wave frequency and phase velocity. The influences of small-scale parameters, initial stress and elastic medium on wave propagation behaviors of the graphene sheets are explored. It is found that the developed model reasonably interprets the softening effects of flexural frequencies and phase velocities. Unlike the classical (scaling-free) model, the developed size-dependent model shows a reasonably good agreement with the experimental frequencies and phase velocities. The wave frequencies and phase velocities of single layer graphene sheets (SLGS) will decrease with increasing compression load, and can increase by increasing tension load. The developed size-dependent 2D continuum model is hopeful to provide a possible theoretical approach to explore the wave behaviors of Graphene-like 2D materials.