The impacts of variable nonlocal, length-scale factors and surface energy on hygro-thermo-mechanical vibration and buckling behaviors of viscoelastic FGP nanosheet on viscoelastic medium

The main goal of this paper is to present the free vibration and buckling of viscoelastic functionally graded porous (FGP) nanosheet based on nonlocal strain gradient (NSGT) and surface elasticity theories. The nanosheets are placed on a visco-Pasternak medium in a hygro-temperature environment with nonlinear rules. The viscoelastic material characteristics of nanosheets are based on Kelvin’s model. The unique point of this study is to consider the change of nonlocal and length-scale coefficients according to thickness, similar to the laws of the material properties. The Galerkin approach based on the Kirchhoff-love plate theory is applied to determine the natural frequency and critical buckling load of the viscoelastic FGP nanosheet with various boundary conditions. The accuracy of the proposed method is verified through reliable publications. The outcome of this study highlights the significant effects of the nonlocal and length-scale parameters on the vibration and buckling behaviors of viscoelastic FGP nanosheets.