Analysis of the Impact of the Viscoelastic Foundation on Bending and Vibration of FG Porous Nanoplates within Integral Higher-Order Shear Deformation Theory

This work examines the bending and vibration responses of a functionally graded (FG) 2D nanostructure resting on the viscoelastic foundation. The FG structure properties vary gradually in the thickness direction. In this investigation, three porosity patterns are examined. The nonlocal equilibrium equations are derived by Hamilton’s principle using Eringen’s nonlocal elasticity theory, which incorporates the integral plate theory with a reduced number of unknowns. The results computed for the studied simply supported FG nanoplates are compared with those published in the open literature. Several parametric studies are performed to illustrate various influences of the plate geometry, material inhomogeneity, elastic damping coefficient, and nonlocal effect on the stresses, frequency, and central deflection of FG nanoplates.