Free vibration and buckling analyses of a rectangular sandwich plate with an auxetic honeycomb core and laminated three-phase polymer/GNP/fiber face sheets

In this paper, the free vibration and uniaxial, biaxial, and shear buckling analyses of a sandwich plate with an auxetic honeycomb core and two laminated three-phase polymer/GNP/fiber face sheets are investigated. The sinusoidal shear deformation theory (SSDT) is utilized to model the plate, Hamilton’s principle is hired to derive the governing equations and boundary conditions, and a numerical solution is performed via the differential quadrature method (DQM). The effects of various parameters on the critical buckling loads and the natural frequencies of such a plate are examined such as the geometrical parameters of the auxetic honeycomb core, mass fractions of the GNPs and the fibers, and total thickness of the plate. Numerical results reveal that by increasing the thickness of the auxetic honeycomb core the critical buckling loads decrease and the natural frequencies experience an initial growth followed by a small reduction. It is concluded that the inclined angle in the auxetic honeycomb core has no remarkable effect on the critical buckling load, but affects the natural frequencies in all vibrational modes. •Free vibration and buckling analyses of a sandwich plate with an auxetic honeycomb core are studied.•The auxetic is covered with two laminated three-phase polymer/GNP/fiber face sheets.•The plate is modeled based on the sinusoidal shear deformation theory.