A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods

In this paper, bending, buckling and buckling of embedded nano-sandwich plates are investigated based on refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT). In order to present a realistic model, the material properties of system are assumed viscoelastic using Kelvin-Voigt model. The elastic medium is simulated by orthotropic visco-Pasternak medium. Based on energy method and D'Alembert's principle, the derivation of the nonlinear equations of motion is presented. A novel numerical method namely as differential cubature (DC) method is applied for obtaining the static response, the natural frequencies and the buckling loads of nano-sandwich plates. The effects of different parameters such as nonlocal parameter, structural damping, viscoelastic foundation, geometrical parameters, stiffness of core and boundary conditions are shown on the bending, buckling and vibration behaviors of nanostructure. The accuracy of the proposed method is verified by comparing its numerical predictions with other published works as well as solution of system with differential quadrature (DQ) and harmonic differential quadrature (HDQ) methods. The numerical investigation shows that RZT is highly accurate in predicting the deflection, frequency and buckling load of nano-sandwich plates without requiring any shear correction factors.