Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory

Abstract

This paper deals with the vibration, buckling and bending analyses of annular nanoplate integrated with piezoelectric layers at the top and bottom surfaces. The higher order nonlocal theory for size effect and Gurtin–Murdochtheory for surface effects are utilized. The governing equations are derived based on the layer-wise (LW) theory and Hamilton’s principle. The differential cubature method (DCM) as a new numerical procedure is utilized to solve the motion equations for obtaining the frequency, buckling load and deflection. The influences of various parameters such as external voltage, boundary condition, surface stresses, nonlocal parameter, outer to inner radius ratio and core to top layer thickness ratio were shown on the vibration, buckling and bending responses of the nanostructure. The results of vibration, buckling and bending are validated with other published works. The outcomes show that the surface stresses have a significant effect on the increases of the frequency and buckling load and decrease of the deflection.