Bending information and dynamic stability of the laminated axisymmetric nanoplate on the linear and torsional elastic substrate based on zigzag theory

In the current work, for the first time, bending and vibration information of the axisymmetric thick annular nanoplate made of laminated composite layers is studied. The structure is placed on Winkler-Pasternak substrate with elastic and tortional coefficients. Initial stress as an external load is also considered in the composite structure. For modeling the mechanical deformation in layer-wise composite materials, zigzag theory that its functions themselves are continues in the interface of layers is presented. By coupled quasi-3D new refined theory (Q3D-NRT) and nonlocal strain gradient theory are used for obtaining the nonclassical governing equations a general boundary condition of the current composite nanoplate. Also, for obtaining the static and dynamic equations of the current nanostructure, Hamilton's, and Minimum total potential energy principles are used, respectively. Via differential quadrature method with weighting factors and nth-order derivative, the nonclassical governing equations with the aid of size-dependent boundary conditions are solved. By comparing the current results with the outputs of previous reports, the accuracy of the results is shown.