Stress-driven Approach to Vibrational Analysis of FGM Annular ‎Nano-plate based on First-order Shear Deformation Plate Theory

Vibrational behavior of small-scale functionally graded annular plate based on the first-order shear deformation theory, and non-local stress-driven model is investigated. For the first time, generalized differential quadrature rule is utilized to solve the governing equation and related boundary conditions. The convergence, accuracy, and efficiency of the generalized differential quadrature rule are investigated using problem-solving for different situations. The effects of parameters such as size parameter, inhomogeneity coefficient of functionally graded materials, thickness to outer radius ratio, inner radius to outer radius ratio, and boundary conditions on the natural frequency of the structure have been investigated. Results show that, unlike the strain-driven model, the non-local stress-driven theory predicts the same behavior for all boundary conditions and increasing the size parameter has led to a stiffening behavior and an increase in the natural frequency of the structure.