Free vibration analysis of functionally graded rectangular nano-plates considering spatial variation of the nonlocal parameter

Alipour Ghassabi, Ata
This study presents a new nonlocal elasticity based analysis method for free vibrations of functionally graded rectangular nano-plates. The method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. All required material properties are assumed to be functions of thickness coordinate in the derivations. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature. Further numerical results are generated by considering functionally graded simply-supported and cantilever nano-plates undergoing free vibrations. These findings demonstrate influences of factors such as dimensionless plate length, plate theory, nonlocal parameter ratio, and power-law index upon natural vibration frequencies.