Bending and vibration analysis of generalized gradient elastic plates

The governing equations of motion of generalized gradient Kirchhoff and Mindlin plates are derived on the basis of the generalized gradient elasticity with both stress and strain gradient parameters. The present plate models incorporate two material length scale parameters that can capture the size effect. The proposed models are capable of dealing with size-dependent plates at nanoscale dimension with complex geometries and boundary conditions with the help of Hamilton’s principle. The static bending and free vibration of a rectangular simply supported all around generalized gradient Kirchhoff and Mindlin plates are solved analytically using Navier’s solution. A circular gradient elastic plate, clamped all around, is also analyzed under linear static loading. Finally, the present solutions are discussed in relation to their corresponding conventional ones.