A Levy solution for bending, vibration, and buckling of Mindlin micro plates with modified couple stress theory

Based on the modified couple stress and first-order shear deformation plate theories, a Levy-type solution is presented for bending, vibration, and buckling analyses of rectangular isotropic micro plates with simple supports at opposite edges anddifferent boundary conditions at the other two ones. The modified couple stress theory is taken into account to capture the size effect and the governing equations are derived using the Hamilton s principle, and then solved by a single Fourier series expansion and the state-space method. The results are verified with the existing ones for a fully simply supported micro plate in the literature. Finally, the effect of geometric parameters and length-scale parameter on bending, vibration, and buckling behavior of micro-plates are studied. Since there are no analytical solution for bending, natural frequencies, and buckling loads of Mindlin micro plates with different boundary conditions in the literature, the results presented here can be used as a benchmark in future studies.

Keywords:

Mindlin plate theory , Modified couple stress theory , Levy method , State-space method