Analytical solutions for vibrations and buckling analysis of laminated composite nanoplates based on third-order theory and strain gradient approach

A nonlocal model based on the strain gradient approach is developed within the framework of the Third-order Shear Deformation Theory (TSDT) for the investigation of the free vibrations and the critical buckling loads of laminated composite nanoplates. The theory is suitable to deal with thick and thin plates since it includes also the First-order Shear Deformation Theory (FSDT) and the Classical Laminated Plate Theory (CLPT). An analytical procedure based on the Navier approach is employed to obtain the solutions, which are discussed highlighting the effects of the strain gradient, as well as the influence of the geometric ratios and mechanical properties, on the results. The paper aims at providing reliable benchmarks for further developments of the topic to be used as references in future comparison tests.