An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity

Using an exact analytical approach, free vibration analysis of thick circular/annular FG Mindlin nanoplates is investigated in this paper. Eringen nonlocal elasticity theory is employed to consider small scale effects on natural frequencies. The edges of the nanoplate may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. The material properties change continuously through the thickness of the FG nanoplate, which can vary according to a power-law distribution of the volume fraction of the constituents whereas Poison’s ratio is set to be constant. In order to confirm the reliability of the method considered, the results are compared with those presented in literature. Also the effects of various parameters such as radius of the nanoplate, boundary conditions, material properties, mode number and nonlocal parameter on the natural frequencies are investigated.