Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory

In the present study, buckling and vibration of nanoplates are studied using nonlocal elasticity theory. Navier type solution is used for simply supported plates and Levy type method is used for plates with two opposite edge simply supported and remaining ones arbitrary. Results are given for different nonlocality parameter, different length of plates and different boundary conditions. The results show that nonlocality effects should be considered for nanoscale plates. Clamped boundary conditions are more sensitive to nonlocality effects. In the vibration problem nonlocality effects increase with increase in the mode number. Present result can be used for single layer graphene sheets.