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.

Graphical abstractThe free vibration and buckling is of concern in the context of nonlocal continuum theory using Levy type solution method. The natural frequencies and critical buckling loads are obtained for plates with at least two opposite edge simply supported.Figure optionsDownload full-size imageDownload as PowerPoint slideVariation frequency ratios with plate side length for different nonlocal parameter (SSSS, a/b=1, m=1, n=1).Variation nondimensional critical buckling load parameter ratios with plate side length for different nonlocal parameter (SSSS, a/b=1).Research highlights► The free vibration and buckling is studied using nonlocal elasticity. ► Levy type solution method is used in the formulation. ► The plates with at least two opposite edge simply supported are considered. ► It is obtained that for plates smaller than 50 nm nonlocal elasticity should be used.