Vibration Behavior of Nanocomposite Plate Reinforced by Pristine and Defective Graphene Sheets; an Analytical Approach

Free vibration characteristics of polymer composite plates reinforced by graphene nanosheets employing the Eringen nonlocal elasticity theory were investigated. Theoretical formulations are derived based on Hamilton’s principle implementing linear orthotropic constitutive equations of lamina while the behavior of nanostructure points affected by all other nonlocal points is also taken into account. For obtaining the mechanical properties, a new modified Halpin–Tsai model is employed. Governing equations are solved by developing an efficient analytical solution. The accuracy of the presented method is examined, by comparing the results with literature in which a good agreement is observed. Effects of different boundary conditions, volume fraction, graphene sheets orientation angle and Eringen nonlocal parameter on frequency of nanocomposite are analyzed. Effects of the presence of vacancy defects in the nanosheet on the behavior of reinforced composites were also studied. The results illustrate that by increasing the nonlocal parameter the natural frequency showed a decreasing trend while by increasing the graphene sheet’s volume fraction, natural frequencies significantly increased. It could be concluded that the orientation angle variations in graphene sheets, did not play an important role on the natural frequency of nanocomposite as well as degradation of properties resulted in from vacancy defects.