Analytical investigation on free vibration frequencies of polymer nano composite plate: Effect of graphene grading and non-uniform edge loading. (September 2020) - Gunasekaran, Vijay; Pitchaimani, Jeyaraj; Mailan Chinnapandi, Lenin Babu
Highlights: Critical buckling load parameter is significantly influenced by the nature of non-uniform edge load. The fundamental buckling mode for α = 2 load case is (2, 1) while for the remaining load case it is (1, 1). It is noted that minute increase in Wgpl of GPLs results in significant increase of the stiffness parameter of rectangular FG-GRC plate, as an outcome it leads to rise in buckling load and natural frequencies. The distribution pattern of GPLs for a given fraction of GPL has huge impact on the stiffness parameter of rectangular FG-GRC plate. It is noted that FG-GRCC pattern shows the superior buckling and free vibration characteristics when compared to the other cases due to the enhanced bending stiffness associated with FG-GRCC pattern. Abstract: An analytical investigation carried out on free vibration characteristics of functionally graded graphene reinforced nanocomposite (FG-GRC) plate under different non-uniform edge loads is presented. Graphene nano-platelets (GPLs) are homogeneously dispersed and graded by varying weight fraction through the thickness. An analytical method based on strain energy approach is adopted to estimate the buckling load. Natural frequencies of the FG-GRC plate are attained using analytical solutions derived based on Reddy's third-order shear deformation theorem (TDST). Results revealed that buckling and free vibration behavior of the plate is influenced by the GPLs dispersion pattern and weight fraction under non-uniform edge loads. It is also observed that buckling mode and the fundamental vibration mode of the plate under combined tensile-compression load is entirely different from the other non-uniform edge load cases.