Free Vibration Analysis of BDFG-GPLs Plates Partially Supported by Kerr Foundation using a Finite Element Procedure

The main objective of this article is to examine the free vibration of bi-directional functionally graded graphene platelets reinforced plates (so-called BDFG-GPLs plates) partially supported by Kerr foundation (KF). The governing equation of motion is derived from Hamilton's principle. A finite element procedure based on a refined higher-order shear deformation theory (r-HSDT) is introduced using the four-node rectangular (Q4) element with eight degrees of freedom (DOFs) per node based on the combination of Lagrange functions and Hermite polynomials to degenerate the C1 continuity into C0 continuity of the displacement field by adding new displacement variables. The efficiency and accuracy of the proposed method are confirmed by comparing the obtained results with those available in previously published literature. Then, the influence of geometric parameters, material properties, and boundary conditions (BCs) on the free vibration of BDFG-GPLs plates partially supported by KF is studied in detail. An interesting result is that the incorporation of only 1% volume of GPLs can increase the fundamental frequency of BDFG-GPLs by about 108% compared to the homogeneous epoxy plate. Besides, this work provides new and general insights into the free vibration of BDFG-GPLs plates.