Vibration and transient response analysis of bi-directional functionally graded graphene platelets reinforced plates resting on a Kerr foundation using a refined finite-element procedure

The primary objective of this paper is to investigate the vibration and transient response of bi-directional functionally graded graphene platelet (2DFG-GPL) reinforced plates resting on a Kerr foundation (KF). To achieve this, a finite-element procedure based on refined higher-order shear deformation theory (r-HSDT) is developed using a four-node rectangular (Q4) element with eight degrees of freedom (DOFs) per node. This approach combines Lagrange functions and Hermite polynomials to transform C1 continuity into C0 continuity by introducing additional displacement variables. To solve the problem, a computational program is implemented in M atlab using the Newmark-β method. The accuracy and efficiency of the proposed method are validated by comparing the results with those available in the existing literature. Furthermore, a detailed parametric study is conducted to analyse the effects of geometric parameters, material properties and boundary conditions (BCs) on the vibration and transient response of 2DFG-GPL reinforced plates resting on KF.