The natural frequency analysis of in-plane bi-directional functionally graded plates under various boundary conditions

In this paper, a refined shear deformation plate theory which eliminates the use of a shear correction factor was presented for the natural frequency analysis of in-plane bi-directional functionally graded (IBFG) plates under various boundary conditions. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of IBFG are assumed to vary continuously along with two different directions simultaneously, i.e., the longitudinal and transversal ones, respectively. Governing equations and boundary conditions are derived. Analytical solutions were obtained for buckling analysis of (IBFG) plates. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed theory. The effects of material gradations, boundary conditions and aspect ratios on IBFG plate responses are examined in detail as well. The analysis of the numerical results confirms that material grading; boundary condition and other design parameters have a significant influence on the frequency response characteristics of a single/multi-directional porous FG structure. The study demonstrates that material gradation, aspect ratio, and boundary conditions significantly influence the dynamic and buckling behavior of IBFG plates. Higher aspect ratios and stiffer boundary conditions increase natural frequencies, while specific material gradations optimize stiffness and mass distribution. The proposed theory accurately predicts these responses, providing a simplified yet robust framework for designing advanced engineering structures.