Probabilistic vibration characteristics of bi-directional functionally graded plates with various boundary conditions

The present work examines the free vibration response of bi-directional functionally graded (Bi-FGM) plates considering both deterministic and probabilistic analyses under four boundary conditions: CFFF, CFCF, SSSS, and CCCC. The material properties vary continuously in the two in-plane directions and are described using a two-parameter power-law distribution. The governing equations are formulated according to First-Order Shear Deformation Theory (FSDT) and solved using an eight-node finite element model. Uncertainty in material parameters is introduced through Monte Carlo simulation (MCS) to determine the first three natural frequencies. The parametric investigation indicates that the NFs decrease as the geometry ratio, material gradation index, and temperature increase, whereas an increase in plate thickness leads to higher frequencies. Among the boundary conditions considered, the fully clamped plate (CCCC) exhibits the highest frequencies, while the cantilever configuration (CFFF) shows the lowest values, with CFCF and SSSS lying between these two extremes. Probability analysis also reveals that the frequency distribution is broader for plates with weaker edge constraints, indicating greater sensitivity to variations in material properties.