Vibration and Buckling of Composite Cantilever Plates Considering Three Distinct Cross-sectional Configurations

This study investigates the vibration and buckling characteristics of functionally graded graphene platelet (FGGP) reinforced cantilever plates with three distinct variable cross-sectional configurations: convex-curved (Pattern 1), linear (Pattern 2) and concave-curved (Pattern 3) boundaries. A combined analytical–numerical framework is developed, integrating the Halpin–Tsai micromechanical model with first-order shear deformation theory (FSDT) and the Rayleigh–Ritz method to predict the structural responses. The proposed methodology is validated through systematic comparisons with established benchmark solutions. Parametric studies elucidate the influence of critical design factors, including graphene distribution patterns, layer numbers, cross-sectional geometries and dimensional parameters on the plates’ dynamic and stability performance. The cross-sectional geometry demonstrates profound configuration-dependent effects, governing: frequency veering positions in free vibration spectra, torsional mode dominance in modal responses and secondary buckling mode transformations. The findings provide fundamental insights for optimizing lightweight, high-performance composite structures in aerospace applications.