Analytical investigation of free vibration analysis in functionally graded graphene platelet-reinforced composite beams

Graphene, due to its exceptional mechanical properties, is increasingly recognized as a highly effective reinforcement material for composite structures. Its application in functionally graded graphene platelet-reinforced composite (FG-GPRC) laminated and sandwich beams holds significant potential in various engineering fields. However, accurately predicting the natural frequencies of these beams remains challenging due to limited understanding of interlaminar stress compatibility conditions in current higher-order models. This study addresses this gap by presenting a free vibration analysis of FG-GPRC structures using an improved zigzag beam theory. This theory incorporates transverse shear stresses at layer interfaces, enhancing the accuracy of dynamic analysis. By employing a preprocessing approach based on 3D elasticity equations and Reissner's mixed variational theorem (RMVT), we derive analytical solutions for simply supported laminated and sandwich beams utilizing Hamilton's principle. The proposed model achieves less than 3 % deviation from exact 3D elasticity solutions in predicting natural frequencies, whereas existing higher-order models exhibit deviations exceeding 280 %. Additionally, comprehensive investigations assess the impact of various factors, including graphene volume fractions, distribution profiles, stacking sequences, and geometric attributes. The findings demonstrate that increased graphene volume fractions significantly enhance the natural frequencies of laminated beams, while their effect on sandwich beams is minimal. Furthermore, distribution patterns such as UD and FG-X contribute to higher natural frequencies, and larger span-to-thickness ratios result in increased vibration frequencies. These factors significantly influence the dynamic behavior of FG-GPRC structures, offering valuable insights for design and optimization. This study provides a novel and reliable approach to accurately predicting the dynamic properties of FG-GPRC laminated and sandwich beams, contributing essential knowledge to the field of composite material engineering.