Optimization of vibration analysis for functionally graded graphene platelets (FGGP) reinforced twisted cantilever thin shallow shell blades subjected to axial loading

Vibration characteristics for rotating thin shallow shell blades reinforced with functionally graded graphene platelets (FGGP) under the axial force are conducted. The blade is modeled as four twisted cantilever thin shallow shells, each with a unique shape cylindrical shallow shell panel with a straight or curved boundary as the cantilever side, spherical shallow shell panel and hyperbolic parabolic shallow shell panel. The Halpin–Tsai model, the first-order shear deformation theory and the Rayleigh–Ritz method are used to calculate the frequencies and mode shapes of the blade. The results are validated by comparing them with previous literature and ANSYS. An analysis is conducted on a range of parameters, encompassing graphene properties, rotational velocity, torsional angle, curvature radius, aspect ratio and axial forces, in order to assess their influence on the vibrational properties of the blade. The vibration behaviors of a rotating cylindrical shallow shell panel with a straight cantilever edge are found to be distinctive. The findings indicate that the blade’s stiffness is significantly higher when reinforced with FGGP-X compared to FGGP-U distribution, with FGGP-O distribution exhibiting the lowest stiffness. Furthermore, the study implies that a total layer count exceeding ten has a negligible impact on the degree of graphene distribution. Finally, the study concludes that the curvature and graphene distribution pattern significantly influence the vibration characteristics of the blade.