Analysis of traveling wave vibration of GNPs-reinforced bi-directional functionally graded rotating joined cylindrical–conical–cylindrical shells

This article systematically examines the traveling wave vibration characteristics of graphene nanoplatelets (GNPs) reinforced bi-directional functionally graded rotating joined cylindrical–conical–cylindrical (JCCC) shells. Initially, combined with the Donnell thin shell theory and the Halpin–Tsai model, the energy equation of the functionally graded materials (FGMs) JCCC shells is derived. Subsequently, Chebyshev polynomials are utilized to express the displacement function, and the modal frequency equation of the shells is established using the Rayleigh–Ritz method. Finally, the accuracy of the theoretical model is validated through the utilization of case studies, and parameter studies are conducted in the end. The results indicate that the gradient exponent in the thickness direction predominantly influences the vibration characteristics. The FG-X distribution of GNPs has the most significant effect on the JCCC shells. The rigidity of the JCCC shells decreases with an increase in the semi cone angle. As porosity increases, the total mass fraction and surface area of GNPs exhibit a more effective reinforcing effect. As the temperature increases, the stiffness of the structure decreases. The intrinsic frequencies of the structure increase almost linearly with increase in thickness.