Semi-analytical modeling and vibration analysis of joined FGP-GPLRC thin-walled cylindrical-spherical shells with arbitrary boundary conditions

In this paper, the vibration characteristics of the joined thin-walled cylindrical-spherical shells with graphene platelet (GPL) reinforcement in metal foams are investigated based on a relatively novel Gegenbauer-Ritz method. The material properties of the coupled shells are also obtained using the Halpin-Tsai micromechanical modeling. The equations for the mechanical modeling of the coupled shell are given by applying the first-order shear deformation theory (FSDT) and the energy method. In addition, the spring stiffness penalty method is employed to obtain arbitrary boundary conditions at both ends of the shell. The final solution for the coupled shell is obtained by the Gegenbauer-Ritz method. Finally, the results of this paper are compared with the literature results and those obtained by the finite element method (FEM) to prove the accuracy of the approach. On this basis, the effects of arbitrary boundary conditions, GPL distribution modes, porosity distribution patterns, structural openings, and geometrical parameters on the vibration characteristics of the joined cylindricalspherical shells are discussed.