Nonlinear Forced Vibration and Bifurcation Points Analysis of PFG-GPLRC Cylindrical Shell: Analysis of Internal Resonance

Porous functionally graded graphene platelet-reinforced composites (PFG-GPLRC) combine advanced graphene materials with graded porosity to enhance mechanical performance and tailor properties for specific applications. This innovative approach offers significant improvements in strength, flexibility, and weight reduction. In this study, the primary objective is to investigate the nonlinear vibrational behavior of PFG-GPLRC cylindrical shells subjected to parametric loading and 1/2 subharmonic and 1:1 internal resonance. To achieve this, we examine five graphene platelets (GPLs) dispersion patterns (GPL-O, GPL-A, GPL-V, GPL-U, and GPL-X) and two porosity distributions in metal foam (non-uniform symmetric and non-uniform asymmetric). The study employs first-order shear deformation theory for the displacement field, and incorporates von Kármán nonlinearity to derive the governing motion equations for the cylindrical shell. Using the Galerkin method and under the assumption of simple boundary conditions, we derive the two-degree-of-freedom nonlinear equations of motion. Perturbation theory and the multiple scales method are subsequently employed to determine the stable and unstable frequency responses of the cylindrical shell. The analysis includes the investigation of instability ranges and bifurcation points to assess the effects of parametric excitation on the cylindrical shell. Additionally, the influence of geometric dimensions is explored, along with the impact of porosity and GPLs within the metal foam on the vibrational behavior. The novelty of this study lies in analyzing nonlinear forced vibrations of PFG-GPLRC cylindrical shells under combined 1:1 internal and 1/2 subharmonic resonance, accounting for porosity, thermal effects, and material gradation.