Nonlinear forced vibration analysis of PFG-GPLRC conical shells under parametric excitation considering internal and external resonances

Abstract

Comprehending the vibration dynamics of porous functionally graded-graphene platelet reinforced composite (PFG-GPLRC) structures is vital for accurate predictions and reliability in practical applications. This study addresses gaps in nonlinear dynamics, instability, and frequency response research within truncated PFG-GPLRC conical shells under parametric loading and ½ subharmonic and 1:1 internal resonance. To achieve this, three porosity distributions in metal foam (uniform, non-uniform symmetric, and non-uniform asymmetric) are considered, along with various graphene platelet dispersion patterns (GPL-O, GPL-V, GPL-U, GPL-A, and GPL-X) within the matrix. These considerations lead to a comprehensive conical shell model. Utilizing the first-order shear deformation theory and von-Karman's assumptions, stress-strain relations are extracted, yielding nonlinear motion equations for the truncated conical shell. Employing Galerkin's method and considering simply supported boundaries, two-degree-of-freedom equations of motion are derived. The research culminates in steady state frequency responses obtained through perturbation theory and the multiple scales method, encompassing ½-subharmonic excitation resonance and 1:1 internal resonance. Bifurcation points are analysed to highlight the influence of parametric excitation and system instabilities. A parametric study underscores the significance of porosity and graphene platelets within the metal foam in relation to system instability, revealing their intricate impact on PFG-GPLRC structure behavior.