Free Vibration of Functionally Graded Graphene Nanoplatelets-Reinforced Saturated Porous Cylindrical Shell Panel

This study investigates the free vibration behavior of cylindrical shell panel nanocomposite foams composed of polyurethane (PU) integrated with graphene nanoplatelets (GNPs). The analysis highlights the critical role of agglomeration effects and the adoption of an appropriate micromechanical model. Accordingly, this work presents, for the first time, a modified Halpin–Tsai model that incorporates experimental data and employs a genetic algorithm (GA) to extract the exponential shape factor, optimizing the model’s alignment with experimental results. Given the significance of GNP flake size, the study systematically examines its influence on the vibration characteristics. Three commercially available GNP types, with flake sizes of 24, 5, and [Formula: see text], are analyzed. To more accurately capture practical conditions, a saturated porous material model based on the Biot constitutive law is employed as an alternative to the conventional Hooke’s law to characterize the closed-cell structure of PU foam. The governing equations of motion are formulated using Hamilton’s principle, grounded in the first-order shear deformation theory (FSDT) plate theory and implemented through the finite element method (FEM). This research presents a comprehensive parametric investigation, examining for the first time the influence of geometric parameters, porosity characteristics, GNP weight fractions, and reinforcement configurations (X, O, U, and V patterns) on the vibration response of nanocomposite structures. For variations in weight fraction, GNP-5 and GNP-24 demonstrated an initial increase in natural frequency; however, beyond a certain threshold, the added mass surpassed the stiffness enhancement, leading to a reduction in natural frequency. In contrast, GNP-1.5 exhibited a lower natural frequency compared to pure PU.