Dynamic modeling and stability assessment of functionally graded graphene platelet-reinforced composite multi-Disk rotors

The demand for lightweight, high-strength rotors with reliable vibration stability is rapidly increasing across aerospace, automotive, turbomachinery, and energy systems. Functionally graded graphene platelet-reinforced composites (FG-GPLRCs) offer a promising solution by enabling tailored stiffness and damping, achieving both weight reduction and enhanced dynamic performance. This study presents a novel analysis of the nonlinear dynamics of axially restrained FG-GPLRC multi-disk shafts under imbalance excitation, explicitly accounting for large-deflection behavior and multi-disk imbalance. The governing equations of the composite shaft-disk system are first derived and reduced using a fundamental-mode Galerkin approximation. The resulting reduced-order model is then analyzed via the method of multiple scales to obtain analytical expressions for the natural frequencies, which are subsequently validated through finite element simulations in ANSYS, confirming predictive accuracy. The investigation systematically examines how four reinforcement patterns, graphene platelet weight fraction, number of layers, and geometric ratios influence the vibration behavior and stability of the system. Results indicate that increasing the graphene platelet content from 0% to 2.5% substantially enhances performance, with natural frequencies rising by 170%-270% and critical damping by nearly 300%, while simultaneously reducing critical eccentricity and jump-down length by 80% and 8%, respectively. The reinforcement pattern and the number of graphene layers further shift frequencies by up to 37%, modify critical damping by 25%, affect jump-down length by 18%, and alter critical eccentricity by up to 30%. Overall, the findings highlight the potential of FG-GPLRC shafts for stable jump-free operation and the reliable design of high-speed rotor systems. © 2026 .