Distribution Influence of Functional Gradient Graphene Reinforced Composites in Solving Differential Equations

Duanyin Shi and Chunyan Zhao

DOI: https://doi.org/10.64486/m.65.2.8
Online publication date: December 5, 2025

Abstract: To investigate the effects of different graphene block distribution modes on the vibration characteristics of functionally graded graphene-reinforced composite materials, this study first establishes the motion control differential equations based on the Halpin–Tsai micromechanical model and Hamilton’s principle. The nonlinear and free vibration behaviors of the materials are also analyzed. The results indicate that different graphene mass fractions and distribution pat-terns have varying degrees of influence on the resonance characteristics and mechanical properties of functionally graded graphene layer–reinforced composites. Among them, the cross distribution pattern exhibits the most effective vibration suppression under specific conditions. These findings provide a theoretical foundation for the development of lightweight, high-strength materials and contribute to understanding the inherent relationship between the distribution of graphene blocks and material properties.

Keywords: functional gradient graphene; differential equations; reinforced composites

This article is published online first and will appear in Metalurgija, Vol. 65, Issue 2 (2026).