Numerical Solution for Dynamic Analysis of Multi-Scale Hybrid Stepped Annular Plates Reinforced with CF and Agglomerated GPLs

This study examines the vibration and dynamic behavior of multi-scale hybrid stepped annular plates reinforced with carbon fiber (CF) and graphene nanoplatelets (GPLs), considering complete and partial GPL agglomeration. The Eshelby–Mori–Tanaka approach models effective material properties, while governing equations are derived using the principle of minimum potential energy based on axisymmetric elasticity theory. A parametric study explores the effects of GPL, CF, plate dimensions, and boundary conditions. Results show significant increases in natural frequency with higher CF and GPL fractions. Pure epoxy exhibits a natural frequency of 195[Formula: see text]Hz, which increases to 802[Formula: see text]Hz (a 311% rise) with the addition of 5% GPL and to 834[Formula: see text]Hz (a 327% rise) with a CF volume fraction of 0.5. Notably, the hybrid configuration achieves a remarkable natural frequency of 1327[Formula: see text]Hz, representing a 579% improvement over pure epoxy. In terms of deflection, plates with 3% GPL exhibit a deflection of 0.46[Formula: see text]mm, outperforming those reinforced with CF alone (0.70[Formula: see text]mm at 0.1[Formula: see text]volume fraction). The multi-scale hybrid composites further reduce deflection to 0.28[Formula: see text]mm, highlighting their superior performance. Additionally, it is observed that below a GPL mass fraction of 2.3%, the unidirectional (U-pattern) reinforcement yields the highest natural frequency, whereas the X-pattern outperforms above this threshold.