Free Vibration Analysis of CNT- and MXene-Reinforced Epoxy/Glass Fiber Annular Plates Using TSDT and GDQ

This paper presents the first comprehensive investigation on the free vibration behavior of multi-scale hybrid-reinforced annular composite plates incorporating carbon nanotubes (CNTs) and MXene nanosheets dispersed within an epoxy matrix and laminated with E-glass fibers. The vibration analysis of thick annular plates is modeled using Reddy's third-order shear deformation theory (TSDT), which fully accounts for higher-order shear and rotary inertia effects critical for accurate thick-plate dynamics. The generalized differential quadrature (GDQ) method is employed for numerical discretization, with explicit formulation of strain-displacement operators and mass matrix components. Results demonstrate that natural frequencies are significantly governed by reinforcement type, boundary conditions, volume fraction, spatial distribution, fiber orientation, and geometric parameters. Notably, CNTs exhibit approximately 2.5 times higher frequency enhancement per 1% volume fraction compared to MXene, revealing their superior effectiveness in bending-dominated vibrations. The FG-X distribution pattern yields the highest frequency elevation (up to 11.5% increase), whereas the FG-O pattern shows minimal benefit due to reinforcement placement near the neutral axis. An unexpected non-monotonic frequency variation is observed with fiber orientation: natural frequencies at 60° can exceed those at 50°, attributed to bending-stretching coupling effects in the constitutive relations. Parametric studies reveal that increasing the plate radius reduces natural frequencies, while greater thickness substantially raises frequencies, particularly for higher-order modes. Boundary conditions exert a dominant influence on fundamental modes, with fully clamped supports providing maximum frequency values. These findings provide critical design guidelines for optimizing composite annular components, such as turbine shrouds, spacers, and containment rings, where high dynamic stiffness and vibrational stability are paramount.