Free Vibration Characteristics of Cylindrical Structures for Aircraft Connections Under Complex Boundary Conditions

Driven by the urgent aerospace demand for lightweight, high-performance cylindrical connection structures with versatile boundaries and dimensions, this study enhances traditional aluminum by incorporating graphene nanoplatelets (GPLs) and investigates the free vibration of functionally graded graphene-reinforced aluminum matrix composite (FG-GPL/Al) cylindrical connection structures under complex boundary conditions. The equivalent mechanical properties of the composite are first determined using the modified Halpin–Tsai micromechanical model and the rule of mixture. Subsequently, the governing equations of motion for the FG-GPL/Al cylindrical structure are derived based on Reddy’s first-order shear deformation theory and Hamilton’s principle. The natural frequencies and mode shapes of the structure are finally obtained via the Ritz method, with admissible functions constructed by coupling Chebyshev polynomials and Fourier series. Results demonstrate that under clamped–clamped (C–C) and clamped–free (C–F) boundaries, all natural frequencies decrease with an increasing length-to-radius ratio, a trend especially pronounced in lower-order modes, highlighting their greater sensitivity to geometric changes. In contrast, the free–free (F–F) condition leads to distinct modal grouping: while one group of frequencies decreases with the length-to-radius ratio, another exhibits a slight increase. This differentiated behavior underscores how boundary conditions modulate vibrational energy distribution. The findings provide theoretical and design guidance for applying such graphene-reinforced composite cylindrical connection structures in aerospace and related engineering fields.