Free vibration analysis of rotating functionally graded triply periodic minimal surface cylindrical shells

This study presents, for the first time, a comprehensive free vibration analysis of a rotating functionally graded triply periodic minimal surface (FG-TPMS) cylindrical shell under various boundary conditions. The shell is constructed from advanced FG-TPMS materials, where three types of TPMS (i.e., Primitive (P), Gyroid (G), and I-graph and wrapped package-graph (IWP)), each analyzed with varying mass density patterns, are considered. The first-order shear deformation theory (FSDT) and the Rayleigh–Ritz approach are employed to formulate the governing equations for the free vibration analysis of the rotating FG-TPMS cylindrical shell. The proposed solution is subsequently validated against benchmark solutions in the available literature. Finally, the influence of various factors (TPMS kinds, circumferential wave number, boundary conditions, rotational speed, and geometric dimensions) on the natural frequency of spinning FG-TPMS cylindrical shells is examined. The findings serve as a foundational reference for the design of advanced FG-TPMS-based rotating components in aerospace, mechanical, and biomedical applications.