This study investigates the free vibration behavior of joined conical shell assemblies made of functionally graded hybrid CNT/GPL nanocomposites using the First-Order Shear Deformation Theory (FSDT) combined with the Generalized Differential Quadrature (GDQ) method. Such multi-segment conical configurations offer a novel structural archetype for next-generation sport helmet liners, where segmented designs enhance impact management and customizable fit. The effective material properties are evaluated through a two-stage Halpin–Tsai homogenization considering various CNT and GPL distributions. Validation against finite element results confirms excellent accuracy, with frequency deviations below 1%. The results reveal several notable and unexpected findings. Results demonstrate that hybrid reinforcement offers superior tunability of vibrational performance—critical for managing impact energy and mitigating concussion risk—compared to single-reinforcement systems. Furthermore, interface continuity is shown to significantly influence the global frequency response, underscoring the importance of bond integrity in helmet liner design. Hybrid CNT/GPL reinforcement enhances the fundamental frequency by up to 25% compared with CNT-only and by 15% compared with GPL-only shells. Among all distribution types, the FG-X pattern—which concentrates nanofillers near the surfaces—provides the highest stiffness gain, while other patterns yield significantly lower frequencies. Moreover, varying the second cone angle from 30° to 90° leads to a nonlinear, non-monotonic trend, where mode interaction and geometry softening cause distinct turning points in the frequency response. At large angles, the effect of material distribution diminishes, and geometry becomes dominant. These findings demonstrate that the hybrid reinforcement strategy and proper selection of geometric parameters enable effective tunability of the dynamic characteristics of joined nanocomposite conical shells, offering design guidance for advanced next-generation protective sport helmets.
Gao et al. (Fri,) studied this question.