In this research, the free vibrations of a truncated conical sandwich shell with a re-entrant auxetic core and polymeric nanocomposite face sheets reinforced with graphene nanoplatelets (GNPs) are investigated. This study explores, for the first time, the influence of GNP distribution patterns, honeycomb core geometry, and shell parameters on the natural frequencies of truncated conical shells. A first-order shear deformation shell theory (FSDT) is applied to enhance the accuracy of results, especially for thick shells. The mechanical properties of the nanocomposite face sheets are calculated using the rule of mixtures and the Halpin-Tsai model. The governing equations and boundary conditions are derived using Hamilton’s principle. Exact solutions for the governing equations in the circumferential direction are obtained using harmonic trigonometric functions, while the differential quadrature method (DQM) is employed for solving equations along the shell. After verifying the convergence and accuracy of the proposed analysis, the effects of various factors on the natural frequencies are examined, including the geometric characteristics of the auxetic honeycomb core, the mass fraction and distribution pattern of GNPs, the shell geometry, and the boundary conditions. The results show that increasing the side thickness in the core cells of the auxetic honeycomb decreases natural frequencies. However, increasing the core’s overall thickness relative to the shell thickness can either increase or decrease the natural frequencies, depending on the vibration mode. Additionally, distributing GNPs near the inner and outer surfaces of the shell yields the highest natural frequencies due to enhanced flexural stiffness. This study provides valuable insights for designing advanced conical shell structures with optimized vibration performance, applicable in aerospace, automotive, and civil engineering industries.
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