Using novel materials, including auxetic structures, has witnessed significant growth. Consequently, a comprehensive examination of their mechanical behavior becomes imperative. This study delves into the free vibration characteristics of a three-layer cylindrical shell containing liquid. The central layer of this structure features a re-entrant honeycomb auxetic pattern, while the inner and outer layers are assumed to be isotropic and constructed from aluminum. The liquid within the shell is considered ideal and incompressible, with no consideration for wave effects on its free surface. To model this problem, we employ a modified high-order shear deformation theory (HSDT). By applying Hamilton's principle, we derive fundamental equations and solve them using the Galerkin weighted residual method. We compare our findings with results published in authoritative articles and outcomes obtained from finite element analysis in ABAQUS to validate them. Our investigation explores the impact of various parameters on the natural frequencies of the cylindrical body. These parameters include the geometrical dimensions of the sandwich cylindrical cover, adjustable auxetic core parameters, and liquid characteristics. Given the widespread use of cylindrical sandwich shells across diverse industries, our study provides valuable insights into the phenomenon of free vibration in these structures. Remarkably, previous studies have not investigated the free vibration of a three-layered cylindrical shell with an auxetic structure and liquid interaction.
