Free vibration and buckling analyses of sandwich cylindrical shells with anti-tetrachiral core and composite face sheets

This article investigates the free vibration and axial buckling of sandwich cylindrical shells with anti-tetrachiral auxetic core and laminated composite face sheets using third-order shear deformation and Donnell’s shell theories. By applying Hamilton’s principle, the equations of motion are extracted, and the natural frequencies and buckling loads for various boundary conditions are obtained using Fourier series and state-space methods. A homogenization-based approach is utilized to calculate the mechanical properties of the anti-tetrachiral core. The results are validated with available data from prior studies and through finite element simulations. Numerical studies are presented to investigate the influence of geometric parameters of the anti-tetrachiral cell, boundary conditions, and face sheet lay-ups on the natural frequencies and buckling loads. Findings reveal that while the geometric parameters of anti-tetrachiral auxetic cells significantly affect the natural frequencies (up to six-fold) and buckling loads (by nearly two orders of magnitude) in single-layer anti-tetrachiral auxetic shells, the Poisson’s ratio remains constant near −1. However, in sandwich shells with composite face sheets, these geometric variations have milder influence on both natural frequencies and buckling loads. Moreover, the auxetic core reverses the trend of natural frequency variations in different cross-ply laminated shell configurations compared to non-auxetic ones.