A novel graded auxetic honeycomb core model for sandwich structures with increasing natural frequencies

A novel angle graded auxetic honeycomb (AGAH) core is designed for sandwich structures in the present study. The angle of the cells is varied through the thickness of the AGAH core using linear functions. Therefore, the thickness of the cell walls is kept constant along the gradation of the cell angle, and the length of the cell walls is changed through the core thickness as the result of angle variation. New analytical relations are proposed to predict the equivalent elastic properties of the AGAH core. The performance of the new proposed core is analytically assessed for the vibrational behavior of a sandwich plate. The governing equations are deduced adopting Hamilton's principle under the assumption of quasi-3D exponential plate theory. Three-dimensional finite element (3D-FE) simulation is accomplished to verify the analytical results of the vibrational response of the sandwich structure. The influence of variation of the cell wall, the cell angle and cell aspect ratio of AGAH core, and geometric parameters of the sandwich structure are investigated on the vibration response of the sandwich panel. The present graded design of the auxetic honeycomb enhances the specific stiffness (i.e., stiffness to density ratio) and consequently increases the natural frequencies of sandwich structures with this type of core.