Free vibration analysis of rectangular doubly curved auxetic-core sandwich panels integrated with CNT-reinforced composite layers using Galerkin method

In this paper, the free vibrations of a three-layer doubly curved panel with honeycomb auxetic core and reinforced composite face sheets by carbon nanotubes with different distributions are investigated. The governing equations of the structure are derived based on the new fifth-order shear deformation theory. The sandwich panel consists of three layers, aluminum core layer with cell inclined angle which creates negative Poisson's ratio in the honeycomb structure, composites skins with a uniform distribution (UD) as well as functionally graded (FG) distributions of carbon nanotubes (CNTs) in the simply supported boundary condition. Effective material properties of single-walled (SW) carbon nanotube reinforced composite skins are achieved by applying the extended rule of mixtures. The equations of motion are obtained using the Hamilton principle and solved using the Galerkin residual weight method. The effect of auxetic cell parameters including cell angle, cell aspect ratio, rib thickness ratio as well as distribution and content of carbon nanotubes, length to thickness ratio, and core thickness to total panel thickness ratio are examined and discussed. At the end, free vibration was obtained and compared for other shapes of sandwich panels such as hyperbolic parabolic sandwich panels, cylindrical sandwich panels and sandwich plates.The results showed that the core with negative Poisson's ratio as well as the functionally graded distribution (FG) of carbon nanotubes in the upper and lower composite surfaces reduced the natural frequency of the studied sandwich panel.