Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer

A review of the literature reveals a dearth of works on functionally graded material sandwich shells having an auxetic core layer. This study contributes an analytical approach for the free vibration analysis of doubly curved stiffened sandwich shells with the face sheets of functionally graded materials and the core layer of the auxetic honeycomb material. The theoretical formulation is established based on first-order shear deformation theory associated with the smeared stiffener method. The free vibration solution of simply supported shallow shells with the rectangular platform is derived using Navier's form. The proposed methodology is general and can be applied to examine the natural frequencies of various shell types, including flat, cylindrical, spherical, and hyperbolic paraboloidal panels. Numerical results indicate that the fundamental frequency is largely influenced by the relative proportion of the constituent materials of the face layers, the geometrical parameters of the auxetic honeycomb core layer, as well as the stiffeners. Additionally, a simple optimization technique based on Rao algorithms is introduced to obtain the maximum fundamental frequency of the shell. It is shown that the shell parameters, particularly the thickness of the auxetic core and the number of stiffeners, can be tailored to maximize the natural frequency. Moreover, the optimal solutions are fully dependent on the material proportion of the functionally graded material, the geometry of the shell, and the geometrical parameters of the auxetic honeycomb core.