Free vibrational behavior of a conical sandwich shell with a functionally graded auxetic honeycomb core

In the presented paper, the free vibration of a conical sandwich shell with a re-entrant auxetic honeycomb (AH) core made of ceramic-metal functionally graded material (FGM) is analyzed. The percentage (volume fraction) of ceramic in the functionally graded auxetic honeycomb (FGAH) core changes from zero at the inner surface of the core to one at the outer surface according to a power-law function. The FGAH core is enfolded with a homogenous outer face layer made of ceramic and a homogenous inner one made of metal. The shell is modeled based on the first-order shear deformation theory (FSDT), and Hamilton's principle is utilized to attain the governing equations and boundary conditions. A trigonometric-based analytical solution is carried out in the circumferential direction, and an approximate solution is presented in the meridional direction via the differential quadrature method (DQM). The impacts of various factors on the natural frequencies are inspected like the thickness of the core-to-thickness of the shell ratio, geometric factors of the cells in the FGAH core, and material gradation in the FGAH core.