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This paper is devoted to the supersonic flutter analysis of a ring-stiffened conical three-layered sandwich shell consisting of an auxetic honeycomb (AH) core fabricated from functionally graded material (FGM). The face sheets are manufactured of FGM as well in which the volume fraction of the ceramic increases from zero at the inner surface to one at the outer surface based on a power-law function. The sandwich shell is mathematically modeled based on the Murakami's zig-zag shell theory and the aerodynamic pressure is modeled utilizing piston theory. The derivation of governing equations along with compatibility and boundary conditions are performed using Hamilton's principle and are solved through a semi-analytical solution consisting of an exact solution in the circumferential direction followed by an approximate solution in the meridional direction. The flutter boundaries are attained to investigate the variations of the natural frequencies and damping ratios to find the critical aerodynamic pressure (CAP). The impacts of several factors on the CAP are examined such as the power-law index, geometric characteristics of the cells in the FGAH, thickness of the honeycomb core, location of the ring, and boundary conditions. It is observed that an optimal location can be found for the ring support somewhere between the middle length and large radius of a conical shell that provides the best aeroelastic stability.
Abasi et al. (Sun,) studied this question.