The free vibration analysis of ring-stiffened FG conical sandwich shells with auxetic and non-auxetic honeycomb cores

In this paper, the natural frequencies of a ring-stiffened conical sandwich shell with a functionally graded (FG) honeycomb core are calculated. The core can be either a non-auxetic honeycomb (NAH) or an auxetic honeycomb (AH). The honeycomb core and face layers are fabricated from metal-ceramic functionally graded material (FGM) in which the volume fraction of the ceramic increases from zero at the inner surface of the shell to one at its outer surface based on either power-law function (P-FGM), sigmoid function (S-FGM), or exponential function (E-FGM). The sandwich shell is modeled based on Murakami’s zig-zag theory and the intermediate ring support is modeled as a rigid structure. Hamilton’s principle is employed to derive the governing equations, compatibility conditions, and boundary conditions. A semi-analytical solution is presented which includes an exact solution in the circumferential direction followed by an approximate numerical solution via the differential quadrature method (DQM) in the meridional direction. It is concluded that for each vibrational mode, optimal values can be found for the inclined angle, core-to-shell thickness ratio, and location of the ring support which bring about the highest natural frequency. The presented work is the first theoretical work associated with the free vibration analysis of a ring-stiffened FG conical sandwich shell with a honeycomb core which provides a reduction in the mass and improvement in the thermo-mechanical characteristics, simultaneously. Such properties make such a structure widely used in the aerospace industry. Considering the importance of the dynamic characteristics of aerospace structures, the results of this research can be used by these industries in the analysis and optimal design of the main body of airplanes and missiles.