Free Vibration Analysis of A Sandwich Cylindrical Shell with A Functionally Graded Auxetic Honeycomb Core via The zig-zag Theory.

In the present paper, a semi-analytical solution is presented for the free vibration analysis of a sandwich cylindrical shell with a reentrant auxetic honeycomb (AH) core fabricated from metalceramic functionally graded materials (FGM). It is assumed that the volume fraction of the ceramic phase in the functionally graded auxetic honeycomb (FGAH) core increases from zero at the inner surface of the core to one at the outer one according to various patterns including power-law function (P-FGM), sigmoid function (S-FGM), and exponential function (E-FGM). The FGAH core is covered with an isotropic homogenous inner face layer made of metal and an isotropic homogenous outer one made of ceramic. The sandwich shell is modeled via Murakami’s zig-zag theory, and the governing equations are derived using Hamilton’s principle. An exact solution is presented for a simply supported shell via the Navier method to find the natural frequencies of the shell. The effects of various parameters on the natural frequencies are studied such as material gradation, the thickness-to-radius ratio, the core-to-face layers thickness ratio, and geometric factors of the auxetic cells. It is found that for each vibrational mode, an optimal ratio can be found between the thickness of the FGAH core and the thickness of the shell which leads to the highest natural frequency. [ABSTRACT FROM AUTHOR]