Dynamics of a Sandwich Cylindrical Shell with a Functionally Graded Auxetic Honeycomb Core

Abstract

In this paper, a study is conducted regarding the free vibrational analysis of a sandwich cylindrical shell with a re-entrant auxetic honeycomb (AH) core made of ceramic-metal functionally graded material (FGM). The volume fraction (mass fraction) of ceramic in the functionally graded auxetic honeycomb (FGAH) core varies from zero at the inner surface to one at the outer one based on a power-law function. It is supposed that the core is covered with a homogenous inner layer made of metal and a homogenous outer one made of ceramic. The first-order shear deformation theory (FSDT) is hired and the shell is modeled mathematically. The governing equations are attained via Hamilton’s principle, and a semi-analytical solution is presented for various types of standard boundary conditions. This solution consists of an exact solution performed in the circumferential direction of the shell mixed with an approximate numerical one performed in the meridional direction of the shell via the well-known differential quadrature method (DQM). The influences of various factors on the natural frequencies are inspected. It is discovered that the natural frequencies decrease by growing the inclined angle and the thickness of the walls in the cells of the FGAH core but the aspect ratio of the walls in the cells of the FGAH core has a reverse effect. It is concluded that for each vibrational mode, there is an optimal ratio between the values of the thickness of the FGAH core and the thickness of the shell which leads to the highest natural frequency.

Keywords

• free vibration
• cylindrical shell
• sandwich shell
• functionally graded material
• auxetic honeycomb structure