Vibration characteristics of a cylindrical sandwich shell with an FG auxetic honeycomb core and nanocomposite face layers subjected to supersonic fluid flow

In this paper, the flutter analysis is studied for a cylindrical sandwich shell subjected to external supersonic fluid flow. The sandwich shell consists of a re-entrant auxetic honeycomb (AH) core made of functionally graded materials (FGMs) which is covered with two polymeric face layers enriched with either carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), or graphene oxide powders (GOPs). The volume fraction (percentage) of the ceramic phase in the functionally graded auxetic honeycomb (FGAH) core varies from zero at the inner surface to one at the outer one based on either power-law function (P-FGM), exponential function (E-FGM), or sigmoid function (S-FGM). It is assumed that the nanofillers are distributed uniformly inside the face layers. The first-order shear deformation theory (FSDT) and the piston theory are employed to provide the mathematical models of the shell and the aerodynamic pressure, respectively. The governing equations and boundary conditions are derived via Hamilton’s principle. An exact solution is performed in the circumferential direction via harmonic trigonometric functions (sine and cosine) and an approximate solution is performed in the axial direction utilizing the differential quadrature method (DQM). The natural frequencies and corresponding damping ratios are attained through the presented semi-analytical solution and the impacts of several factors on the natural frequencies and the critical aerodynamic pressure of the shell are examined. These factors the type of the FGM, the material index, and inclined angle of the cells in the FGAH core, the thickness of the FGAH core, the type and mass fraction of the nanofillers in the nanocomposite face layers, and boundary conditions.