Effects of non-uniformity in thickness and volume fraction of nanofillers on the flutter characteristics of nanocomposite cantilever trapezoidal plates

The aim of this work is to investigate the flutter characteristics of nanocomposite cantilever trapezoidal plates with non-uniform thickness enriched with either carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), or graphene oxide powders (GOPs) which are distributed functionally graded (FG) in the axial direction. It is assumed that the thickness of the plate and the volume fraction of the nanofillers vary in one direction from the wider clamped edge of the plate to the outer narrower free one. The modeling of the plate is done using the first-order shear deformation theory (FSDT) and the aerodynamic pressure generated by the aerodynamic pressure is modeled using the linear approximation of the piston theory. The material properties of the plate are calculated using the mixing rule (ROM) and the Halpin–Tsai model. The governing equations and boundary conditions at the clamped and free edges of the plate are derived via Hamilton’s principle. An approximate solution is applied using the differential quadrature method (DQM) to calculate the natural frequencies and the damping ratios of the plate. Numerical examples show that it is possible to find an optimal thickness variation profile that provides the greatest aeroelastic stability. It is concluded that by considering the same value for the mass fractions of the nanofillers, the highest aeroelastic stability can be attained by utilizing the GNPs as the reinforcers. It is found that to attain further improvement in aeroelastic stability, most nanofillers should be distributed near the clamped edge and away from the outer free edge.