Optimization for flutter boundaries of cantilevered trapezoidal thick plates

In this paper, based on the first-order shear deformation theory for modeling the structure and the supersonic Piston theory to estimate the aerodynamic pressure, the set of governing equations and boundary conditions for flutter analysis of a trapezoidal thick plate with variable thickness are derived. Using a transformation of coordinates, governing equations and boundary conditions are converted from the original coordinates into a new computational one. Using differential quadrature method, natural frequencies, damping ratio, and corresponding mode shapes are derived, and critical aerodynamic pressure and flutter frequency are determined. Critical aerodynamic pressure of the plate is considered as an objective function to increase and using particle swarm optimization, optimum values of aspect ratio, thickness, variation of thickness, and angles of the plate are found. Meanwhile, some constrains on the volume (weight) and area (lift force) of the plate are considered. This constrained optimization can be considered as a useful tool for design wing and tail fin of aircrafts.