Flutter evaluation and control of an airfoil solved in the Laplace domain

Aeroelasticity is concerned with the interaction of aerodynamic forces and the resulting structural deformations for a structure in an airflow. Flutter, which is one example of an aeroelastic phenomena, may result in the catastrophic failure of an aircraft. The traditional methods of predicting the flutter velocity, namely the $U - g$ and $p - k$, have been used with great success. However, in recent years, new methods have been suggested which approximate the unsteady aerodynamic forces and moments by rational functions. The resulting equations are then solved in the Laplace domain. The goals of this work are twofold. Firstly, to solve the equations of motion for an airfoil, in both incompressible and transonic flow, in the Laplace domain using rational functions to approximate the unsteady aerodynamics. Secondly, to implement active control for the airfoil in incompressible flow with the aim of increasing the critical flutter speed. The solution of the aeroelastic equations of motion in the Laplace domain proved to be a powerful tool in the analysis of flutter