Nonlinear equations of motion for a flexibly supported rigid airfoil with additional degree of freedom for controlling of the profile motion by a trailing edge flap are derived for large vibration amplitudes. Preliminary results for numerical simulation of flow-induced airfoil vibrations in a laminar incompressible flow are presented for the NACA profile 0012 with three-degrees of freedom (vertical translation, rotation around the elastic axis and rotation of the flap). The developed numerical solution of the Navier – Stokes equations and the Arbitrary Eulerian-Lagrangian approach enable to consider the moving grid for the finite element modelling of the fluid flow around the oscillating airfoil. A sequence of numerical simulation examples is presented for Reynolds numbers up to about Re ≈10e5, when the system loses the aeroelastic stability, and when the large displacements of the profile and a post-critical behaviour of the system take place.
flow – induced vibration, aeroelasticity, nonlinear vibrations, numerical simulations