Investıgatıon of The Effects of Structural Nonlınearıtıes on the Aeroelastıc Stabılıty of Two Dımensıonal Aırfoıl

Abstract

In this thesis, the effects of nonlinear structural components on the aeroelastic stability of a 2D airfoil section which is studied in the academic and industrial environments since the theoretical foundation that was published in 1940s, is investigated. The aerodynamic forces obtained from the potential flow theory were used in the studies. Potential flow theory is decided to be used in this thesis as it is a widely used in aeroelastic studies hence it gives successful results at subsonic speeds and can be applied mathematically quickly and simply. The time integration methods are found to be time inefficient especially at higher airspeed where the oscillation amplitudes are high as well. It is also realized that time integration methods are not capable of describing the stability and bifurcations in details. For these reasons, numerical continuation methods are decided to be used to obtain detailed stability and bifurcation characteristics of the system in shorter times. The flutter speed of the linear system is found with solving eigenvalue problem which is derived from equation of motion. Again using this equations and mathematical expressions of the nonlinear structural components, the nonlinear differential equations were obtained. The nonlinear structural components cubic stiffness, quadratic damping and free-play are studied in this thesis. The numerical continuation analyzes are performed in an open source MATLAB package software MATCONT. In these analyzes, it was observed that the nonlinear components have important impact on the stability of the system and caused to arise limit cycle oscillations. It is also found that, the stability and amplitude of the limit cycle oscillations are highly effected from the coefficients of nonlinear components and the degree of freedom where the nonlinear components are introduced.