Effects of combined hardening and free-play nonlinearities on the response of a typical aeroelastic section

Abstract

This paper presents an investigation about the dynamic response of a three-degree of freedom airfoil with hardening nonlinearity in the pitching stiffness and free-play nonlinearity in the control surface stiffness using bifurcation and HOS analysis. An experimental apparatus was conceived to test an airfoil aeroelastic responses when nonlinearities of varying intensities are present. A numerical model is also used to simulate at the same conditions of the experimental tests. It is based on the classical theory for the linear unsteady aerodynamics with corrections for arbitrary motions coupled to a three-degree of freedom typical aeroelastic section, where the hardening effect is modeled by means of rational polynomial function, while the free-play is represented by hyperbolic functions combination. Aeroelastic responses are analyzed from numerical and experimental results. Hopf bifurcations are identified and diagrams of amplitudes versus airspeeds are used to investigate the conditions in which the system is supercritical or subcritical. Higher-order spectra analysis is also used to check on frequency couplings, thereby allowing to identify quadratic- and cubic-like nonlinear behavior. The study of the phenomena associated with the hardening, free-play and their intensity variation effects may be useful in the mitigation of undesired responses of aeroelastic systems.