NONLINEAR ANALYSIS OF A 2-DOF PIECEWISE LINEAR AEROELASTIC SYSTEM Tarek A. Elgohary Department of Aerospace Engineering Texas A&M University College Station, Texas, 77843 Email: t.gohary@gmail.com Tam ´ as Kalm ´ ar-Nagy Visiting Scholar University of Illinois at Urbana-Champaign Urbana - IL Email: kalmarnagy@gmail.com ABSTRACT Aerodynamic forces for a 2-DOF aeroelastic system oscillat- ing in pitch and plunge are modeled as a piecewise linear func- tion. Equilibria of the piecewise linear model are obtained and their stability/bifurcations analyzed. Two of the main bifurca- tions are border collision and rapid/Hopf bifurcations. Contin- uation is used to generate the bifurcation diagrams of the sys- tem. Chaotic behavior following the intermittent route is also observed. To better understand the grazing phenomenon sets of initial conditions associated with the system behavior are defined and analyzed. NOMENCLATURE α Pitch DOF y Plunge DOF α eff Effective angle of attack α stall Stall angle of attack α switch Angle of switch α bound Angle of model bound c 0 − c 4 Line segments parameters b Semichord of wing S Wing span m Mass of the system k y Spring constant plinge DOF k α Spring constant pitch DOF c y Viscous damping plunge DOF c α Viscous damping pitch DOF I cg Mass moment of inertia ρ Air density L Aerodynamic lift M Aerodynamic moment U Freestream velocity INTRODUCTION Nonlinear analysis of airfoils is a topic that is extensively covered in the literature [1–4]. In general, nonlinearities of air- foils are structural and/or aerodynamic. A comprehensive anal- ysis for such nonlinearities was presented in [4]. The equations of motion of a 2D airfoil oscillating in pitch and plunge were derived. Cubic, freeplay and hysteresis nonlinearities were in- vestigated. Numerical simulations investigating system stability, bifurcations and chaos were presented. Nonlinear aeroelasticity and its effects on flight and its association with limit cycle oscil- lations (LCO’s) was investigated in [1]. Gilliat et al. [2] investi- gated both structural and aerodynamic nonlinearities with arising from stall conditions. An experimental investigation of structural nonlinearity with emphasis given to continuous nonlinearities arising from spring hardening/softening effects was presented in [5], [6]. The aeroe- lastic response of a 2D airfoil with bilinear and cubic structural nonlinearities was investigated in [7]. Numerical simulations ap- plying the finite difference method were compared against the analytical describing function method. LCO’s were found to ex- ist at a velocity below the divergent flutter limit. Chaotic be- havior was investigated with the application of preload and bi- furcation diagrams showing period doubling were plotted as a 1 Copyright © 2012 by ASME Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2012 August 12-15, 2012, Chicago, IL, USA DETC2012-70038