Investigations of Nonlinear Pathologies in Aeroelastic Systems Thomas W. Strganac (and many others) Department of Aerospace Engineering Texas A&M University College Station, Texas

RIGID BODY Aeroelasticity ThermalControl

+ frequency domain solutions time domain simulations V < V flutter V > V flutter V f  f

USAF SEEK EAGLE OFFICE Eglin AFB, Florida

Limit Cycle Oscillations > Nonlinear behavior leads to “Wing-with-Store Flutter” > Found in high performance aircraft > Flutter is a linear case of aeroelastic instability > LCOs are bounded amplitude oscillatory responses Placards are required … restricting mission performance.

Characteristics ( Flight Test & Lab Observations ) o LCOs below linear flutter predictions o LCOs as low as M ~ 0.6 o configuration dependent o spring-hardening stiffness evident o onset sensitive to AOA and maneuvers o hysteresis exists in recovery o performance limiting – pilot and aircraft

downloading case configuration case Flight Operation Placards Altitude kft Velocity, KCAS

NATA - Nonlinear Aeroelastic Test Apparatus continuous nonlinearities (seen in flight vehicles) Large amplitude LCOs Simulation & Validation Tools Ko and Thompson

Nonlinear Example: Pendulum w/ Extension Motion

Nonlinear system response to gust input “detuned” system tuned to a 2:1 resonance Shift in c.m. c.m. Small shift in store center of mass (within mil. std.) Duangsungnaen

Autoparametric (internal) resonances 2 DOF nonlinear aeroelastic system Cubic nonlinearity in aero Frequencies depend on V Commensurate frequencies occur at 3:1 and 2:1 (below flutter V) Large response at 3:1 only     V  flutter Gilliatt

Related findings of interest : + Transient Response External Forcing o A stiffening (continuous) structural nonlinearity is present o if modified frequencies are commensurate, then large amplitude LCO response is found at sub-flutter conditions. o linear theory fails to predict this response Thompson

Kim, Nichkawde Large wing deformations + Aerodynamic stall (subsonic) + Rigid store kinematics

Dz << Dx r CG = 0 O (3) terms retained Store terms : ( ) s, ( ) m, ( )* +/- x EA locations

Treatment of all nonlinearities is required W - large beam deformations A - aerodynamic stall S - store rigid-body kinematics LCO unstable LCO decay to 0, 0 {

o full system nonlinearities are required. o mimics flight test observations … - LCO depends on magnitude of input, > pilot control input > gust load or turbulence level > maneuver loads - hysteresis exists in onset/recovery speed bifurcation depends on system parameters - store mass and inertia - store chordwise and spanwise location - pylon length A subcritical bifurcation occurs for specific system nonlinearities.

Streamwise position placed to achieve LCO Underwing store CM located on elastic axis at midspan 1 ft below midplane Store mass = wing mass / AFRL w/Beran et al.

LCOs and Subcritical Bifurcations

Subcritical Bifurcations analysis via AUTO Helios

TAMU 2’x3’ Low Speed Wind Tunnel Barnett, O’Neil, Block, Kajula top view side view leading edgetrailing edge

Active Control – Theory and Experiments  Linear multivariable control - LQG ( Block )  Feedback Linearization ( Ko, Kurdila* )  Adaptive feedback linearization ( Ko, Kurdila* )  Model reference adaptive control ( Junkins*, Kurdila*, Akella* )  Adaptive control of a multi-control surface wing ( Platanitis )

Active Aeroelastic Wing

measured ∆ r = -2 ○ r = -0.7 □ r = 0  LL  r   r  r rev  ∞  r rigid wing    r  Insufficient loads Suppression of Roll Reversal Platanitis r =  LE /  TE  LE  TE V

Partial Feedback Control note: animation of measured data (via Working Model)

Structured Model Reference Adaptive Control note: animation of measured data (via Working Model)

  Free Response Closed Loop Response LE ctrl. defl. (deg) time (s) meas. cmd. Free ResponseClosed Loop Response Measured response Simulated response Closed-loop responses: LCO control (wing w/ leading & trailing edge control) Platanitis

Intelligent Technologies in a UAV Demonstrator Demo Features/Lessons u Wing Warping Control u Highly Deformable Wings u Fluid-Structure Interaction u Composite wing spar u Autonomous control u AUVSI UAV Student Competition (Summer 2004) u Indoor Flight Capabilities Future u Semi-autonomous –Micro-autopilot: onboard 3-axis accels, 3-axis rate gyro, and GPS –position and altitude sensors programmable for waypoints and control laws u Distributed Control for Flexible Wings –Piezoelectric –SMA wires –Micro-servos Specifications u Total Vehicle Weight = 4.5 lb u Available Payload Weight = 1.5 lb u Wing Span = 14 ft; Airfoil: SA7038 u AR = 15, W/S =.35 lb/ft 2, L/D = 20 u Electric engine (lithium polymer batt.) –variable speed, thrust = 1.4 lb u V MAX = 31 mph, V STALL = 10 mph u Roll control via active wing warping conventional pitch & yaw control The Albatross CRCD Project – Fall 2003   w/o skin wing w/ skin 