Investigations of Nonlinear Investigations of Nonlinear PathologiesPathologies

in Aeroelastic Systemsin Aeroelastic Systems

Thomas W. StrganacThomas W. Strganac(and many others)(and many others)

Department of Aerospace EngineeringDepartment of Aerospace EngineeringTexas A&M UniversityTexas A&M UniversityCollege Station, TexasCollege Station, Texas

RIGID BODY

Aeroelasticity

Thermal Control

0

0yKm mr y y L

Kmr I M

tittist eeYeYeYq )(}{

}{)}({}]{[}]{[}]{[ BtFqKKqCCqMM AAA

+

frequency domain

solutions

time domain simulations

V < Vflutter

V > Vflutter

Vf 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

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-5

0

5

Pitch angle (rad.)

Mo

men

t(N

-m)

Modeled (Polynomial)Measured

continuous nonlinearities

(seen in flight vehicles)

Large amplitude LCOs

Simulation & Validation Tools

Ko and Thompson

m

L

k

x

pendulumn

lextensionan

LgwhereL

gm

kwherexmkx

motionofequationsLINEARthetoleads

xxx

linearize

gxLx

mgkxLxmxm

MotionofEquationsNonlinear

2

2

22

5342

2

0

0

0.....

...!5!3

sin...!4!2

1cos

...

0sin2)(

0cos)(

Nonlinear Example: Pendulum w/ Extension Motion

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

ssssss

Nonlinear

Linear

“Flutter”

3 : 1

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

0 10 20 30 40 50 60 70 80 90

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Pitc

h D

ispl

acem

ent

[alp

ha]

(rad

)

0 10 20 30 40 50 60 70 80 90

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Pitc

h D

ispl

acem

ent

[alp

ha]

(rad

)

Related findings of interest :

+

Transient Response External Forcing

0 10 20 30 40 50 60 70 80 90

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Pitc

h D

ispl

acem

ent

[alp

ha]

(rad

)

0 10 20 30 40 50 60 70 80 90

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Pitc

h D

ispl

acem

ent

[alp

ha]

(rad

)

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 topredict this response

Thompson

Kim, Nichkawde

Lift

AOA

subsonic stall

Large wing deformations

+

Aerodynamic stall (subsonic)

+

Rigid store kinematics

( , ) ( *, ) ( *, )

( *, )

s sb

IVs m w x ws

mw s t m w s t I w s t

m x s t c w D w G L

( , ) ( *, ) ( *, )

( *, )

s sb

IVs m w x ws

mw s t m w s t I w s t

m x s t c w D w G L

( *, ) ( *, )y sg m s

y s

J s t I x m w s t

c D G M

( *, ) ( *, )y sg m s

y s

J s t I x m w s t

c D G M

2

2

0

2

2 2

[ ( ) ] ( )

1

2

( *, )[ ( ( *, ))( ( *, ) ))

2

( ( *, ) ( *, ) ( *, ) )]

ws x x z

s s

x l

s m m

s m m

G D w w w D D w

J w m w w ds ds

s tm s t z s t x

m z s t s t x s t

2

2

0

2

2 2

[ ( ) ] ( )

1

2

( *, )[ ( ( *, ))( ( *, ) ))

2

( ( *, ) ( *, ) ( *, ) )]

ws x x z

s s

x l

s m m

s m m

G D w w w D D w

J w m w w ds ds

s tm s t z s t x

m z s t s t x s t

2 2

2

( ) ( )( )

( *, )( *, )( ( *, ) )

2

s x z z x

s m m

G D D w J J w

s tm w s t z s t x

2 2

2

( ) ( )( )

( *, )( *, )( ( *, ) )

2

s x z z x

s m m

G D D w J J w

s tm w s t z s t x

Dz << Dx

rCG = 0

O(3) terms retained

Store terms : ( )s , ( )m, ( )*

+/- xEA locations

-0.4 -0.2 0 0.2 0.4-10

-5

0

5

10

.

Source of nonlinearity V/Vf = 0.95 V/Vf = 1.12

Wing (W) alone decay growth

Aero (A) alone decay LCO

Store (S) alone decay Growth

W + A decay LCO

W + S decay Growth

A + S decay LCO

W + A + S subcritical LCO

0 5 10

-0.2

-0.1

0

0.1

0.2

0.3

Time

Treatment of all nonlinearities is requiredW - large beam deformationsA - aerodynamic stallS - store rigid-body kinematics

LCO

0 5 10

-0.2

-0.1

0

0.1

0.2

0.3

Time

unstable LCO

decay to 0, 0

{

V / VF = 1

Amp

V

incr. store mass

o full system nonlinearitiesare required.

o mimics flight testobservations …

- 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

Amp

1

fully linear

fully nonlinear

stall

A subcritical bifurcation occurs for specific system nonlinearities.

x ls

ycoff

U

cs

ea

lw

cw

y

x

z

4 ft

20 ft

1/3 ft

Structural Grid Point

• Streamwise position placed to achieve LCO• Underwing store CM located on elastic axis

at midspan 1 ft below midplane• Store mass = wing mass / 10

Goland+ wingwith store

@ AFRL w/Beran et al.

LCOs and Subcritical Bifurcations

Velocity (Ft/Sec)

Pea

kL

iftC

oef

ficie

nt

350 400 450 500 550 600 650 700

0.25

0.5

0.75

1

1.25 One Ft Offset - Mach 0.91One Ft Offset - Mach 0.93Two Ft Offset - Mach 0.91Two Ft Offset - Mach 0.93

Branch I

Unstable Branch(speculated)

Branch II

Mach

Vel

oci

ty(F

t/S

ec)

0.7 0.75 0.8 0.85 0.9 0.95300

350

400

450

500

550

600

650

700

CAPTSDv (FE Modes)8

CAPTSDv-NLS (Beam Model)MSC/NASTRAN (FE Modes)7

0 20 40 60 80 100 120

-0.02

0

0.02

0.04

0.06

0.08

0.1

V (m/s)

w

0 10 20 30 40 50 60 70 80 90 100 110

-0.02

0

0.02

0.04

0.06

0.08

0.1

V (m/s)

Subcritical Bifurcationsanalysis via AUTO

Helios

TAMU 2’x3’Low Speed Wind

Tunnel

Barnett, O’Neil, Block, Kajula

top view

side view

leading edge trailing 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

-0.5

0.0

0.5

1.0

0.0 0.5 1.0 1.5

measured∆ r = -2○ r = -0.7□ r = 0

L

r

r

rrev

∞

rrigid wing

r

Insufficient loads

Suppression of Roll Reversal

Platanitis

r = LE/TE

LE

T

E

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)

-0.02

0

0.02

plun

ge (

m)

-20

0

20

pitc

h (d

eg)

5 6 7 8 9 10 11 12 13 14 15-30

0

30

cont

rol

de

fl. (

deg)

time (s)

Free Response Closed Loop Response

-0.02

0

0.02

plun

ge (

m)

-20

0

20

pitc

h (d

eg)

-30

0

30

TE

ctr

l.de

fl. (

deg)

10 11 12 13 14 15 16 17 18 19 20-30

0

30

LE c

trl.

defl.

(de

g)

time (s)

meas.cmd.

Free Response Closed Loop Response

Measured responseSimulated response

Closed-loop responses: LCO control(wing w/ leading & trailing edge control)

Platanitis

Intelligent Technologies in a UAV DemonstratorDemo Features/Lessons Wing Warping Control Highly Deformable Wings Fluid-Structure Interaction Composite wing spar Autonomous control AUVSI UAV Student Competition

(Summer 2004) Indoor Flight Capabilities

Future Semi-autonomous

– Micro-autopilot: onboard 3-axis accels, 3-axis rate gyro, and GPS

– position and altitude sensors programmable for waypoints and control laws

Distributed Control for Flexible Wings – Piezoelectric– SMA wires

– Micro-servos

Specifications Total Vehicle Weight = 4.5 lb Available Payload Weight = 1.5 lb Wing Span = 14 ft; Airfoil: SA7038 AR = 15, W/S = .35 lb/ft2, L/D = 20 Electric engine (lithium polymer

batt.)– variable speed, thrust = 1.4 lb

VMAX = 31 mph, VSTALL = 10 mph Roll control via active wing warping

conventional pitch & yaw control

The Albatross CRCD Project – Fall 2003

w/o skin

wing w/ skin