l8 research areas of aeroelasticity
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8/10/2019 L8 Research Areas of Aeroelasticity
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8th Research Areas ofAeroelasticity
Xie Changchuan2014 Autumn
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Content1Aeroelasticity of complete aircraft
2Aeroservoelasticity
3Techniques in aeroelastic test4Aeroelasticity of very flexible aircraft
5Aeroelastic tailoring
6Aeroservoelasticity
Main AimsRealize thejobs in aeroelastic design and
analysis which have not taught in this lesson.Furthermore, some new research areas and
state of arts.
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Modern flight dynamics/aeroelasticity
Aeroelasticity of complete aircraft
Frequency range of
rigid movements
Frequency
difference
The highest frequency
of rigid movement
The lowest frequency of
elastic vibration
Frequency
Frequency range of
elastic vibrations
Frequency range of fight control
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Movement equations of
Rigid/Elastic couplingconsider together:
freedoms of rigid motion
freedoms of elastic motion
Problemshow to deal with the
inertial and aerodynamic
coupling between these two
kinds of freedoms?
Equilibrium equations
of static aeroelastici tyProblems: how to solve them
when structure is deformed?
Small disturbance equation
state space model
Problems: how to calculate the
unsteady aerodynamics with
rigid/elastic coupling?
Solution of full motion
equations in time domain
Flight dynamic
equations
Trim analysis
Control and
stability analysis
Design of
control law
Flight simulation
Modern flight dynamics/aeroelasticity
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State of arts theory of f light dynamics of elastic aircraft
1960s, Dusto introduced the method of influence
coefficient to solve the stability problem of elastic
aircraft
Rough description to
structure and aerodynamics
1980s, Rodden established equations of quasi-
steady flight for elastic aircraft, to solve the divergence,
trim and flight load distribution, etc.
Can not give out
dynamic analysis
later in 1980s, Waszak and Schmidt establishedequations by energy method for elastic aircraft flight
with the mean axes, including the rigid and elastic
mode simultaneously.
The aerodynamics aresimple (quasi-steady theory)
2000s, Meirovitch and Tuzcu established rigid-
elastic coupled state equations based on quasi-coordinate theory in multi-body dynamics, to deal with
stability and control response of elastic aircraft.
Complicated equations
The aerodynamics are
simple (strip theory)
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Equations motion of motion ofrigid aircraft (flat irrotational earth)
| ( | ) |V VI I I Aero Prop
d d dm m m
dt dt dt = = + +
p Vg F F
I earth frame, inertial coordinates
( ).
. .|V I
V I V I V I Aero Prop
Vol
d
dVdt
+ = +
p p
p M M
|VI V V V V
dU V W
dt= + +
pV i j k V V Vx y z= + +p i j k
x V y V z Vg g g= + +g i j k .I V V V VP Q R= + + i j k
Aero Ax V Ay V Az VF F F= + +F i j k Prop Px V Py V Pz V F F F= + +F i j k
Aero A V A V A VL M N= + +M i j k Prop P V P V P V L M N= + +M i j k
From these relations above, the equations can be written as
scalar form
Vector form
V body-fixed frame, noninertial coordinates
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Aeroelasticity of complete aircraft
D. K. Schimidt, Modern Flight Dynamics, McGraw Hill, New York, 2012
Full motion
Nonlinear
Equations
Nonlinear reference equations
Solve a certain fl ight state
Linear disturbed equationsStability, flight/control derivatives
Rigid/elastic modes
Small motion/deformation response
Equations motion of motion forelastic aircraft (flat irrotational earth)
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Aeroservoelasticity
Tetrahedron of aeroservoelasticity
A aerodynamics E elastic forces
I inertial forces S control forces
S
EI
W2
xs
Motion singnal transformation
Elastic aircraft Mode parameters
Servo actuator Servo system Auto control system Sensors
s
W1W3W4
q
xi
Structural feedback loop
Structural feedback control loop
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Equation of aeroservoelasticity
s s s s s s s sq q + + = +M q C q K q A q M A
Output of
overload factor
12 2( ) ( )s s s s s
s s s q s q s
= + + + q M C K A M A
Frequency domain method, Laplace transform
2 2
( ) ( ) ( ) ( ) ( ) ( )s s s s s s s ss s s s s q s s s q s + + = +M q C q K q A q M A
1z s
g= =n Fq
Output transform 21( ) ( )ss s sg=
y Fq
Transfer function
12 2 21
( )s s s s ss s s s q s qg
= + + + G F M C K A M A
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Time domain method, state space model
= +
= +
x Ax Bu
Cx Du
Note: most unsteady aerodynamics calculations are in
frequency domain. They should be fitted in time domain.The analysis methods forSISO and MIMO are different.
Research work: stability of aeroservoelasticity (servo flutter)
flutter suppression, gust alleviation
maneuver load alleviation, flight simulation
Equation of aeroservoelasticity
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Gust response and alleviation of large aspect ratio wing
Gust generator The wing has innerand outercontrol
surfaces on trailing edge
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Support system
Has freedoms of pitching
and plunging
Wind tunnel test
Gust response and alleviation of elastic aircraft
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Aeroelastic test
Types of test
Stiffness test of components
GVT of components
Wind tunnel test of componentsScaled complete aircraft wind
tunnel test
GVT of complete aircraft
Servoelastic test of complete aircraftFlight test
Overall design
Researching test
Empirical formula
Simplified calculation
Parts & componentsdesi n
Flutter test model,Stiffness & GVT,
Flutter tesr
Normal modes
Flutter analysisVerified by test
Prototype ofaircraft
Stiffness & GVT
Model test in doubt case
Update model
Flutter analysis to eliminateroblems in calculation
Limitations to flight
Flight vibration& flutter test
Dynamic response calculationverified by flight test
Solve the problemsin flight test
Prototype verified
Jobs in aeroelastic design
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Relationship of normal modes test, dynamic analysis and
structure design
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Model design and GVT system
Typical scaled model of
large aspect ratio wing
GVT system
Similarity law
of mechanics
Geometry
Stiffness Mass
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HeliosGlobal eagle
Typical long endurance UAV
Geometrical nonlinear flight dynamics/aeroelasticity
Aeroelasticity of very flexible aircraft
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Cruise stateCruise state, vertical, vertical
displacement is about 3.6mdisplacement is about 3.6m
Ground stateGround state, the wing has no, the wing has no
much bendingmuch bending
Maximum load stateMaximum load state, vertical
displacement is about 7.9m
TheThe deformationdeformation will be morewill be moresignificantsignificant adoptingadopting compositecomposite
materialmaterial than metallic materialthan metallic material
Boeing 787Boeing 787
Wing span almost 60m
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ChartChart 1818
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State of artUSA Michigan Universitysmart structure and aeroelastic Lab
Prof. Cesnik one of the first researchers on geometrical aeroelasticity
of fixed wing aircraft
Projects: HALEX-HALE NASA, Boeing, US air force supportingfunding sum beyond 10 million US dollars
Alabama Universitygroup of aeroelasticity and flight simulation
flight simulation platform of very flexible aircraft
UK Bristol Universitynonlinearity and aeroelasticity Lab
Prof. Cooper large deformation of joint-wing NASA supporting
aeroelasticity and design of large deformed wing and complete aircraft
Airbus supportingfunding sum beyond 8 million US dollars
Imperial Collegegroup on dynamics and aeroelasticity
Royal aeronautical society supporting
Prof. Palacios geometrical nonlinear flight dynamics and aeroelasticityconstructed software SHARP
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Aeroelasticity Lab in Beihang Univ. (My work)
Nonlinear static aeroelasticity and flutterof very flexible wing
Nonlinear flight load and flutterof very flexible complete aircraft
GVT and wind tunnel test of large deformed wing
Fixed
end
Wing Beam Wing FrameMid of slender
tube
After cone
Front cone
Fuselage
Wingtip storeCG
Wing spar
All-removableHorizontal tail
Rotational axis
Aileron
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Engineering applications
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
VF
/V*
Load Scale
Stable margin
Load condition
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Aeroelastic tailoring
Optimization
problem
Steady aeroelastic trimflutter analysis
N
Define the optimizestrategy and parameters
Generate initial population P(t)(structural and contro l variables)
Individual fitnessassessment
Convergence
condition
Generate new population P(t+1)
End
P(t)
P(t+1)Y
min F (v)
cnj = 1,
dni = 1,
s.t. 1( )( )( )
F
Fg
F=
vv
v
2 21
1
( )( ) ( ) ( )
tn
i
i i
FF v
v=
=
v
v
1
( )( ) 0
tnj
j i
i i
gg v
v=
+
vv
lower upper ( ) ( )i i i i iv v v v v+
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Footholdsyntheses design of structure, aerodynamics
and control law
Aeroelastictailoring/design
Aeroelastic solver
Optimize method
The law of design parameters on aircraft performance
The requirements of large-scale optimization on
aeroelastic solver The patterns of MDO strategy and variables selection
The methods of MD coupling and rapid solving
The choice and hybrid of optimizing methods
Aeroelastic tailoring
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Aerothermoelasticity
The coupling relationships
of aerothermoelasticity
Aerothermoelasticmodel based on 2
way coupling
Aerodynamic
heating
Heat
conduction
Aerothermal
Aerodynamics Elasticdeformation
Inertial
1
aeroelasticity
2
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Coupl ing calculation of aerodynamic
heating and aeroelasticity
Aerothermoelasticity
Aerodynamicheating and
conduction
Aeroelasticity
t
t +tAT
tAT
tAE
t +2tAT
UpdatedT
field
UpdatedT
field
UpdatedT
field
Updated
flowp
Updated
flowp
Updated
flowp
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Any adviceson this course
END
Thank you
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